Metrics for Hyperbolic arcsine

analyze122.0ms (1.6%)

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
25%	25%	75%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
62.5%	62.5%	37.5%	0%	0%	0%	0%	5
68.8%	68.7%	31.2%	0%	0%	0%	0%	6
71.9%	71.8%	28.1%	0%	0%	0%	0%	7
73.4%	73.4%	26.5%	0%	0%	0%	0%	8
74.2%	74.2%	25.8%	0%	0%	0%	0%	9
74.6%	74.6%	25.4%	0%	0%	0%	0%	10
74.8%	74.8%	25.2%	0%	0%	0%	0%	11
74.9%	74.9%	25.1%	0%	0%	0%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-add: 35.0ms (54.9% of total)

ival-log: 10.0ms (15.7% of total)

ival-mult: 8.0ms (12.5% of total)

ival-sqrt: 8.0ms (12.5% of total)

const: 1.0ms (1.6% of total)

backward-pass: 0.0ms (0% of total)

sample2.6s (33.7%)

Results

1.2s	2750×	2	valid
801.0ms	3311×	1	valid
207.0ms	2195×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-log: 778.0ms (47.8% of total)

ival-mult: 246.0ms (15.1% of total)

ival-add: 214.0ms (13.2% of total)

ival-sqrt: 187.0ms (11.5% of total)

backward-pass: 182.0ms (11.2% of total)

const: 18.0ms (1.1% of total)

Bogosity

preprocess24.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

216×	`fnmadd-define`
196×	`fmsub-define`
192×	`fnmsub-define`
148×	`sum3-define`
128×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	34	19
2	62	19
3	109	19
4	249	19
5	451	19
6	652	19
7	795	19
8	826	19
0	7	8
1	13	6
2	14	6
3	15	6
0	15	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(log (+ x (sqrt (+ (* x x) 1))))

Outputs
(log (+ x (sqrt (+ (* x x) 1))))
(log.f64 (+.f64 x (hypot.f64 #s(literal 1 binary64) x)))

Call 2

Inputs
(log (+ x (sqrt (+ (* x x) 1))))
(log (+ (neg x) (sqrt (+ (* (neg x) (neg x)) 1))))
(neg (log (+ (neg x) (sqrt (+ (* (neg x) (neg x)) 1)))))

Outputs
(log (+ x (sqrt (+ (* x x) 1))))
(log (+ x (hypot 1 x)))
(log (+ (neg x) (sqrt (+ (* (neg x) (neg x)) 1))))
(log (- (hypot 1 x) x))
(neg (log (+ (neg x) (sqrt (+ (* (neg x) (neg x)) 1)))))
(neg (log (- (hypot 1 x) x)))

explain215.0ms (2.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
106	-	-	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
80	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
73	-	-	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
0	-	-	`x`
0	-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`#s(literal 1 binary64)`

Results

99.0ms	146×	2	valid
56.0ms	208×	1	valid
16.0ms	158×	0	valid

Compiler

Compiled 80 to 23 computations (71.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-log: 37.0ms (45.1% of total)

backward-pass: 12.0ms (14.6% of total)

ival-mult: 11.0ms (13.4% of total)

ival-add: 11.0ms (13.4% of total)

ival-sqrt: 9.0ms (11% of total)

const: 1.0ms (1.2% of total)

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	34.9%	(log.f64 (+.f64 x (hypot.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(hypot.f64 #s(literal 1 binary64) x)
✓	cost-diff	(+.f64 x (hypot.f64 #s(literal 1 binary64) x))
✓	cost-diff	(log.f64 (+.f64 x (hypot.f64 #s(literal 1 binary64) x)))

Rules

8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
4×	`+-commutative`
2×	`hypot-1-def`
2×	`sqrt-lowering-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	14	16
2	15	16
0	15	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(log (+ x (sqrt (+ (* 1 1) (* x x)))))
(+ x (sqrt (+ (* 1 1) (* x x))))
x
(sqrt (+ (* 1 1) (* x x)))
1

