Metrics for VandenBroeck and Keller, Equation (20)

analyze326.0ms (1.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	75%	0%	0%	25%	0%	3
0%	0%	62.5%	0%	0%	25%	12.5%	4
0%	0%	56.2%	0%	0%	25%	18.7%	5
0%	0%	53.1%	0%	0%	25%	21.9%	6
3.1%	1.6%	48.4%	0%	0%	26.5%	23.4%	7
4.8%	2.3%	46.1%	0%	0%	27.3%	24.2%	8
5.6%	2.7%	45.7%	0%	0%	27.3%	24.2%	9
6%	2.9%	45.5%	0%	0%	27.3%	24.2%	10
6.3%	3%	45.4%	0%	0%	27.3%	24.2%	11
6.4%	3.1%	45.2%	0%	0%	27.4%	24.3%	12

Compiler

Compiled 39 to 17 computations (56.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 172.0ms

ival-exp: 37.0ms (21.5% of total)

ival-div: 33.0ms (19.2% of total)

ival-mult: 33.0ms (19.2% of total)

ival-neg: 25.0ms (14.5% of total)

ival-add: 11.0ms (6.4% of total)

ival-log: 11.0ms (6.4% of total)

ival-sub: 9.0ms (5.2% of total)

ival-pi: 8.0ms (4.6% of total)

const: 3.0ms (1.7% of total)

backward-pass: 1.0ms (0.6% of total)

sample6.6s (35.1%)

Results

2.7s	7317×	1	invalid
2.4s	7696×	1	valid
209.0ms	177×	2	valid
93.0ms	383×	0	valid
1.0ms	5×	0	unsamplable
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 4.5s

ival-exp: 1.4s (31.5% of total)

ival-div: 730.0ms (16.3% of total)

ival-mult: 492.0ms (11% of total)

backward-pass: 381.0ms (8.5% of total)

ival-log: 366.0ms (8.1% of total)

ival-neg: 335.0ms (7.5% of total)

ival-add: 299.0ms (6.7% of total)

ival-pi: 212.0ms (4.7% of total)

ival-sub: 212.0ms (4.7% of total)

const: 50.0ms (1.1% of total)

Bogosity

preprocess312.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

2270×	`sum3-define`
1954×	`fnmadd-define`
1910×	`fnmadd-define`
1778×	`fma-define`
1496×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	115
1	94	96
2	259	96
3	651	96
4	1406	96
5	2471	96
6	3785	96
7	4366	96
8	4932	96
9	5419	96
10	6095	72
11	7412	69
0	16	36
1	51	32
2	131	32
3	284	32
4	481	32
5	699	32
6	936	32
7	1243	32
8	1893	32
9	2337	32
10	3078	32
11	4771	32
12	5330	32
13	5594	32
14	6132	32
15	7538	32
0	8072	32

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

Inputs
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

Outputs

(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Call 2

Inputs

(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))

(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f)))))))))

(neg (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))))))))

Outputs
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f)))) (- (exp (* (/ (PI) 4) f)) (exp (neg (* (/ (PI) 4) f))))))))
(* (log (+ (recip (+ -1 (sqrt (pow (fast-exp f) (PI))))) (recip (- 1 (pow (pow (fast-exp f) (PI)) -1/2))))) (/ -4 (PI)))
(neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f)))))))))
(* (log (+ (recip (+ -1 (pow (pow (fast-exp f) (PI)) -1/2))) (recip (- 1 (sqrt (pow (fast-exp f) (PI))))))) (/ -4 (PI)))
(neg (neg (* (/ 1 (/ (PI) 4)) (log (/ (+ (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))) (- (exp (* (/ (PI) 4) (neg f))) (exp (neg (* (/ (PI) 4) (neg f))))))))))
(* (/ 4 (PI)) (log (+ (recip (+ -1 (pow (pow (fast-exp f) (PI)) -1/2))) (recip (- 1 (sqrt (pow (fast-exp f) (PI))))))))

explain431.0ms (2.3%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
248	-	1	(0.013418434047536463)	`(-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))`
4	-	0	-	`(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))`
1	-	0	-	`(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))`
0	-	0	-	`(PI.f64)`
0	-	0	-	`(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)`
0	-	0	-	`(neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))`
0	-	0	-	`(/.f64 (PI.f64) #s(literal 4 binary64))`
0	-	0	-	`(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))`
0	-	0	-	`f`
0	-	0	-	`(+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))`
0	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))`
0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(exp.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))`
0	-	0	-	`(exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))`

Results

297.0ms	482×	1	valid
11.0ms	8×	2	valid
4.0ms	22×	0	valid

Compiler

Compiled 434 to 50 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 190.0ms

ival-neg: 42.0ms (22.1% of total)

ival-div: 41.0ms (21.6% of total)

ival-exp: 35.0ms (18.4% of total)

backward-pass: 21.0ms (11.1% of total)

ival-mult: 17.0ms (8.9% of total)

ival-log: 13.0ms (6.8% of total)

ival-add: 8.0ms (4.2% of total)

ival-pi: 6.0ms (3.2% of total)

ival-sub: 5.0ms (2.6% of total)

const: 2.0ms (1.1% of total)

eval0.0ms (0%)

Compiler: Compiled 33 to 15 computations (54.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.5%	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Status

Accuracy

Program

▶

6.5%

(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Compiler

Compiled 33 to 15 computations (54.5% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
✓	cost-diff	(/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
✓	cost-diff	(log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))))
✓	cost-diff	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Rules

852×	`fnmadd-define`
640×	`sum5-define`
558×	`fmsub-define`
556×	`fnmsub-define`
510×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	145
1	29	145
2	45	145
3	66	145
4	85	145
5	129	145
6	208	145
7	322	145
8	491	145
9	864	145
10	1717	145
11	2948	145
12	2950	145
13	2988	145
14	3357	145
15	3373	145
0	3373	145

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
(log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))))
(/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))
(+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(exp (/ (* (PI) f) 4))
(/ (* (PI) f) 4)
(* (PI) f)
(PI)
f
4
(exp (/ (* (PI) f) -4))
(/ (* (PI) f) -4)
-4
(- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(/ (PI) -4)

Outputs
(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))))
(log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))))
(/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))
(/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
(+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(exp (/ (* (PI) f) 4))
(exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64)))
(/ (* (PI) f) 4)
(/.f64 (*.f64 (PI.f64) f) #s(literal 4 binary64))
(* (PI) f)
(*.f64 (PI.f64) f)
(PI)
(PI.f64)
f
4
#s(literal 4 binary64)
(exp (/ (* (PI) f) -4))
(exp.f64 (/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64)))
(/ (* (PI) f) -4)
(/.f64 (*.f64 (PI.f64) f) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))

localize174.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (PI.f64) f)
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	98.0%	(/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))
✓	accuracy	10.1%	(-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64))))

Results

136.0ms	243×	1	valid
4.0ms	4×	2	valid
2.0ms	9×	0	valid

Compiler

Compiled 147 to 16 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-exp: 17.0ms (24.4% of total)

ival-div: 16.0ms (22.9% of total)

backward-pass: 15.0ms (21.5% of total)

ival-add: 6.0ms (8.6% of total)

ival-log: 6.0ms (8.6% of total)

ival-mult: 4.0ms (5.7% of total)

ival-pi: 3.0ms (4.3% of total)

ival-sub: 2.0ms (2.9% of total)

const: 1.0ms (1.4% of total)

series99.0ms (0.5%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))>
#<alt (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))))>
#<alt (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))>
#<alt (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))>
#<alt (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))>
#<alt (* (PI) f)>

Outputs
#<alt (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI)))>
#<alt (+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* -2 (/ (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))))>
#<alt (+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* -2 (/ (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (PI))) (* -2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))))>
#<alt (+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* -2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))) (* f (+ (* -2 (/ (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))) (* -2/3 (/ (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))) (PI))))))))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f)))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* 1/2 (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))>
#<alt (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (+ (* 1/6 (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))) (* 1/2 (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))>
#<alt (/ 2 (* f (- (* 1/4 (PI)) (* -1/4 (PI)))))>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))>
#<alt 2>
#<alt (+ 2 (* f (+ (* -1/4 (PI)) (* 1/4 (PI)))))>
#<alt (+ 2 (* f (+ (* -1/4 (PI)) (+ (* 1/16 (* f (pow (PI) 2))) (* 1/4 (PI))))))>
#<alt (+ 2 (* f (+ (* -1/4 (PI)) (+ (* 1/4 (PI)) (* f (+ (* 1/16 (pow (PI) 2)) (* f (+ (* -1/384 (pow (PI) 3)) (* 1/384 (pow (PI) 3))))))))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))>
#<alt (* f (- (* 1/4 (PI)) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (* 1/122880 (pow (PI) 5)) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (+ (* 1/122880 (pow (PI) 5)) (* (pow f 2) (- (* 1/82575360 (pow (PI) 7)) (* -1/82575360 (pow (PI) 7))))) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>

Calls

18 calls:

Time	Variable		Point	Expression
44.0ms	f	@	inf	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
42.0ms	f	@	-inf	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
8.0ms	f	@	0	(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
1.0ms	f	@	0	(log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))))
1.0ms	f	@	0	(- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))

rewrite347.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4608×	`-lowering-.f32`
4608×	`-lowering-.f64`
3824×	`/-lowering-/.f32`
3824×	`/-lowering-/.f64`
1170×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	116
1	102	112
2	710	45
0	8678	45

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 549

Calls

Call 1

Inputs
(/ (log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))) (/ (PI) -4))
(log (/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))))
(/ (+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))) (- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4))))
(+ (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(- (exp (/ (* (PI) f) 4)) (exp (/ (* (PI) f) -4)))
(* (PI) f)