Outputs
(log (+ x (sqrt (+ (* 1 1) (* x x)))))
(log.f64 (+.f64 x (hypot.f64 #s(literal 1 binary64) x)))
(+ x (sqrt (+ (* 1 1) (* x x))))
(+.f64 x (hypot.f64 #s(literal 1 binary64) x))
x
(sqrt (+ (* 1 1) (* x x)))
(hypot.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)

localize153.0ms (2%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(hypot.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(+.f64 x (hypot.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(log.f64 (+.f64 x (hypot.f64 #s(literal 1 binary64) x)))

Results

127.0ms	179×	5	exit
8.0ms	77×	0	valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-log: 29.0ms (30.9% of total)

backward-pass: 22.0ms (23.5% of total)

compiled-spec: 20.0ms (21.3% of total)

ival-add: 11.0ms (11.7% of total)

ival-mult: 7.0ms (7.5% of total)

ival-sqrt: 3.0ms (3.2% of total)

const: 1.0ms (1.1% of total)

series4.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (log (+ x (sqrt (+ (* 1 1) (* x x)))))>
#<alt (+ x (sqrt (+ (* 1 1) (* x x))))>
#<alt (sqrt (+ (* 1 1) (* x x)))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))>
#<alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))>
#<alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))>

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log (+ x (sqrt (+ (* 1 1) (* x x)))))
1.0ms	x	@	-inf	(log (+ x (sqrt (+ (* 1 1) (* x x)))))
1.0ms	x	@	inf	(log (+ x (sqrt (+ (* 1 1) (* x x)))))
0.0ms	x	@	-inf	(+ x (sqrt (+ (* 1 1) (* x x))))
0.0ms	x	@	inf	(+ x (sqrt (+ (* 1 1) (* x x))))

rewrite29.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

12×	`pow-to-exp`
12×	`exp-lowering-exp.f32`
12×	`exp-prod`
12×	`exp-lowering-exp.f64`
10×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	18	14
2	25	14
3	33	14
4	49	14
5	58	14
6	65	14
0	65	14

Stop Event

1×	iter limit
1×	saturated

Counts

3 → 8

Calls

Call 1

Inputs
(log (+ x (sqrt (+ (* 1 1) (* x x)))))
(+ x (sqrt (+ (* 1 1) (* x x))))
(sqrt (+ (* 1 1) (* x x)))

Outputs
(log.f64 (+.f64 x (hypot.f64 #s(literal 1 binary64) x)))
(+.f64 x (hypot.f64 #s(literal 1 binary64) x))
(+.f64 (hypot.f64 #s(literal 1 binary64) x) x)
(exp.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 (.f64 x x))))
(hypot.f64 #s(literal 1 binary64) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (*.f64 x x)))

simplify241.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

3490×	`+-lowering-+.f64`
3490×	`+-lowering-+.f32`
2464×	`-lowering-.f32`
2464×	`-lowering-.f64`
1576×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	434
1	355	365
2	1103	351
3	3794	340
0	8358	340

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(+ (log 1/2) (log (/ -1 x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal 3/40 binary64)))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 3/40 binary64) (.f64 (*.f64 x x) #s(literal -5/112 binary64))))))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal -3/32 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (+.f64 (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal -3/32 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))))))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (.f64 x x))))))))

eval5.0ms (0.1%)

Compiler: Compiled 564 to 183 computations (67.6% saved)

prune10.0ms (0.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	37	7	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	7	45

Accuracy

100.0%

Counts

45 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
	28.6%	(log.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x))
	29.3%	(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
▶	28.6%	(log.f64 (/.f64 #s(literal -1/2 binary64) x))
▶	2.3%	(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
▶	30.5%	(log.f64 (+.f64 x x))
▶	44.5%	x

Compiler

Compiled 126 to 84 computations (33.3% saved)

simplify151.0ms (2%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
✓	cost-diff	0	(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
✓	cost-diff	256	(+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x))
✓	cost-diff	256	(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
✓	cost-diff	0	(log.f64 (/.f64 #s(literal -1/2 binary64) x))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(log.f64 (+.f64 x x))
✓	cost-diff	0	(*.f64 x #s(literal -1/6 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/6 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))