Outputs
(+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (neg.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (/.f64 #s(literal -4 binary64) (PI.f64))))
(+.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (log.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(neg.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/.f64 #s(literal -4 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
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(.f64 (/.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (.f64 (/.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)))))) #s(literal 1 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))) (exp.f64 (.f64 (*.f64 (PI.f64) f) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(.f64 (/.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 1 binary64)) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 3/4 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -3/4 binary64)))))) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)))) (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))))) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(.f64 (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)))) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 3/4 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -3/4 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (+.f64 (exp.f64 (.f64 (*.f64 (PI.f64) f) #s(literal -1/2 binary64))) #s(literal -1 binary64)))))
(.f64 (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))))) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))
(.f64 (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 3/4 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -3/4 binary64)))))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (+.f64 (exp.f64 (.f64 (*.f64 (PI.f64) f) #s(literal -1/2 binary64))) #s(literal -1 binary64)))))
(.f64 (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 3/4 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -3/4 binary64)))) (+.f64 (exp.f64 (.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) #s(literal 3 binary64)))) (-.f64 (+.f64 (exp.f64 (+.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)) (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 (.f64 (*.f64 (PI.f64) f) #s(literal 1/2 binary64))) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 3/4 binary64))) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -3/4 binary64)))) (-.f64 (exp.f64 (+.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)) (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64)))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal -1/2 binary64)))) #s(literal 2 binary64)))) (-.f64 (exp.f64 (.f64 (.f64 (PI.f64) f) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 (*.f64 (PI.f64) f) #s(literal -1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) f)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) f)))
(*.f64 (PI.f64) f)
(*.f64 (PI.f64) (neg.f64 (-.f64 #s(literal 0 binary64) f)))
(.f64 (PI.f64) (.f64 #s(literal 1 binary64) f))
(*.f64 f (PI.f64))
(.f64 (.f64 (PI.f64) f) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) f))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) f))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) f)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) f)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) f))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) f))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) f))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (PI.f64) f)))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) f)))
(*.f64 (-.f64 #s(literal 0 binary64) f) (-.f64 #s(literal 0 binary64) (PI.f64)))
(.f64 (.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 f (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) f)) (PI.f64))
(.f64 (.f64 #s(literal 1 binary64) f) (PI.f64))
(.f64 (.f64 f (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 f (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 f (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 f (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 f (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 f (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))

simplify251.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2958×	`-lowering-.f32`
2958×	`-lowering-.f64`
2784×	`+-lowering-+.f64`
2784×	`+-lowering-+.f32`
1328×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	1552
1	627	1346
2	2752	1289
0	9144	1289

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI)))
(+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* -2 (/ (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))))
(+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* -2 (/ (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (PI))) (* -2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))))))
(+ (* -4 (/ (+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f))) (PI))) (* f (+ (* -2 (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))) (PI))) (* f (+ (* -2 (/ (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (PI))) (* -2/3 (/ (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))) (PI))))))))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))) (PI)))
(+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (* -1 (log f)))
(+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* 1/2 (* f (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))
(+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* f (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI)))))))))
(+ (log (/ 2 (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* -1 (log f)) (* f (+ (* 1/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (+ (* 1/6 (* f (+ (* -3/2 (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (+ (* 1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 3) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 3))) (* 3 (* (- (* 1/4 (PI)) (* -1/4 (PI))) (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))) (* 1/2 (+ (* -1/4 (* (pow (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) 2) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2))) (* (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(log (/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))))
(/ 2 (* f (- (* 1/4 (PI)) (* -1/4 (PI)))))
(/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)
(/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)
(/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
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(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
2
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(/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)
(/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)
(/.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) f)
(/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)
(/ (+ (* f (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (+ (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* 1/16 (/ (pow (PI) 2) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* f (- (+ (* -1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/384 (/ (pow (PI) 3) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (/ (* (+ (* -1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI))))) (* 1/4 (/ (PI) (- (* 1/4 (PI)) (* -1/4 (PI)))))) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3)))) (- (* 1/4 (PI)) (* -1/4 (PI))))))) (* 2 (/ (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))) (pow (- (* 1/4 (PI)) (* -1/4 (PI))) 2)))))))) (* 2 (/ 1 (- (* 1/4 (PI)) (* -1/4 (PI)))))) f)
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
(/ (+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI))))) (- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI))))))
(/.f64 (+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f)))) (-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f)))))
2
#s(literal 2 binary64)
(+ 2 (* f (+ (* -1/4 (PI)) (* 1/4 (PI)))))
#s(literal 2 binary64)
(+ 2 (* f (+ (* -1/4 (PI)) (+ (* 1/16 (* f (pow (PI) 2))) (* 1/4 (PI))))))
(+.f64 #s(literal 2 binary64) (.f64 f (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) (.f64 (PI.f64) f)))))
(+ 2 (* f (+ (* -1/4 (PI)) (+ (* 1/4 (PI)) (* f (+ (* 1/16 (pow (PI) 2)) (* f (+ (* -1/384 (pow (PI) 3)) (* 1/384 (pow (PI) 3))))))))))
(+.f64 #s(literal 2 binary64) (.f64 f (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) (.f64 (PI.f64) f)))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(+ (exp (* -1/4 (* f (PI)))) (exp (* 1/4 (* f (PI)))))
(+.f64 (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))))
(* f (- (* 1/4 (PI)) (* -1/4 (PI))))
(.f64 (PI.f64) (.f64 f #s(literal 1/2 binary64)))
(* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (* 1/384 (pow (PI) 3)) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))
(.f64 f (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 1/192 binary64) (*.f64 f f)))))
(* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (* 1/122880 (pow (PI) 5)) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))
(.f64 f (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/192 binary64))) (.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) (.f64 #s(literal 1/61440 binary64) (.f64 f f)))))))
(* f (- (+ (* 1/4 (PI)) (* (pow f 2) (- (+ (* 1/384 (pow (PI) 3)) (* (pow f 2) (- (+ (* 1/122880 (pow (PI) 5)) (* (pow f 2) (- (* 1/82575360 (pow (PI) 7)) (* -1/82575360 (pow (PI) 7))))) (* -1/122880 (pow (PI) 5))))) (* -1/384 (pow (PI) 3))))) (* -1/4 (PI))))
(.f64 f (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (.f64 f f) (+.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/192 binary64))) (.f64 (.f64 f f) (+.f64 (.f64 (pow.f64 (PI.f64) #s(literal 5 binary64)) #s(literal 1/61440 binary64)) (.f64 (.f64 f f) (*.f64 (pow.f64 (PI.f64) #s(literal 7 binary64)) #s(literal 1/41287680 binary64)))))))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(- (exp (* 1/4 (* f (PI)))) (exp (* -1/4 (* f (PI)))))
(-.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) f))) (exp.f64 (.f64 (PI.f64) (.f64 #s(literal -1/4 binary64) f))))
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)

eval132.0ms (0.7%)

Compiler: Compiled 31831 to 2882 computations (90.9% saved)

prune109.0ms (0.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	729	18	747
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	730	18	748

Accuracy

99.9%

Counts

748 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.5%	(/.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	97.5%	(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (.f64 #s(literal 0 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	98.4%	(/.f64 (/.f64 (neg.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
	99.4%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (PI.f64))
▶	99.4%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))
	99.2%	(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
	97.5%	(/.f64 (-.f64 (pow.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))) (+.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))) (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))))
	97.7%	(/.f64 (-.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))) (*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
▶	96.0%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	97.8%	(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.6%	(/.f64 (+.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (-.f64 (.f64 f (.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))) (.f64 f #s(literal 1/2 binary64)))) (log.f64 f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	99.1%	(/.f64 (*.f64 (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64))) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (sqrt.f64 (PI.f64)))
▶	96.0%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.7%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
▶	97.6%	(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
	99.2%	(*.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64))))
	99.2%	(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))

Compiler

Compiled 1074 to 574 computations (46.6% saved)

simplify264.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	cost-diff	0	(log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	cost-diff	0	(/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	256	(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
✓	cost-diff	0	(*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))
✓	cost-diff	0	(/.f64 (neg.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))) (sqrt.f64 (PI.f64)))
✓	cost-diff	64	(neg.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64)))
✓	cost-diff	12928	(/.f64 (/.f64 (neg.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
✓	cost-diff	0	(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f))
✓	cost-diff	0	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)
✓	cost-diff	0	(log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
✓	cost-diff	0	(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	cost-diff	0	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
✓	cost-diff	0	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))

Rules

3136×	`-lowering-.f32`
3136×	`-lowering-.f64`
2190×	`/-lowering-/.f32`
2190×	`/-lowering-/.f64`
2006×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	317
1	109	299
2	264	299
3	624	297
4	1661	297
5	5529	297
0	8331	297

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (log (tanh (/ f (/ 4 (PI))))) (PI)) 1/4)
(/ (log (tanh (/ f (/ 4 (PI))))) (PI))
(log (tanh (/ f (/ 4 (PI)))))
(tanh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
4
(PI)
1/4
(/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (PI) -4))
(log (/ (/ 2 (* (PI) 1/2)) f))
(/ (/ 2 (* (PI) 1/2)) f)
(/ 2 (* (PI) 1/2))
2
(* (PI) 1/2)
(PI)
1/2
f
(/ (PI) -4)
-4
(/ (- (log (/ 2 (* (PI) 1/2))) (log f)) (/ (PI) -4))
(- (log (/ 2 (* (PI) 1/2))) (log f))
(log (/ 2 (* (PI) 1/2)))
(/ 2 (* (PI) 1/2))
2
(* (PI) 1/2)
(PI)
1/2
(log f)
f
(/ (PI) -4)
-4
(/ (/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI))) (sqrt (PI)))
(/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI)))
(neg (* (log (tanh (/ f (/ 4 (PI))))) -4))
(* (log (tanh (/ f (/ 4 (PI))))) -4)
(log (tanh (/ f (/ 4 (PI)))))
(tanh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
4
(PI)
-4
(sqrt (PI))
(- (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4)) (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4)))
(/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4))
(log (* 2 (cosh (/ f (/ 4 (PI))))))
(* 2 (cosh (/ f (/ 4 (PI)))))
2
(cosh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
4
(PI)
(/ (PI) -4)
-4
(/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4))
(log (* 2 (sinh (/ f (/ 4 (PI))))))
(* 2 (sinh (/ f (/ 4 (PI)))))
(sinh (/ f (/ 4 (PI))))