Rules

2068×	`fnmsub-define`
1332×	`div-sub`
1230×	`+-lowering-+.f64`
1230×	`+-lowering-+.f32`
1136×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	36	57
2	64	56
3	150	56
4	205	56
5	634	56
6	2133	56
7	4932	56
8	7866	56
0	8133	56

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
x
(* x (+ 1 (* x (* x -1/6))))
x
(+ 1 (* x (* x -1/6)))
1
(* x (* x -1/6))
(* x -1/6)
-1/6
(log (+ x x))
(+ x x)
x
(log (/ -1/2 x))
(/ -1/2 x)
-1/2
x
(log (+ x (- (/ -1/2 x) x)))
(+ x (- (/ -1/2 x) x))
x
(- (/ -1/2 x) x)
(/ -1/2 x)
-1/2

Outputs
x
(* x (+ 1 (* x (* x -1/6))))
(.f64 x (-.f64 (.f64 x (*.f64 x #s(literal -1/6 binary64))) #s(literal -1 binary64)))
x
(+ 1 (* x (* x -1/6)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
1
#s(literal 1 binary64)
(* x (* x -1/6))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* x -1/6)
(*.f64 x #s(literal -1/6 binary64))
-1/6
#s(literal -1/6 binary64)
(log (+ x x))
(log.f64 (*.f64 x #s(literal 2 binary64)))
(+ x x)
(*.f64 x #s(literal 2 binary64))
x
(log (/ -1/2 x))
(log.f64 (/.f64 #s(literal -1/2 binary64) x))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
x
(log (+ x (- (/ -1/2 x) x)))
(log.f64 (/.f64 #s(literal -1/2 binary64) x))
(+ x (- (/ -1/2 x) x))
(/.f64 #s(literal -1/2 binary64) x)
x
(- (/ -1/2 x) x)
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)

localize130.0ms (1.7%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
✓	accuracy	100.0%	(+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x))
✓	accuracy	100.0%	(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(log.f64 (/.f64 #s(literal -1/2 binary64) x))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(log.f64 (+.f64 x x))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/6 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/6 binary64))

Results

110.0ms

256×

invalid

Compiler

Compiled 72 to 16 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-log: 37.0ms (65% of total)

ival-mult: 7.0ms (12.3% of total)

ival-add: 4.0ms (7% of total)

...c/correct-round.rkt:119:19: 4.0ms (7% of total)

ival-div: 2.0ms (3.5% of total)

ival-sub: 1.0ms (1.8% of total)

const: 1.0ms (1.8% of total)

backward-pass: 0.0ms (0% of total)

series121.0ms (1.6%)

Counts

11 → 132

Calls

Call 1

Inputs
#<alt (* x (+ 1 (* x (* x -1/6))))>
#<alt (+ 1 (* x (* x -1/6)))>
#<alt (* x (* x -1/6))>
#<alt (* x -1/6)>
#<alt (log (+ x x))>
#<alt (+ x x)>
#<alt (log (/ -1/2 x))>
#<alt (/ -1/2 x)>
#<alt (log (+ x (- (/ -1/2 x) x)))>
#<alt (+ x (- (/ -1/2 x) x))>
#<alt (- (/ -1/2 x) x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ (- (* -1 (pow x 2)) 1/2) x)>
#<alt (/ (- (* -1 (pow x 2)) 1/2) x)>
#<alt (/ (- (* -1 (pow x 2)) 1/2) x)>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>

Calls

33 calls:

Time	Variable		Point	Expression
30.0ms	x	@	-inf	(log (/ -1/2 x))
28.0ms	x	@	0	(log (+ x x))
22.0ms	x	@	-inf	(log (+ x x))
12.0ms	x	@	0	(log (/ -1/2 x))
9.0ms	x	@	inf	(log (/ -1/2 x))

rewrite239.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1394×	`-lowering-.f32`
1394×	`-lowering-.f64`
1208×	`/-lowering-/.f32`
1208×	`/-lowering-/.f64`
1102×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	46	45
2	118	44
3	391	44
4	1251	44
5	7052	44
0	8072	44