Outputs
(/ (/ (log (tanh (/ f (/ 4 (PI))))) (PI)) 1/4)
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/ (log (tanh (/ f (/ 4 (PI))))) (PI))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
(log (tanh (/ f (/ 4 (PI)))))
(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(tanh (/ f (/ 4 (PI))))
(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(/ f (/ 4 (PI)))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
1/4
#s(literal 1/4 binary64)
(/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (/ 2 (* (PI) 1/2)) f))
(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
(/ (/ 2 (* (PI) 1/2)) f)
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 2 (* (PI) 1/2))
(/.f64 #s(literal 4 binary64) (PI.f64))
2
#s(literal 2 binary64)
(* (PI) 1/2)
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(PI)
(PI.f64)
1/2
#s(literal 1/2 binary64)
f
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ (- (log (/ 2 (* (PI) 1/2))) (log f)) (/ (PI) -4))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(- (log (/ 2 (* (PI) 1/2))) (log f))
(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f))
(log (/ 2 (* (PI) 1/2)))
(log.f64 (/.f64 #s(literal 4 binary64) (PI.f64)))
(/ 2 (* (PI) 1/2))
(/.f64 #s(literal 4 binary64) (PI.f64))
2
#s(literal 2 binary64)
(* (PI) 1/2)
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(PI)
(PI.f64)
1/2
#s(literal 1/2 binary64)
(log f)
(log.f64 f)
f
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ (/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI))) (sqrt (PI)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI)))
(*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))))
(neg (* (log (tanh (/ f (/ 4 (PI))))) -4))
(*.f64 #s(literal 4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(* (log (tanh (/ f (/ 4 (PI))))) -4)
(*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))
(log (tanh (/ f (/ 4 (PI)))))
(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(tanh (/ f (/ 4 (PI))))
(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(/ f (/ 4 (PI)))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
-4
#s(literal -4 binary64)
(sqrt (PI))
(sqrt.f64 (PI.f64))
(- (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4)) (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4)))
(.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))
(/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4))
(/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (* 2 (cosh (/ f (/ 4 (PI))))))
(log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(* 2 (cosh (/ f (/ 4 (PI)))))
(*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
2
#s(literal 2 binary64)
(cosh (/ f (/ 4 (PI))))
(cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(/ f (/ 4 (PI)))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4))
(/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (* 2 (sinh (/ f (/ 4 (PI))))))
(log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(* 2 (sinh (/ f (/ 4 (PI)))))
(*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(sinh (/ f (/ 4 (PI))))
(sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))

localize290.0ms (1.5%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.5%	(log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	accuracy	98.5%	(log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	accuracy	99.5%	(/.f64 (/.f64 (neg.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
✓	accuracy	99.4%	(/.f64 (neg.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))) (sqrt.f64 (PI.f64)))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.4%	(sqrt.f64 (PI.f64))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.7%	(-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f))
✓	accuracy	99.5%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	96.9%	(log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	100.0%	(log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f))
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	99.4%	(/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)
✓	accuracy	100.0%	(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
✓	accuracy	99.9%	(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	accuracy	99.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))

Results

199.0ms	252×	0	valid
11.0ms	4×	2	valid

Compiler

Compiled 326 to 38 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-div: 35.0ms (38.6% of total)

ival-log: 22.0ms (24.2% of total)

ival-pi: 12.0ms (13.2% of total)

ival-mult: 7.0ms (7.7% of total)

ival-sub: 3.0ms (3.3% of total)

ival-cosh: 3.0ms (3.3% of total)

ival-sqrt: 2.0ms (2.2% of total)

ival-sinh: 2.0ms (2.2% of total)

ival-tanh: 2.0ms (2.2% of total)

const: 1.0ms (1.1% of total)

backward-pass: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

series453.0ms (2.4%)

Counts

23 → 228

Calls

Call 1

Inputs
#<alt (/ (/ (log (tanh (/ f (/ 4 (PI))))) (PI)) 1/4)>
#<alt (/ (log (tanh (/ f (/ 4 (PI))))) (PI))>
#<alt (log (tanh (/ f (/ 4 (PI)))))>
#<alt (tanh (/ f (/ 4 (PI))))>
#<alt (/ 2 (* (PI) 1/2))>
#<alt (/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (PI) -4))>
#<alt (log (/ (/ 2 (* (PI) 1/2)) f))>
#<alt (/ (/ 2 (* (PI) 1/2)) f)>
#<alt (/ (- (log (/ 2 (* (PI) 1/2))) (log f)) (/ (PI) -4))>
#<alt (- (log (/ 2 (* (PI) 1/2))) (log f))>
#<alt (log (/ 2 (* (PI) 1/2)))>
#<alt (/ (/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI))) (sqrt (PI)))>
#<alt (neg (* (log (tanh (/ f (/ 4 (PI))))) -4))>
#<alt (/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI)))>
#<alt (* (log (tanh (/ f (/ 4 (PI))))) -4)>
#<alt (- (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4)) (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4)))>
#<alt (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4))>
#<alt (log (* 2 (cosh (/ f (/ 4 (PI))))))>
#<alt (* 2 (cosh (/ f (/ 4 (PI)))))>
#<alt (/ f (/ 4 (PI)))>
#<alt (PI)>
#<alt (sqrt (PI))>
#<alt (log (* 2 (sinh (/ f (/ 4 (PI))))))>

Outputs
#<alt (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))>
#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (/ (+ (log f) (log (* 1/4 (PI)))) (PI))>
#<alt (+ (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))) (+ (/ (log f) (PI)) (/ (log (* 1/4 (PI))) (PI))))>
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#<alt 2>
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#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>
#<alt (log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))>

Calls

57 calls:

Time	Variable		Point	Expression
146.0ms	f	@	inf	(- (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4)) (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4)))
66.0ms	f	@	-inf	(/ (/ (log (tanh (/ f (/ 4 (PI))))) (PI)) 1/4)
56.0ms	f	@	-inf	(- (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4)) (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4)))
51.0ms	f	@	inf	(/ (- (log (/ 2 (* (PI) 1/2))) (log f)) (/ (PI) -4))
29.0ms	f	@	inf	(/ (/ (log (tanh (/ f (/ 4 (PI))))) (PI)) 1/4)

rewrite516.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4512×	`-lowering-.f32`
4512×	`-lowering-.f64`
2960×	`/-lowering-/.f32`
2960×	`/-lowering-/.f64`
1906×	`--lowering--.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	190
1	236	176
2	2037	176
0	8548	176

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 1364

Calls

Call 1

Inputs
(/ (/ (log (tanh (/ f (/ 4 (PI))))) (PI)) 1/4)
(/ (log (tanh (/ f (/ 4 (PI))))) (PI))
(log (tanh (/ f (/ 4 (PI)))))
(tanh (/ f (/ 4 (PI))))
(/ 2 (* (PI) 1/2))
(/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (PI) -4))
(log (/ (/ 2 (* (PI) 1/2)) f))
(/ (/ 2 (* (PI) 1/2)) f)
(/ (- (log (/ 2 (* (PI) 1/2))) (log f)) (/ (PI) -4))
(- (log (/ 2 (* (PI) 1/2))) (log f))
(log (/ 2 (* (PI) 1/2)))
(/ (/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI))) (sqrt (PI)))
(neg (* (log (tanh (/ f (/ 4 (PI))))) -4))
(/ (neg (* (log (tanh (/ f (/ 4 (PI))))) -4)) (sqrt (PI)))
(* (log (tanh (/ f (/ 4 (PI))))) -4)
(- (/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4)) (/ (log (* 2 (sinh (/ f (/ 4 (PI)))))) (/ (PI) -4)))
(/ (log (* 2 (cosh (/ f (/ 4 (PI)))))) (/ (PI) -4))
(log (* 2 (cosh (/ f (/ 4 (PI))))))
(* 2 (cosh (/ f (/ 4 (PI)))))
(/ f (/ 4 (PI)))
(PI)
(sqrt (PI))
(log (* 2 (sinh (/ f (/ 4 (PI))))))

Outputs
(+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))))
(+.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (+.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(+.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (+.f64 (.f64 #s(literal 4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(+.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (fma.f64 (neg.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))) #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(+.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))
(+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(+.f64 (fma.f64 #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (PI.f64)) (neg.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64) (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (PI.f64)) (neg.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))) (fma.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))))
(+.f64 (fma.f64 #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (PI.f64)) (neg.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64))))) (fma.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)))))
(+.f64 (fma.f64 #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (PI.f64)) (neg.f64 (.f64 #s(literal 4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64)))))) (fma.f64 #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64))) (.f64 #s(literal 4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64))))))
(+.f64 (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64) (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))) (fma.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))))
(+.f64 (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64))))) (fma.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)))))
(+.f64 (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (.f64 #s(literal 4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64)))))) (fma.f64 #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64))) (.f64 #s(literal 4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64))))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (neg.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64) (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))) (fma.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (neg.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64))))) (fma.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (neg.f64 (.f64 #s(literal 4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64)))))) (fma.f64 #s(literal -4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64))) (.f64 #s(literal 4 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (-.f64 #s(literal 0 binary64) (PI.f64))))))
(+.f64 (fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))) (/.f64 #s(literal 4 binary64) (PI.f64)) (neg.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64) (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))) (/.f64 #s(literal 4 binary64) (PI.f64)) (neg.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))) (fma.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))))
(+.f64 (fma.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))) (/.f64 #s(literal 4 binary64) (PI.f64)) (neg.f64 (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64))))) (fma.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1 binary64)))))
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(+.f64 (fma.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (neg.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal 1 binary64) (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (neg.f64 (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))) (fma.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))))
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(/.f64 (-.f64 (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64))))) (exp.f64 (+.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))) (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))
(*.f64 (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))) #s(literal 2 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) f) (/.f64 #s(literal -4 binary64) (PI.f64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))))
(/.f64 (/.f64 f #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) f)) (/.f64 #s(literal 4 binary64) (PI.f64)))
(/.f64 (*.f64 f (PI.f64)) #s(literal 4 binary64))
(/.f64 (*.f64 f #s(literal 1 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64)))
(/.f64 (/.f64 f #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)))
(pow.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))
(*.f64 (PI.f64) (/.f64 f #s(literal 4 binary64)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) f) #s(literal -1 binary64)))
(.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) f)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f) #s(literal -1 binary64)))
(*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) f)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(*.f64 (-.f64 #s(literal 0 binary64) f) (/.f64 (PI.f64) #s(literal -4 binary64)))
(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) f) #s(literal -1 binary64)))
(*.f64 (/.f64 f #s(literal 4 binary64)) (PI.f64))
(*.f64 (/.f64 f #s(literal 1 binary64)) (/.f64 (PI.f64) #s(literal 4 binary64)))
(.f64 (.f64 (/.f64 f #s(literal 4 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (/.f64 f #s(literal 4 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (/.f64 f #s(literal 4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (/.f64 f #s(literal 2 binary64)) (.f64 (PI.f64) #s(literal 1/2 binary64)))
(*.f64 (/.f64 f #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(.f64 (/.f64 f #s(literal -2 binary64)) (.f64 (PI.f64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 f (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) f) #s(literal -1 binary64)) (/.f64 (PI.f64) #s(literal 4 binary64)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (PI.f64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (PI.f64) (PI.f64)))) #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (PI.f64) (PI.f64))))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 1 binary64)))
(fabs.f64 (sqrt.f64 (PI.f64)))
(fabs.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(sqrt.f64 (PI.f64))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/2 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (fabs.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(+.f64 (log.f64 (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))) #s(literal 3 binary64))) (exp.f64 (.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))) #s(literal 3 binary64))))) (log.f64 (+.f64 (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))) (+.f64 (exp.f64 (+.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))) (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))) (exp.f64 (+.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))))))
(-.f64 (log.f64 (-.f64 (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64))))) (exp.f64 (+.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))) (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))))) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))))
(-.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (log.f64 (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (log.f64 (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))

simplify335.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

4056×	`-lowering-.f32`
4056×	`-lowering-.f64`
2086×	`+-lowering-+.f64`
2086×	`+-lowering-+.f32`
1532×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	6510
1	1407	5489
2	6290	5412
0	8025	5412

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI)))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))
(+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(/ (+ (log f) (log (* 1/4 (PI)))) (PI))
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(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))
(log (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))
(log.f64 (-.f64 (exp.f64 (.f64 f (.f64 #s(literal 1/4 binary64) (PI.f64)))) (exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 f (PI.f64))))))

eval457.0ms (2.4%)

Compiler: Compiled 71566 to 5543 computations (92.3% saved)

prune239.0ms (1.3%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	2397	18	2415
Fresh	9	4	13
Picked	4	1	5
Done	0	0	0
Total	2410	23	2433

Accuracy

99.9%

Counts

2433 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f64 (/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -4 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
▶	99.4%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (PI.f64))
	98.3%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
	97.5%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) #s(literal 1/4 binary64))
	95.7%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))) #s(literal 1/4 binary64))
	99.0%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) #s(literal 1/4 binary64))
✓	99.4%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))
	99.2%	(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
	95.8%	(/.f64 (-.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 f))) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 16 binary64)))
	99.4%	(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64)))) (.f64 (PI.f64) (PI.f64)))
	95.9%	(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.9%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.9%	(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.6%	(/.f64 (+.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (-.f64 (.f64 f (.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))) (.f64 f #s(literal 1/2 binary64)))) (log.f64 f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.0%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	94.8%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -4 binary64)))
	95.5%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
	96.7%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
	95.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
▶	95.9%	(-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (/.f64 (log.f64 f) (PI.f64)) #s(literal -1/4 binary64)))
▶	95.8%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
	95.9%	(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))

Compiler

Compiled 780 to 604 computations (22.6% saved)

simplify201.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -4 binary64)))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
✓	cost-diff	12864	(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (PI.f64))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	256	(-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (/.f64 (log.f64 f) (PI.f64)) #s(literal -1/4 binary64)))
✓	cost-diff	0	(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 #s(literal -4 binary64) (PI.f64))
✓	cost-diff	0	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	cost-diff	0	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (PI.f64))
✓	cost-diff	128	(/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64))

Rules

3730×	`-lowering-.f32`
3730×	`-lowering-.f64`
2628×	`/-lowering-/.f32`
2628×	`/-lowering-/.f64`
1066×	`times-frac`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	38	215
1	99	214
2	218	214
3	524	214
4	1373	214
5	3321	211
0	8153	211

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4) (PI))
(/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4)
(log (/ 1 (tanh (/ f (/ 4 (PI))))))
(/ 1 (tanh (/ f (/ 4 (PI)))))
1
(tanh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
4
(PI)
-1/4
(* (/ -4 (PI)) (log (/ 4 (* f (PI)))))
(/ -4 (PI))
-4
(PI)
(log (/ 4 (* f (PI))))
(/ 4 (* f (PI)))
4
(* f (PI))
f
(/ 4 (/ (PI) (log (tanh (/ f (/ 4 (PI)))))))
4
(/ (PI) (log (tanh (/ f (/ 4 (PI))))))
(PI)
(log (tanh (/ f (/ 4 (PI)))))
(tanh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
(- (/ (log (/ 4 (PI))) (/ (PI) -4)) (/ (/ (log f) (PI)) -1/4))
(/ (log (/ 4 (PI))) (/ (PI) -4))
(log (/ 4 (PI)))
(/ 4 (PI))
4
(PI)
(/ (PI) -4)
-4
(/ (/ (log f) (PI)) -1/4)
(/ (log f) (PI))
(log f)
f
-1/4
(/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (pow (sqrt (PI)) 2) -4))
(log (/ (/ 2 (* (PI) 1/2)) f))
(/ (/ 2 (* (PI) 1/2)) f)
(/ 2 (* (PI) 1/2))
2
(* (PI) 1/2)
(PI)
1/2
f
(/ (pow (sqrt (PI)) 2) -4)
(pow (sqrt (PI)) 2)
(sqrt (PI))
-4

Outputs
(/ (/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4) (PI))
(/.f64 (log.f64 (tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4)
(/.f64 (log.f64 (tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))) #s(literal 1/4 binary64))
(log (/ 1 (tanh (/ f (/ 4 (PI))))))
(log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))))
(/ 1 (tanh (/ f (/ 4 (PI)))))
(/.f64 #s(literal 1 binary64) (tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))))
1
#s(literal 1 binary64)
(tanh (/ f (/ 4 (PI))))
(tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))
(/ f (/ 4 (PI)))
(*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
-1/4
#s(literal -1/4 binary64)
(* (/ -4 (PI)) (log (/ 4 (* f (PI)))))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/ -4 (PI))
(/.f64 #s(literal -4 binary64) (PI.f64))
-4
#s(literal -4 binary64)
(PI)
(PI.f64)
(log (/ 4 (* f (PI))))
(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
4
#s(literal 4 binary64)
(* f (PI))
(*.f64 f (PI.f64))
f
(/ 4 (/ (PI) (log (tanh (/ f (/ 4 (PI)))))))
(/.f64 (log.f64 (tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))) (/.f64 (PI.f64) #s(literal 4 binary64)))
4
#s(literal 4 binary64)
(/ (PI) (log (tanh (/ f (/ 4 (PI))))))
(/.f64 (PI.f64) (log.f64 (tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))))
(PI)
(PI.f64)
(log (tanh (/ f (/ 4 (PI)))))
(log.f64 (tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))))
(tanh (/ f (/ 4 (PI))))
(tanh.f64 (*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64))))
(/ f (/ 4 (PI)))
(*.f64 f (/.f64 (PI.f64) #s(literal 4 binary64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
(- (/ (log (/ 4 (PI))) (/ (PI) -4)) (/ (/ (log f) (PI)) -1/4))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (-.f64 (log.f64 f) (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64)))))
(/ (log (/ 4 (PI))) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ 4 (PI)))
(log.f64 (/.f64 #s(literal 4 binary64) (PI.f64)))
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ (/ (log f) (PI)) -1/4)
(/.f64 (log.f64 f) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/ (log f) (PI))
(/.f64 (log.f64 f) (PI.f64))
(log f)
(log.f64 f)
f
-1/4
#s(literal -1/4 binary64)
(/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (pow (sqrt (PI)) 2) -4))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (/ 2 (* (PI) 1/2)) f))
(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
(/ (/ 2 (* (PI) 1/2)) f)
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 2 (* (PI) 1/2))
(/.f64 #s(literal 4 binary64) (PI.f64))
2
#s(literal 2 binary64)
(* (PI) 1/2)
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(PI)
(PI.f64)
1/2
#s(literal 1/2 binary64)
f
(/ (pow (sqrt (PI)) 2) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
(pow (sqrt (PI)) 2)
(PI.f64)
(sqrt (PI))
(sqrt.f64 (PI.f64))
-4
#s(literal -4 binary64)

localize331.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)
✓	accuracy	98.5%	(PI.f64)
✓	accuracy	98.5%	(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
✓	accuracy	98.5%	(sqrt.f64 (PI.f64))
✓	accuracy	99.6%	(-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (/.f64 (log.f64 f) (PI.f64)) #s(literal -1/4 binary64)))
✓	accuracy	99.5%	(/.f64 (log.f64 f) (PI.f64))
✓	accuracy	98.5%	(PI.f64)
✓	accuracy	96.9%	(log.f64 (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	99.6%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
✓	accuracy	99.5%	(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.5%	(PI.f64)
✓	accuracy	99.6%	(*.f64 f (PI.f64))
✓	accuracy	99.5%	(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
✓	accuracy	99.3%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
✓	accuracy	98.5%	(PI.f64)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	accuracy	99.5%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (PI.f64))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.5%	(PI.f64)

Results

188.0ms	252×	0	valid
66.0ms	4×	5	exit

Compiler

Compiled 242 to 39 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 123.0ms

ival-log: 61.0ms (49.7% of total)

ival-div: 32.0ms (26.1% of total)

ival-tanh: 12.0ms (9.8% of total)

ival-mult: 6.0ms (4.9% of total)

ival-pow: 4.0ms (3.3% of total)

ival-sqrt: 2.0ms (1.6% of total)

backward-pass: 2.0ms (1.6% of total)

const: 1.0ms (0.8% of total)

ival-pi: 1.0ms (0.8% of total)

ival-sub: 1.0ms (0.8% of total)

series83.0ms (0.4%)