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 777

Calls

Call 1

Inputs
(* x (+ 1 (* x (* x -1/6))))
(+ 1 (* x (* x -1/6)))
(* x (* x -1/6))
(* x -1/6)
(log (+ x x))
(+ x x)
(log (/ -1/2 x))
(/ -1/2 x)
(log (+ x (- (/ -1/2 x) x)))
(+ x (- (/ -1/2 x) x))
(- (/ -1/2 x) x)

Outputs
(+.f64 x (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))) #s(literal 0 binary64))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))) #s(literal -1 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))) #s(literal -1 binary64))))
(+.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(+.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) x)
(+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) #s(literal 0 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(+.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) #s(literal -1 binary64)) #s(literal 0 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(+.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) #s(literal -1 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(+.f64 (-.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) #s(literal 0 binary64)) x)
(-.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(-.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(-.f64 (-.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) x)
(fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)
(fma.f64 (.f64 x #s(literal -1/6 binary64)) (.f64 x x) x)
(fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) x x)
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(fma.f64 (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))) #s(literal 1 binary64) x)
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/6 binary64)) x)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))) x)
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/6 binary64) x)
(fma.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) x) x)
(neg.f64 (.f64 x (-.f64 #s(literal -1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))) #s(literal 1 binary64))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 x (-.f64 #s(literal -1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64))) x) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))) #s(literal -1 binary64))
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(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x x))) x)
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x)))) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64)))) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) x))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal -2 binary64) x))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -2 binary64))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 (.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) x)
(/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) x))
(/.f64 (*.f64 (+.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) #s(literal -2 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(literal 0 binary64) x)) #s(literal 2 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal -2 binary64)) x)
(/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64))) x) #s(literal 2 binary64))
(/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (/.f64 x #s(literal 1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x)) #s(literal -2 binary64))
(/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 2 binary64)) x)
(/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal -1 binary64)) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(/.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x)
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal 1/2 binary64))) (/.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (+.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) (/.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 x (-.f64 #s(literal -1/2 binary64) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) x) x))
(*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) x) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -1 binary64) (+.f64 x (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/2 binary64) x))
(.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64)) x)
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64))
(*.f64 (+.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) x) x) x) x)
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) #s(literal -1/2 binary64))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) x) #s(literal 1/2 binary64))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x)) #s(literal -1/2 binary64))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(*.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal -1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(literal -1/2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x)))

simplify165.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

2848×	`-lowering-.f32`
2848×	`-lowering-.f64`
948×	`fmsub-define`
848×	`fmm-def`
800×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	673
1	116	585
2	279	576
3	818	567
4	3351	567
5	7720	567
0	8009	567

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ -1 x)))
(+ (log 1/2) (log (/ -1 x)))
(+ (log 1/2) (log (/ -1 x)))
(+ (log 1/2) (log (/ -1 x)))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log -1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ -1 x)))
(+ (log 1/2) (log (/ -1 x)))
(+ (log 1/2) (log (/ -1 x)))
(+ (log 1/2) (log (/ -1 x)))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ (- (* -1 (pow x 2)) 1/2) x)
(/ (- (* -1 (pow x 2)) 1/2) x)
(/ (- (* -1 (pow x 2)) 1/2) x)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* -1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* -1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(+ 1 (* -1/6 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(+ 1 (* -1/6 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* -1 (pow x 2)) 1/2) x)
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(/ (- (* -1 (pow x 2)) 1/2) x)
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(/ (- (* -1 (pow x 2)) 1/2) x)
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)

eval122.0ms (1.6%)

Compiler: Compiled 11623 to 2009 computations (82.7% saved)

prune95.0ms (1.2%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	1056	0	1056
Fresh	0	2	2
Picked	0	5	5
Done	0	0	0
Total	1056	7	1063

Accuracy

100.0%

Counts

1063 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
▶	28.6%	(log.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x))
▶	29.3%	(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
✓	28.6%	(log.f64 (/.f64 #s(literal -1/2 binary64) x))
✓	2.3%	(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
✓	30.5%	(log.f64 (+.f64 x x))
✓	44.5%	x

Compiler

Compiled 63 to 42 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
✓	cost-diff	(+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
✓	cost-diff	(/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
✓	cost-diff	(log.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x))
✓	cost-diff	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
✓	cost-diff	(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
✓	cost-diff	(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))