Counts

25 → 204

Calls

Call 1

Inputs
#<alt (/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4)>
#<alt (/ (/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4) (PI))>
#<alt (log (/ 1 (tanh (/ f (/ 4 (PI))))))>
#<alt (/ 1 (tanh (/ f (/ 4 (PI)))))>
#<alt (* (/ -4 (PI)) (log (/ 4 (* f (PI)))))>
#<alt (/ -4 (PI))>
#<alt (PI)>
#<alt (log (/ 4 (* f (PI))))>
#<alt (/ 4 (/ (PI) (log (tanh (/ f (/ 4 (PI)))))))>
#<alt (/ (PI) (log (tanh (/ f (/ 4 (PI))))))>
#<alt (log (tanh (/ f (/ 4 (PI)))))>
#<alt (- (/ (log (/ 4 (PI))) (/ (PI) -4)) (/ (/ (log f) (PI)) -1/4))>
#<alt (/ (log (/ 4 (PI))) (/ (PI) -4))>
#<alt (log (/ 4 (PI)))>
#<alt (/ 4 (PI))>
#<alt (pow (sqrt (PI)) 2)>
#<alt (/ 2 (* (PI) 1/2))>
#<alt (/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (pow (sqrt (PI)) 2) -4))>
#<alt (log (/ (/ 2 (* (PI) 1/2)) f))>
#<alt (/ f (/ 4 (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (* f (PI))>
#<alt (/ (log f) (PI))>
#<alt (sqrt (PI))>
#<alt (/ (/ 2 (* (PI) 1/2)) f)>

Outputs
#<alt (* -4 (+ (log (/ 4 (PI))) (* -1 (log f))))>
#<alt (+ (* -4 (+ (log (/ 4 (PI))) (* -1 (log f)))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))))>
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#<alt (+ (* 4 (/ (+ (log f) (log (* 1/4 (PI)))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* 2/3 (/ (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (PI))) (* 2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (PI))))))))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (* 4 (/ (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))>
#<alt (/ (PI) (+ (log f) (log (* 1/4 (PI)))))>
#<alt (+ (* -2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))) (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (+ (* f (- (* -1 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (* (PI) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))) (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (+ (* f (- (* f (- (* -1 (* f (+ (* -2 (/ (* (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (* (PI) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* (PI) (+ (log f) (log (* 1/4 (PI))))))) (+ (* -1 (/ (* (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (+ (log f) (log (* 1/4 (PI)))) 3))) (* 1/6 (/ (* (PI) (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI)))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))))) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (* (PI) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))) (/ (PI) (+ (log f) (log (* 1/4 (PI))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ (PI) (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI)))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 1/2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI)))))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* 1/6 (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI))))))) (* 1/2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (log f) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (log f) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (log f) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (log f) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* 4 (/ (log (/ 1 f)) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* 4 (/ (log (/ 1 f)) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* 4 (/ (log (/ 1 f)) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* 4 (/ (log (/ 1 f)) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (- (* -4 (/ (log (/ 4 (PI))) (PI))) (* -4 (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ 1 f)) (log (/ 4 (PI)))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (* -4 (/ (+ (log (/ -4 (PI))) (log (/ -1 f))) (PI)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 4 (PI))) (* -1 (log f)))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ 1 f)) (log (/ 4 (PI))))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (+ (log (/ -4 (PI))) (log (/ -1 f)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (* f (PI))>
#<alt (/ (log f) (PI))>
#<alt (/ (log f) (PI))>
#<alt (/ (log f) (PI))>
#<alt (/ (log f) (PI))>
#<alt (* -1 (/ (log (/ 1 f)) (PI)))>
#<alt (* -1 (/ (log (/ 1 f)) (PI)))>
#<alt (* -1 (/ (log (/ 1 f)) (PI)))>
#<alt (* -1 (/ (log (/ 1 f)) (PI)))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))>
#<alt (/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>
#<alt (/ 4 (* f (PI)))>

Calls

51 calls:

Time	Variable		Point	Expression
31.0ms	f	@	inf	(/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4)
28.0ms	f	@	-inf	(/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4)
3.0ms	f	@	0	(/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4)
2.0ms	f	@	0	(/ (PI) (log (tanh (/ f (/ 4 (PI))))))
2.0ms	f	@	0	(/ (/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4) (PI))

rewrite461.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4834×	`/-lowering-/.f32`
4834×	`/-lowering-/.f64`
2586×	`-lowering-.f32`
2586×	`-lowering-.f64`
1702×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	149
1	247	149
2	2045	149
0	8800	149

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 1544

Calls

Call 1

Inputs
(/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4)
(/ (/ (log (/ 1 (tanh (/ f (/ 4 (PI)))))) -1/4) (PI))
(log (/ 1 (tanh (/ f (/ 4 (PI))))))
(/ 1 (tanh (/ f (/ 4 (PI)))))
(* (/ -4 (PI)) (log (/ 4 (* f (PI)))))
(/ -4 (PI))
(PI)
(log (/ 4 (* f (PI))))
(/ 4 (/ (PI) (log (tanh (/ f (/ 4 (PI)))))))
(/ (PI) (log (tanh (/ f (/ 4 (PI))))))
(log (tanh (/ f (/ 4 (PI)))))
(- (/ (log (/ 4 (PI))) (/ (PI) -4)) (/ (/ (log f) (PI)) -1/4))
(/ (log (/ 4 (PI))) (/ (PI) -4))
(log (/ 4 (PI)))
(/ 4 (PI))
(pow (sqrt (PI)) 2)
(/ 2 (* (PI) 1/2))
(/ (log (/ (/ 2 (* (PI) 1/2)) f)) (/ (pow (sqrt (PI)) 2) -4))
(log (/ (/ 2 (* (PI) 1/2)) f))
(/ f (/ 4 (PI)))
(/ 4 (* f (PI)))
(* f (PI))
(/ (log f) (PI))
(sqrt (PI))
(/ (/ 2 (* (PI) 1/2)) f)

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -1/4 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 (log.f64 #s(literal -1 binary64)) #s(literal -1/4 binary64)) (/.f64 (log.f64 (-.f64 #s(literal 0 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 1/4 binary64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64)))))) #s(literal 1/4 binary64)))
(-.f64 (/.f64 (log.f64 (expm1.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 f #s(literal 4 binary64))) (PI.f64)))) #s(literal 1/4 binary64)) (/.f64 (log1p.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 f #s(literal 4 binary64))) (PI.f64)))) #s(literal 1/4 binary64)))
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(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (neg.f64 (-.f64 #s(literal 0 binary64) f)))
(/.f64 #s(literal -4 binary64) (*.f64 f (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal -4 binary64) (neg.f64 (neg.f64 (*.f64 f (-.f64 #s(literal 0 binary64) (PI.f64))))))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) f))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) f))))
(/.f64 #s(literal 2 binary64) (.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 2 binary64) (neg.f64 (.f64 (.f64 (PI.f64) #s(literal -1/2 binary64)) f)))
(/.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 2 binary64) (neg.f64 (.f64 f (.f64 (PI.f64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -2 binary64) (.f64 (.f64 (PI.f64) #s(literal -1/2 binary64)) f))
(/.f64 #s(literal -2 binary64) (neg.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal -2 binary64) (.f64 f (.f64 (PI.f64) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 f (/.f64 #s(literal -4 binary64) (PI.f64))))
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) f) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 f #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) f) (PI.f64))
(/.f64 (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) f))
(/.f64 (neg.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (neg.f64 (*.f64 f #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal 4 binary64) f)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1 binary64)) f)
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) f)) (.f64 (PI.f64) #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) f)) (.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) f)) #s(literal 1/2 binary64))
(/.f64 (/.f64 #s(literal 2 binary64) f) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64))) (neg.f64 (.f64 #s(literal 1/2 binary64) f)))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 4 binary64) f))) (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) f))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) f))) (.f64 (PI.f64) #s(literal -1/2 binary64)))
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(/.f64 (neg.f64 (/.f64 (/.f64 #s(literal 4 binary64) f) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (neg.f64 (cbrt.f64 (PI.f64))))
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(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64))))
(.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (.f64 f (PI.f64))))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) f))
(.f64 #s(literal -4 binary64) (/.f64 #s(literal 1 binary64) (.f64 f (-.f64 #s(literal 0 binary64) (PI.f64)))))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) f)))
(.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) f)))
(*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) f))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 4 binary64) f))
(*.f64 (/.f64 #s(literal 1 binary64) f) (/.f64 #s(literal 4 binary64) (PI.f64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 f (PI.f64))) #s(literal 4 binary64))
(*.f64 (/.f64 #s(literal 4 binary64) f) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) f)) (/.f64 #s(literal -4 binary64) (PI.f64)))
(.f64 (pow.f64 (.f64 (/.f64 f #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(.f64 (pow.f64 (.f64 (/.f64 f #s(literal 4 binary64)) (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 f #s(literal 4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 f #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 (pow.f64 (/.f64 f #s(literal -4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))))
(.f64 (pow.f64 (/.f64 f #s(literal -2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 f (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1 binary64)) #s(literal 2 binary64))

simplify230.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

2658×	`-lowering-.f32`
2658×	`-lowering-.f64`
1552×	`sum3-define`
1480×	`+-lowering-+.f64`
1480×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	5368
1	1125	4420
2	5170	3664
0	10503	3664

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* -4 (+ (log (/ 4 (PI))) (* -1 (log f))))
(+ (* -4 (+ (log (/ 4 (PI))) (* -1 (log f)))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))))
(+ (* -4 (+ (log (/ 4 (PI))) (* -1 (log f)))) (* f (+ (* -2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* -1/2 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))))))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))))))
(+ (* -4 (+ (log (/ 4 (PI))) (* -1 (log f)))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* -2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* -1/2 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))))))) (* -2/3 (* f (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (+ (* -3 (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))) (* -3/2 (* (PI) (+ (* -32 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 3))) (+ (* -2 (/ (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (pow (PI) 2))))))))))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))
(* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI)))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* f (+ (* -2 (/ (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* -1/2 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))))))) (PI))) (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))))))
(+ (* -4 (/ (+ (log (/ 4 (PI))) (* -1 (log f))) (PI))) (* f (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (pow (PI) 2))) (* f (+ (* -2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* -1/2 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))))) (PI))) (* -2/3 (/ (* f (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (+ (* -3 (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))) (* -3/2 (* (PI) (+ (* -32 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 3))) (+ (* -2 (/ (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (pow (PI) 2)))))))))) (PI))))))))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(* -4 (/ (log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))) (PI)))
(+ (log (/ 4 (PI))) (* -1 (log f)))
(+ (log (/ 4 (PI))) (+ (* -2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (* -1 (log f))))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* f (+ (* -2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* 1/2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* -1/2 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))))))))))))
(+ (log (/ 4 (PI))) (+ (* -1 (log f)) (* f (+ (* -2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* 1/6 (* f (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (+ (* -3 (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))) (* -3/2 (* (PI) (+ (* -32 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 3))) (+ (* -2 (/ (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (pow (PI) 2))))))))))) (* 1/2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* -1/2 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))))))))))))
(log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(log (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
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(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))
(/ 4 (* f (PI)))

Outputs
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(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(* 1/4 (* f (PI)))
(.f64 (PI.f64) (.f64 f #s(literal 1/4 binary64)))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(* f (PI))
(*.f64 (PI.f64) f)
(/ (log f) (PI))
(/.f64 (log.f64 f) (PI.f64))
(/ (log f) (PI))
(/.f64 (log.f64 f) (PI.f64))
(/ (log f) (PI))
(/.f64 (log.f64 f) (PI.f64))
(/ (log f) (PI))
(/.f64 (log.f64 f) (PI.f64))
(* -1 (/ (log (/ 1 f)) (PI)))
(/.f64 (log.f64 f) (PI.f64))
(* -1 (/ (log (/ 1 f)) (PI)))
(/.f64 (log.f64 f) (PI.f64))
(* -1 (/ (log (/ 1 f)) (PI)))
(/.f64 (log.f64 f) (PI.f64))
(* -1 (/ (log (/ 1 f)) (PI)))
(/.f64 (log.f64 f) (PI.f64))
(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(/ (+ (log -1) (* -1 (log (/ -1 f)))) (PI))
(/.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) f))) (PI.f64))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))
(/ 4 (* f (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) f))

eval386.0ms (2%)

Compiler: Compiled 49948 to 5735 computations (88.5% saved)

prune256.0ms (1.4%)

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	2358	10	2368
Fresh	9	8	17
Picked	2	3	5
Done	0	1	1
Total	2369	22	2391

Accuracy

99.9%

Counts

2391 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 (/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)) (PI.f64))
	96.7%	(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (-.f64 #s(literal 0 binary64) (.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/768 binary64)) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/128 binary64))))) (.f64 (PI.f64) (PI.f64))) f))))) f)) #s(literal -1/4 binary64)) (PI.f64))
	98.3%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
✓	99.4%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (PI.f64))
	98.3%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
	97.5%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) #s(literal 1/4 binary64))
	99.0%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) #s(literal 1/4 binary64))
✓	99.4%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))
	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
	95.9%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	96.6%	(/.f64 (+.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (-.f64 (.f64 f (.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))) (.f64 f #s(literal 1/2 binary64)))) (log.f64 f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
▶	96.0%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.7%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
▶	99.2%	(/.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)))
	95.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
	95.9%	(-.f64 (/.f64 (log.f64 #s(literal 4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (*.f64 f (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))))
	95.4%	(.f64 (/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
	95.9%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
▶	95.3%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
	95.8%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 f (*.f64 (PI.f64) #s(literal 1/2 binary64))))))
✓	95.8%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 747 to 554 computations (25.8% saved)

simplify234.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64)))
✓	cost-diff	128	(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64)))))
✓	cost-diff	128	(/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
✓	cost-diff	256	(+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))
✓	cost-diff	0	(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)))
✓	cost-diff	128	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
✓	cost-diff	0	(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 #s(literal -4 binary64) (PI.f64))
✓	cost-diff	0	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (PI.f64))
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)
✓	cost-diff	0	(log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f))
✓	cost-diff	0	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	cost-diff	0	(log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))
✓	cost-diff	0	(/.f64 (/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)) (PI.f64))
✓	cost-diff	128	(/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64))
✓	cost-diff	19520	(+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))))

Rules

3528×	`-lowering-.f32`
3528×	`-lowering-.f64`
1792×	`sum4-define`
1768×	`fma-lowering-fma.f32`
1768×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	426
1	149	373
2	446	333
3	1804	307
4	5382	307
0	8007	307

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4) (PI))
(/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4)
(+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)))
(log (pow (tanh (/ f (/ 4 (PI)))) -1/2))
(pow (tanh (/ f (/ 4 (PI)))) -1/2)
(tanh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
4
(PI)
-1/2
-1/4
(/ (log (/ (/ 4 (PI)) f)) (/ (PI) -4))
(log (/ (/ 4 (PI)) f))
(/ (/ 4 (PI)) f)
(/ 4 (PI))
4
(PI)
f
(/ (PI) -4)
-4
(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))
(/ -4 (PI))
-4
(PI)
(- (log (/ 4 f)) (log (PI)))
(log (/ 4 f))
(/ 4 f)
4
f
(log (PI))
(/ 4 (* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI)))
4
(* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI))
(/ 1 (log (tanh (/ f (/ 4 (PI))))))
1
(log (tanh (/ f (/ 4 (PI)))))
(tanh (/ f (/ 4 (PI))))
(/ f (/ 4 (PI)))
f
(/ 4 (PI))
(PI)
(/ (+ (log (/ 2 (* (PI) 1/2))) (- (* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))) (log f))) (/ (PI) -4))
(+ (log (/ 2 (* (PI) 1/2))) (- (* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))) (log f)))
(log (/ 2 (* (PI) 1/2)))
(/ 2 (* (PI) 1/2))
2
(* (PI) 1/2)
(PI)
1/2
(- (* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))) (log f))
(* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2)))
f
(* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))
(* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192))))
(+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))
(* 1/16 (* (PI) 2))
1/16
(* (PI) 2)
(* -2 (* (* 2 (* (PI) 2)) 1/192))
-2
(* (* 2 (* (PI) 2)) 1/192)
(* 2 (* (PI) 2))
1/192
(* f 1/2)
(log f)
(/ (PI) -4)
-4

Outputs
(/ (/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4) (PI))
(*.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (/.f64 #s(literal -8 binary64) (PI.f64)))
(/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4)
(*.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) #s(literal -8 binary64))
(+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)))
(*.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(log (pow (tanh (/ f (/ 4 (PI)))) -1/2))
(log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))
(pow (tanh (/ f (/ 4 (PI)))) -1/2)
(pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(tanh (/ f (/ 4 (PI))))
(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(/ f (/ 4 (PI)))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
-1/2
#s(literal -1/2 binary64)
-1/4
#s(literal -1/4 binary64)
(/ (log (/ (/ 4 (PI)) f)) (/ (PI) -4))
(/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(log (/ (/ 4 (PI)) f))
(log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))
(/ (/ 4 (PI)) f)
(/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64)))
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
f
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))
(/.f64 (*.f64 #s(literal -4 binary64) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64)))) (PI.f64))
(/ -4 (PI))
(/.f64 #s(literal -4 binary64) (PI.f64))
-4
#s(literal -4 binary64)
(PI)
(PI.f64)
(- (log (/ 4 f)) (log (PI)))
(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64)))
(log (/ 4 f))
(log.f64 (/.f64 #s(literal 4 binary64) f))
(/ 4 f)
(/.f64 #s(literal 4 binary64) f)
4
#s(literal 4 binary64)
f
(log (PI))
(log.f64 (PI.f64))
(/ 4 (* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
4
#s(literal 4 binary64)
(* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI))
(/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/ 1 (log (tanh (/ f (/ 4 (PI))))))
(/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
1
#s(literal 1 binary64)
(log (tanh (/ f (/ 4 (PI)))))
(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(tanh (/ f (/ 4 (PI))))
(tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))
(/ f (/ 4 (PI)))
(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
f
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
(PI)
(PI.f64)
(/ (+ (log (/ 2 (* (PI) 1/2))) (- (* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))) (log f))) (/ (PI) -4))
(/.f64 (+.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (-.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/24 binary64)) (*.f64 f f))) (log.f64 f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(+ (log (/ 2 (* (PI) 1/2))) (- (* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))) (log f)))
(+.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (-.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/24 binary64)) (*.f64 f f))) (log.f64 f)))
(log (/ 2 (* (PI) 1/2)))
(log.f64 (/.f64 #s(literal 4 binary64) (PI.f64)))
(/ 2 (* (PI) 1/2))
(/.f64 #s(literal 4 binary64) (PI.f64))
2
#s(literal 2 binary64)
(* (PI) 1/2)
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(PI)
(PI.f64)
1/2
#s(literal 1/2 binary64)
(- (* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))) (log f))
(-.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/24 binary64)) (*.f64 f f))) (log.f64 f))
(* f (* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2)))
(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 (.f64 (PI.f64) #s(literal 1/24 binary64)) (*.f64 f f)))
f
(* (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))) (* f 1/2))
(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 f (.f64 (PI.f64) #s(literal 1/24 binary64))))
(* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192))))
(.f64 (PI.f64) (.f64 (PI.f64) #s(literal 1/24 binary64)))
(+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))
(*.f64 (PI.f64) #s(literal 1/12 binary64))
(* 1/16 (* (PI) 2))
(*.f64 (PI.f64) #s(literal 1/8 binary64))
1/16
#s(literal 1/16 binary64)
(* (PI) 2)
(*.f64 (PI.f64) #s(literal 2 binary64))
(* -2 (* (* 2 (* (PI) 2)) 1/192))
(*.f64 (PI.f64) #s(literal -1/24 binary64))
-2
#s(literal -2 binary64)
(* (* 2 (* (PI) 2)) 1/192)
(*.f64 (PI.f64) #s(literal 1/48 binary64))
(* 2 (* (PI) 2))
(*.f64 #s(literal 4 binary64) (PI.f64))
1/192
#s(literal 1/192 binary64)
(* f 1/2)
(*.f64 f #s(literal 1/2 binary64))
(log f)
(log.f64 f)
(/ (PI) -4)
(/.f64 (PI.f64) #s(literal -4 binary64))
-4
#s(literal -4 binary64)

localize472.0ms (2.5%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.5%	(+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))
✓	accuracy	98.5%	(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64)))))
✓	accuracy	98.5%	(.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))
✓	accuracy	96.9%	(log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
✓	accuracy	99.5%	(*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.5%	(PI.f64)
✓	accuracy	99.6%	(log.f64 (/.f64 #s(literal 4 binary64) f))
✓	accuracy	99.6%	(-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64)))
✓	accuracy	99.3%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
✓	accuracy	98.5%	(PI.f64)
✓	accuracy	100.0%	(log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f))
✓	accuracy	99.5%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
✓	accuracy	99.4%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)
✓	accuracy	98.5%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))
✓	accuracy	99.5%	(/.f64 (/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)) (PI.f64))
✓	accuracy	99.4%	(/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))
✓	accuracy	98.5%	(PI.f64)