Rules

30×	`/-lowering-/.f32`
30×	`/-lowering-/.f64`
24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
18×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	110
1	29	97
2	52	97
3	59	97
4	60	97
0	60	97

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(log (/ (+ -1/2 (/ 1/8 (* x x))) x))
(/ (+ -1/2 (/ 1/8 (* x x))) x)
(+ -1/2 (/ 1/8 (* x x)))
-1/2
(/ 1/8 (* x x))
1/8
(* x x)
x
(log (/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x))
(/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x)
(+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x))))
(/ -1/16 (* x (* x (* x x))))
-1/16
(* x (* x (* x x)))
x
(* x (* x x))
(* x x)
(+ -1/2 (/ 1/8 (* x x)))
-1/2
(/ 1/8 (* x x))
1/8

Outputs
(log (/ (+ -1/2 (/ 1/8 (* x x))) x))
(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(/ (+ -1/2 (/ 1/8 (* x x))) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(+ -1/2 (/ 1/8 (* x x)))
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
-1/2
#s(literal -1/2 binary64)
(/ 1/8 (* x x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
x
(log (/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x))
(log.f64 (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x (*.f64 x x)))) x))
(/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x)
(/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x (*.f64 x x)))) x)
(+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x))))
(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x (*.f64 x x))))
(/ -1/16 (* x (* x (* x x))))
(/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x (.f64 x x)))
-1/16
#s(literal -1/16 binary64)
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
x
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(+ -1/2 (/ 1/8 (* x x)))
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
-1/2
#s(literal -1/2 binary64)
(/ 1/8 (* x x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
1/8
#s(literal 1/8 binary64)

localize135.0ms (1.8%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 x (.f64 x x))
✓	accuracy	100.0%	(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
✓	accuracy	100.0%	(.f64 x (.f64 x (*.f64 x x)))
✓	accuracy	99.7%	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
✓	accuracy	99.7%	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))

Results

75.0ms	183×	0	invalid
29.0ms	73×	0	valid

Compiler

Compiled 135 to 16 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-div: 30.0ms (63.7% of total)

ival-log: 8.0ms (17% of total)

ival-mult: 6.0ms (12.7% of total)

ival-add: 3.0ms (6.4% of total)

const: 1.0ms (2.1% of total)

backward-pass: 0.0ms (0% of total)

series22.0ms (0.3%)

Counts

11 → 132

Calls

Call 1

Inputs
#<alt (log (/ (+ -1/2 (/ 1/8 (* x x))) x))>
#<alt (/ (+ -1/2 (/ 1/8 (* x x))) x)>
#<alt (+ -1/2 (/ 1/8 (* x x)))>
#<alt (/ 1/8 (* x x))>
#<alt (log (/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x))>
#<alt (/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x)>
#<alt (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x))))>
#<alt (/ -1/16 (* x (* x (* x x))))>
#<alt (* x x)>
#<alt (* x (* x (* x x)))>
#<alt (* x (* x x))>

Outputs
#<alt (+ (log 1/8) (* -3 (log x)))>
#<alt (+ (log 1/8) (+ (* -4 (pow x 2)) (* -3 (log x))))>
#<alt (+ (log 1/8) (+ (* -3 (log x)) (* (pow x 2) (- (* -8 (pow x 2)) 4))))>
#<alt (+ (log 1/8) (+ (* -3 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -64/3 (pow x 2)) 8)) 4))))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log -1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log -1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (+ (log (/ -1 x)) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log 1/2) (+ (log (/ -1 x)) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (/ 1/8 (pow x 3))>
#<alt (/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))>
#<alt -1/2>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt -1/2>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (+ (log -1/16) (* -5 (log x)))>
#<alt (+ (log -1/16) (+ (* -5 (log x)) (* -2 (pow x 2))))>
#<alt (+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* 6 (pow x 2)) 2))))>
#<alt (+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* (pow x 2) (+ 6 (* 40/3 (pow x 2)))) 2))))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log -1/2) (+ (log (/ 1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log -1/2) (+ (log (/ 1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log 1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (/ -1/16 (pow x 5))>
#<alt (/ (- (* 1/8 (pow x 2)) 1/16) (pow x 5))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))>
#<alt -1/2>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt -1/2>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ -1/16 (pow x 4))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