Results

192.0ms	252×	0	valid
188.0ms	4×	5	exit

Compiler

Compiled 467 to 52 computations (88.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 262.0ms

ival-pow: 100.0ms (38.2% of total)

ival-log: 56.0ms (21.4% of total)

ival-mult: 51.0ms (19.5% of total)

ival-div: 26.0ms (9.9% of total)

ival-tanh: 11.0ms (4.2% of total)

...c/correct-round.rkt:119:19: 5.0ms (1.9% of total)

ival-add: 4.0ms (1.5% of total)

ival-sub: 3.0ms (1.1% of total)

backward-pass: 3.0ms (1.1% of total)

const: 2.0ms (0.8% of total)

ival-pi: 2.0ms (0.8% of total)

series299.0ms (1.6%)

Counts

25 → 192

Calls

Call 1

Inputs
#<alt (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)))>
#<alt (/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4)>
#<alt (/ (/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4) (PI))>
#<alt (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))>
#<alt (/ (log (/ (/ 4 (PI)) f)) (/ (PI) -4))>
#<alt (log (/ (/ 4 (PI)) f))>
#<alt (/ (/ 4 (PI)) f)>
#<alt (/ 4 (PI))>
#<alt (* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))>
#<alt (/ -4 (PI))>
#<alt (PI)>
#<alt (- (log (/ 4 f)) (log (PI)))>
#<alt (* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI))>
#<alt (/ 4 (* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI)))>
#<alt (/ 1 (log (tanh (/ f (/ 4 (PI))))))>
#<alt (log (tanh (/ f (/ 4 (PI)))))>
#<alt (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))>
#<alt (/ 2 (* (PI) 1/2))>
#<alt (* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192))))>
#<alt (* 1/16 (* (PI) 2))>
#<alt (/ f (/ 4 (PI)))>
#<alt (pow (tanh (/ f (/ 4 (PI)))) -1/2)>
#<alt (log (/ 4 f))>
#<alt (log (/ 2 (* (PI) 1/2)))>
#<alt (* (* 2 (* (PI) 2)) 1/192)>

Outputs
#<alt (* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f))))>
#<alt (+ (* -2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))))>
#<alt (+ (* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))) (* (pow f 2) (+ (* -2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* f (PI)))) (* -1/4 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))))))))>
#<alt (+ (* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))) (* (pow f 2) (+ (* -2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* f (PI)))) (* f (+ (* -1/4 (/ (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))) f)) (* 1/12 (* f (+ (* -12 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (pow f 2) (pow (PI) 2)))) (* -3 (/ (* (PI) (+ (* -32 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 3))) (+ (* -2 (/ (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (+ (* 4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* f (pow (PI) 3)))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (pow (PI) 2))))))) f))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f))))>
#<alt (+ (* -8 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))))>
#<alt (+ (* -8 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))) (* (pow f 2) (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* f (PI)))) (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))))))>
#<alt (+ (* -8 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))) (* (pow f 2) (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* f (PI)))) (* f (+ (* -1/3 (* f (+ (* -12 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (pow f 2) (pow (PI) 2)))) (* -3 (/ (* (PI) (+ (* -32 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 3))) (+ (* -2 (/ (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (+ (* 4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* f (pow (PI) 3)))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (pow (PI) 2))))))) f))))) (/ (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))) f))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))>
#<alt (* -8 (/ (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f))) (PI)))>
#<alt (+ (* -8 (/ (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f))) (PI))) (* 8 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (pow (PI) 2))))>
#<alt (+ (* -8 (/ (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f))) (PI))) (* (pow f 2) (+ (* 8 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* f (pow (PI) 2)))) (* f (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* f (pow (PI) 3)))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (* f (pow (PI) 2)))))))))>
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#<alt (+ (* f (- (* -1 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (pow (PI) 2) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (/ 1 (+ (log f) (log (* 1/4 (PI))))))>
#<alt (+ (* f (- (* f (- (* -1 (* f (+ (* -2 (/ (* (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (pow (PI) 2) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* (PI) (+ (log f) (log (* 1/4 (PI))))))) (+ (* -1 (/ (* (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/6 (/ (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI))))) (pow (+ (log f) (log (* 1/4 (PI)))) 2))))))) (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* (pow (PI) 2) (pow (+ (log f) (log (* 1/4 (PI)))) 3)))) (* 1/2 (/ (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* (PI) (pow (+ (log f) (log (* 1/4 (PI)))) 2)))))) (/ 1 (+ (log f) (log (* 1/4 (PI))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (/ 1 (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))))))>
#<alt (+ (log f) (log (* 1/4 (PI))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* 2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI)))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 1/2 (* f (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))) (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI)))))))>
#<alt (+ (log f) (+ (log (* 1/4 (PI))) (* f (+ (* 2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (PI))) (* f (+ (* 1/6 (* f (+ (* -48 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 2))) (+ (* 16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 3) (pow (PI) 3))) (* 24 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (PI))))))) (* 1/2 (+ (* -4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 2))) (* 8 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (PI)))))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (log (/ (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 1/4 (* f (PI)))>
#<alt (* 2 (sqrt (/ 1 (* f (PI)))))>
#<alt (/ (+ (* -2 (* (sqrt (/ (pow f 3) (pow (PI) 3))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))) (* 2 (sqrt (/ f (PI))))) f)>
#<alt (/ (+ (* 2 (sqrt (/ f (PI)))) (* (pow f 2) (+ (* -2 (* (sqrt (/ 1 (* f (pow (PI) 3)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))) (* -1/4 (* (sqrt (* f (PI))) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))))))) f)>
#<alt (/ (+ (* 2 (sqrt (/ f (PI)))) (* (pow f 2) (+ (* -2 (* (sqrt (/ 1 (* f (pow (PI) 3)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))) (* f (+ (* -1/4 (* (sqrt (* f (PI))) (+ (* -32 (/ (* (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3)))) (pow (PI) 3))) (+ (* -2 (/ (* (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (+ (* 4 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (* f (pow (PI) 3)))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/384 (pow (PI) 3)))))) (+ (* -1/32 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/1536 (pow (PI) 4)) (* 1/3072 (pow (PI) 4)))))) (+ (* -1/8 (* (PI) (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (* -1/128 (pow (PI) 3))))) (* 1/64 (* (pow (PI) 2) (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))))))) (pow (PI) 2)))))))) (* -1/4 (* (sqrt (/ (PI) f)) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2))))))))))) f)>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))>
#<alt (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (* -1 (log f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log 4) (log (/ 1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>
#<alt (+ (log -4) (log (/ -1 f)))>

Calls

48 calls:

Time	Variable		Point	Expression
189.0ms	f	@	0	(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))
28.0ms	f	@	inf	(+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)))
28.0ms	f	@	-inf	(+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)))
13.0ms	f	@	-inf	(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))
10.0ms	f	@	inf	(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))

rewrite150.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1158×	`-lowering-.f32`
1158×	`-lowering-.f64`
750×	`/-lowering-/.f32`
750×	`/-lowering-/.f64`
260×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	206
1	256	128
0	2037	128

Stop Event

1×	iter limit
1×	iter limit
1×	node limit

Counts

25 → 705

Calls

Call 1

Inputs
(+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)))
(/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4)
(/ (/ (+ (log (pow (tanh (/ f (/ 4 (PI)))) -1/2)) (log (pow (tanh (/ f (/ 4 (PI)))) -1/2))) -1/4) (PI))
(log (pow (tanh (/ f (/ 4 (PI)))) -1/2))
(/ (log (/ (/ 4 (PI)) f)) (/ (PI) -4))
(log (/ (/ 4 (PI)) f))
(/ (/ 4 (PI)) f)
(/ 4 (PI))
(* (/ -4 (PI)) (- (log (/ 4 f)) (log (PI))))
(/ -4 (PI))
(PI)
(- (log (/ 4 f)) (log (PI)))
(* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI))
(/ 4 (* (/ 1 (log (tanh (/ f (/ 4 (PI)))))) (PI)))
(/ 1 (log (tanh (/ f (/ 4 (PI))))))
(log (tanh (/ f (/ 4 (PI)))))
(+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192)))
(/ 2 (* (PI) 1/2))
(* (* (PI) 1/2) (+ (* 1/16 (* (PI) 2)) (* -2 (* (* 2 (* (PI) 2)) 1/192))))
(* 1/16 (* (PI) 2))
(/ f (/ 4 (PI)))
(pow (tanh (/ f (/ 4 (PI)))) -1/2)
(log (/ 4 f))
(log (/ 2 (* (PI) 1/2)))
(* (* 2 (* (PI) 2)) 1/192)

Outputs
(log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))
(log.f64 (exp.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(log.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(+.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (neg.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(-.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(-.f64 (log.f64 (expm1.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)))) (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f))))))
(-.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f))))) (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f))))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 0 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 0 binary64)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(neg.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 4 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))
(/.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal -4 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
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(.f64 #s(literal 1/96 binary64) (.f64 (PI.f64) #s(literal 2 binary64)))

simplify329.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

4744×	`-lowering-.f32`
4744×	`-lowering-.f64`
2062×	`sum4-define`
1936×	`+-lowering-+.f64`
1936×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	6525
1	1397	5360
2	6730	5320
0	8066	5320

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f))))
(+ (* -2 (/ (* f (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2)))) (PI))) (* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))))
(+ (* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f)))) (* (pow f 2) (+ (* -2 (/ (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) (* f (PI)))) (* -1/4 (* (PI) (+ (* -16 (/ (pow (+ (* -1/16 (pow (PI) 2)) (* 1/16 (pow (PI) 2))) 2) (pow (PI) 3))) (* 16 (/ (- (* 1/2 (+ (* -1/4 (* (PI) (+ (* -1/16 (pow (PI) 2)) (* 1/32 (pow (PI) 2))))) (+ (* -1/128 (pow (PI) 3)) (* 1/192 (pow (PI) 3))))) (* 1/128 (pow (PI) 3))) (pow (PI) 2)))))))))
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(sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (* -1 (log f)))
(+ (log 4) (log (/ 1 f)))
(+ (log 4) (log (/ 1 f)))
(+ (log 4) (log (/ 1 f)))
(+ (log 4) (log (/ 1 f)))
(+ (log -4) (log (/ -1 f)))
(+ (log -4) (log (/ -1 f)))
(+ (log -4) (log (/ -1 f)))
(+ (log -4) (log (/ -1 f)))

Outputs
(* 2 (+ (log (* 2 (sqrt (/ f (PI))))) (* -1 (log f))))
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(* 2 (log (sqrt (/ (+ (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI)))))) (- (exp (* 1/4 (* f (PI)))) (/ 1 (exp (* 1/4 (* f (PI))))))))))
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(sqrt.f64 (/.f64 (+.f64 (exp.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/4 binary64)))) (exp.f64 (.f64 (.f64 f (PI.f64)) #s(literal -1/4 binary64)))) (-.f64 (exp.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/4 binary64)))) (exp.f64 (.f64 (.f64 f (PI.f64)) #s(literal -1/4 binary64))))))
(+ (log 4) (* -1 (log f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log 4) (* -1 (log f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log 4) (* -1 (log f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log 4) (* -1 (log f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log 4) (log (/ 1 f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log 4) (log (/ 1 f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log 4) (log (/ 1 f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log 4) (log (/ 1 f)))
(-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 f))
(+ (log -4) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal -4 binary64)))
(+ (log -4) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal -4 binary64)))
(+ (log -4) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal -4 binary64)))
(+ (log -4) (log (/ -1 f)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) f)) (log.f64 #s(literal -4 binary64)))

eval525.0ms (2.8%)

Compiler: Compiled 33335 to 4165 computations (87.5% saved)

prune241.0ms (1.3%)

Pruning

25 alts after pruning (17 fresh and 8 done)

	Pruned	Kept	Total
New	1358	5	1363
Fresh	1	12	13
Picked	1	4	5
Done	0	4	4
Total	1360	25	1385

Accuracy

99.9%

Counts

1385 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f64 (/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
✓	99.4%	(/.f64 (/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)) (PI.f64))
	96.7%	(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (-.f64 #s(literal 0 binary64) (.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/768 binary64)) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/128 binary64))))) (.f64 (PI.f64) (PI.f64))) f))))) f)) #s(literal -1/4 binary64)) (PI.f64))
	98.3%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
✓	99.4%	(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (PI.f64))
	98.3%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
	97.5%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) #s(literal 1/4 binary64))
	99.0%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) #s(literal 1/4 binary64))
✓	99.4%	(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))
	99.2%	(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
	0.0%	(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))
	95.9%	(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.6%	(/.f64 (+.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (-.f64 (.f64 f (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -4 binary64) (.f64 (PI.f64) #s(literal 1/96 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 f #s(literal 1/2 binary64)))) (log.f64 f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
	95.5%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
✓	96.0%	(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	96.7%	(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
	18.5%	(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
✓	99.3%	(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
✓	99.2%	(/.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)))
	95.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
	95.9%	(-.f64 (/.f64 (log.f64 #s(literal 4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (*.f64 f (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))))
	95.9%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
✓	95.3%	(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
	95.8%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 f (*.f64 (PI.f64) #s(literal 1/2 binary64))))))
✓	95.8%	(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Compiler

Compiled 1555 to 591 computations (62% saved)

regimes376.0ms (2%)

Counts

53 → 1

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (-.f64 #s(literal 0 binary64) (.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/768 binary64)) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/128 binary64))))) (.f64 (PI.f64) (PI.f64))) f))))) f)) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 f (*.f64 (PI.f64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (PI.f64)))
(/.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (.f64 f (.f64 (PI.f64) #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) (log.f64 (*.f64 f #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (log.f64 f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1/4 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (PI.f64))
(.f64 (/.f64 #s(literal -4 binary64) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(-.f64 (/.f64 (log.f64 #s(literal 4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (*.f64 f (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(-.f64 (/.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (/.f64 (log.f64 f) (PI.f64)) #s(literal -1/4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal -4 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (PI.f64)) (.f64 (PI.f64) (.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64)))) (.f64 (PI.f64) (PI.f64)))
(/.f64 (-.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 f))) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 16 binary64)))
(/.f64 (+.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (-.f64 (.f64 f (.f64 (.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/8 binary64)) (.f64 #s(literal -4 binary64) (.f64 (PI.f64) #s(literal 1/96 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 f #s(literal 1/2 binary64)))) (log.f64 f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (+.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (-.f64 (.f64 f (.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))) (.f64 f #s(literal 1/2 binary64)))) (log.f64 f))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))) #s(literal 1/4 binary64))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(/.f64 (/.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -1/4 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(/.f64 (/.f64 (neg.f64 (*.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal -4 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64))) (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal -4 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(/.f64 (-.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))))
(/.f64 (-.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))) (*.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (/.f64 (PI.f64) #s(literal -4 binary64))))
(/.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))) (-.f64 (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal 4 binary64))) (exp.f64 (/.f64 (.f64 (PI.f64) f) #s(literal -4 binary64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) #s(literal 1/4 binary64))
(/.f64 (/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))) #s(literal 1/4 binary64))
(/.f64 (/.f64 (+.f64 (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))) #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (.f64 #s(literal 0 binary64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (log.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))))) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))) (+.f64 (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))) (.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (cosh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64))) (/.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))) (/.f64 (PI.f64) #s(literal -4 binary64)))))))

Outputs
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))

Calls

6 calls:

281.0ms	(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)
27.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))
25.0ms	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))
16.0ms	f
12.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))

Results

Accuracy	Segments	Branch
99.4%	1	`f`
99.4%	1	`(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))))`
99.4%	1	`(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))))`
99.4%	1	`(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f))))))`
99.4%	1	`(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)))))`
99.4%	1	`(*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) f)`

Compiler

Compiled 144 to 60 computations (58.3% saved)

regimes7.0ms (0%)

Counts

14 → 1

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (-.f64 #s(literal 0 binary64) (.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/768 binary64)) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/128 binary64))))) (.f64 (PI.f64) (PI.f64))) f))))) f)) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(/.f64 (-.f64 (log.f64 #s(literal 4 binary64)) (log.f64 (*.f64 f (PI.f64)))) (/.f64 (PI.f64) #s(literal -4 binary64)))

Outputs
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

12 → 1

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (-.f64 #s(literal 0 binary64) (.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/768 binary64)) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/128 binary64))))) (.f64 (PI.f64) (PI.f64))) f))))) f)) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))

Outputs
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

11 → 1

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (.f64 f (-.f64 #s(literal 0 binary64) (.f64 #s(literal 16 binary64) (.f64 (/.f64 (+.f64 (.f64 (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/32 binary64))) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal -1/768 binary64)) (.f64 (PI.f64) (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal -1/128 binary64))))) (.f64 (PI.f64) (PI.f64))) f))))) f)) #s(literal -1/4 binary64)) (PI.f64))
(/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64))
(.f64 (+.f64 (log.f64 f) (log.f64 (.f64 #s(literal 1/4 binary64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) f)) (log.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 (log.f64 (/.f64 #s(literal 4 binary64) (PI.f64))) (log.f64 f)))

Outputs

(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 f (*.f64 f (+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
96.7%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

5 → 1

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 f (PI.f64))))))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))

Outputs
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
96.0%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Outputs
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
95.8%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))

Outputs
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
0.0%	1	`f`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	90
1	58	90

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))

Outputs
(/.f64 (/.f64 (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64)))))))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (log.f64 (tanh.f64 (/.f64 f (/.f64 #s(literal 4 binary64) (PI.f64))))))
(/.f64 (log.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 f (.f64 f (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -2 binary64) (.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/192 binary64))))))) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (log.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) f)) (/.f64 (PI.f64) #s(literal -4 binary64)))
(.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (log.f64 (/.f64 #s(literal 4 binary64) (.f64 f (PI.f64)))))
(/.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (PI.f64))

soundness2.8s (14.8%)

Rules

4834×	`/-lowering-/.f32`
4834×	`/-lowering-/.f64`
4608×	`-lowering-.f32`
4608×	`-lowering-.f64`
4512×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	116
1	102	112
2	710	45
0	8678	45
0	16	36
1	51	32
2	131	32
3	284	32
4	481	32
5	699	32
6	936	32
7	1243	32
8	1893	32
9	2337	32
10	3078	32
11	4771	32
12	5330	32
13	5594	32
14	6132	32
15	7538	32
0	8072	32
0	192	1552
1	627	1346
2	2752	1289
0	9144	1289
0	38	149
1	247	149
2	2045	149
0	8800	149
0	44	206
1	256	128
0	2037	128
0	37	190
1	236	176
2	2037	176
0	8548	176

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 169 to 111 computations (34.3% saved)

preprocess48.0ms (0.3%)

Compiler: Compiled 258 to 122 computations (52.7% saved)

analyze326.0ms (1.7%)

sample6.6s (35.1%)

preprocess312.0ms (1.7%)

explain431.0ms (2.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify64.0ms (0.3%)

localize174.0ms (0.9%)

series99.0ms (0.5%)

rewrite347.0ms (1.8%)

simplify251.0ms (1.3%)

eval132.0ms (0.7%)

prune109.0ms (0.6%)

simplify264.0ms (1.4%)

localize290.0ms (1.5%)

series453.0ms (2.4%)

rewrite516.0ms (2.7%)

simplify335.0ms (1.8%)

eval457.0ms (2.4%)

prune239.0ms (1.3%)

simplify201.0ms (1.1%)

localize331.0ms (1.8%)

series83.0ms (0.4%)

rewrite461.0ms (2.4%)

simplify230.0ms (1.2%)

eval386.0ms (2%)

prune256.0ms (1.4%)

simplify234.0ms (1.2%)

localize472.0ms (2.5%)

series299.0ms (1.6%)

rewrite150.0ms (0.8%)

simplify329.0ms (1.7%)

eval525.0ms (2.8%)

prune241.0ms (1.3%)

regimes376.0ms (2%)

regimes7.0ms (0%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

simplify13.0ms (0.1%)

soundness2.8s (14.8%)

preprocess48.0ms (0.3%)

end0.0ms (0%)

Profiling