33 calls:

Time	Variable		Point	Expression
14.0ms	x	@	0	(/ 1/8 (* x x))
1.0ms	x	@	0	(log (/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x))
1.0ms	x	@	0	(log (/ (+ -1/2 (/ 1/8 (* x x))) x))
1.0ms	x	@	inf	(log (/ (+ -1/2 (/ 1/8 (* x x))) x))
0.0ms	x	@	0	(/ -1/16 (* x (* x (* x x))))

rewrite203.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2540×	`/-lowering-/.f32`
2540×	`/-lowering-/.f64`
2448×	`-lowering-.f32`
2448×	`-lowering-.f64`
806×	`neg-lowering-neg.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	91
1	65	78
2	284	78
3	2393	78
0	8577	78

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 477

Calls

Call 1

Inputs
(log (/ (+ -1/2 (/ 1/8 (* x x))) x))
(/ (+ -1/2 (/ 1/8 (* x x))) x)
(+ -1/2 (/ 1/8 (* x x)))
(/ 1/8 (* x x))
(log (/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x))
(/ (+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x)))) x)
(+ (/ -1/16 (* x (* x (* x x)))) (+ -1/2 (/ 1/8 (* x x))))
(/ -1/16 (* x (* x (* x x))))
(* x x)
(* x (* x (* x x)))
(* x (* x x))

Outputs
(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) #s(literal 0 binary64))
(+.f64 (log.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (log.f64 x)))
(+.f64 (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (log.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(+.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (/.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(-.f64 (log.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (log.f64 x))
(-.f64 (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) (log.f64 (-.f64 #s(literal 0 binary64) x)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))))
(-.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (log.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))))
(neg.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x)) #s(literal -1 binary64)))
(.f64 (log.f64 (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (log.f64 (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))
(+.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal 1/8 binary64) x))))
(+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal 1/8 binary64) x))) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))
(+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) (/.f64 #s(literal -1/2 binary64) x))
(exp.f64 (log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x))
(-.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal 1/8 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(neg.f64 (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))) (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))) (.f64 x x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(pow.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal 1 binary64))
(pow.f64 (/.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x))
(.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) #s(literal -1 binary64))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))) #s(literal -1 binary64)))
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(-.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1/8 binary64) #s(literal -1/2 binary64))
(neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(pow.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 #s(literal 1/8 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(neg.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(neg.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/8 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal 1/8 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 8 binary64))
(/.f64 (/.f64 #s(literal 1/8 binary64) x) x)
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(literal -1/8 binary64) x)))
(/.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x #s(literal -1/8 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -8 binary64))
(/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal 1/8 binary64) x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 x (/.f64 #s(literal 1/8 binary64) x)))) #s(literal -1 binary64))
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(neg.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (.f64 x (.f64 x x))))
(neg.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (.f64 x (.f64 x x))) #s(literal 1 binary64)))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (/.f64 #s(literal -1/16 binary64) (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal -1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 x (/.f64 #s(literal -1/16 binary64) x)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) #s(literal -16 binary64))
(/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x (.f64 x x)))
(/.f64 #s(literal -1 binary64) (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1/16 binary64) x)))
(/.f64 (/.f64 #s(literal 1/16 binary64) x) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(/.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x (/.f64 (.f64 x x) #s(literal 1/16 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (.f64 x x) #s(literal 1/16 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x (.f64 x x))) #s(literal 16 binary64))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) (/.f64 x #s(literal -1/16 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (.f64 x (.f64 x x))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) x) (*.f64 x x)) x)
(/.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (/.f64 x #s(literal 1/16 binary64)))
(/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64))
(pow.f64 (/.f64 (.f64 x x) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (.f64 x x) (/.f64 #s(literal -1/16 binary64) (.f64 x x))))) #s(literal -1 binary64))
(.f64 #s(literal -1/16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)))
(.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))
(.f64 #s(literal 1/16 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x (*.f64 x x))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal -1/16 binary64) x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x #s(literal -1/16 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) #s(literal -16 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x x)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal -1/16 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -16 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)) #s(literal -1/16 binary64))
(.f64 (/.f64 #s(literal -1/16 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal -1/16 binary64) x) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1/16 binary64) x) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (.f64 x (/.f64 (*.f64 x x) #s(literal 1/16 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x (/.f64 #s(literal -1/16 binary64) x))))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 x #s(literal -1/16 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (pow.f64 (/.f64 (*.f64 x x) #s(literal 1/16 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x #s(literal -1/16 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -16 binary64)))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x (*.f64 x x))) #s(literal 1/16 binary64))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal -1/16 binary64) x))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -16 binary64)))
(.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) x) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/16 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -16 binary64)))
(.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 (.f64 x (/.f64 (*.f64 x x) #s(literal 1/16 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1/16 binary64) x))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) #s(literal -1 binary64)) (/.f64 #s(literal 1/16 binary64) x))
(.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal -1/16 binary64) (*.f64 x x)))
(.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) #s(literal 1 binary64)) (/.f64 #s(literal -1/16 binary64) x))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(exp.f64 (neg.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 x) #s(literal -2 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(neg.f64 (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(*.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (neg.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal -1 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(exp.f64 (-.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(exp.f64 (-.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) (.f64 (log.f64 x) #s(literal -2 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x)))))
(neg.f64 (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))
(neg.f64 (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1 binary64) x)))
(neg.f64 (/.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(/.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(/.f64 (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x (.f64 x x))))
(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(pow.f64 x #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x x)) #s(literal -1 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 x (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(.f64 (.f64 x x) (*.f64 x x))
(.f64 (.f64 x (*.f64 x x)) x)
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (/.f64 #s(literal -1 binary64) (.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(.f64 (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 4 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x)))))
(.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(.f64 (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64)) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (/.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) x)))
(/.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) x)))

simplify240.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2364×	`+-lowering-+.f64`
2364×	`+-lowering-+.f32`
2068×	`sum3-define`
1824×	`sum4-define`
1754×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1023
1	367	892
2	1071	874
3	2981	874
4	7807	874
0	8307	874

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
(+ (log 1/8) (* -3 (log x)))
(+ (log 1/8) (+ (* -4 (pow x 2)) (* -3 (log x))))
(+ (log 1/8) (+ (* -3 (log x)) (* (pow x 2) (- (* -8 (pow x 2)) 4))))
(+ (log 1/8) (+ (* -3 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -64/3 (pow x 2)) 8)) 4))))
(+ (log -1/2) (log (/ 1 x)))
(- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))
(+ (log -1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log -1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 1/2) (log (/ -1 x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 1/2) (+ (log (/ -1 x)) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(/ 1/8 (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ -1/2 x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/ 1/8 (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(+ (log -1/16) (* -5 (log x)))
(+ (log -1/16) (+ (* -5 (log x)) (* -2 (pow x 2))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* 6 (pow x 2)) 2))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* (pow x 2) (+ 6 (* 40/3 (pow x 2)))) 2))))
(+ (log -1/2) (log (/ 1 x)))
(- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log -1/2) (+ (log (/ 1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log -1/2) (+ (log (/ 1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 1/2) (log (/ -1 x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(/ -1/16 (pow x 5))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 5))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/ -1/2 x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/ -1/16 (pow x 4))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(/ -1/16 (pow x 4))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
(+ (log 1/8) (* -3 (log x)))
(+.f64 (log.f64 #s(literal 1/8 binary64)) (*.f64 #s(literal -3 binary64) (log.f64 x)))
(+ (log 1/8) (+ (* -4 (pow x 2)) (* -3 (log x))))
(+.f64 (+.f64 (log.f64 #s(literal 1/8 binary64)) (.f64 #s(literal -3 binary64) (log.f64 x))) (.f64 #s(literal -4 binary64) (*.f64 x x)))
(+ (log 1/8) (+ (* -3 (log x)) (* (pow x 2) (- (* -8 (pow x 2)) 4))))
(+.f64 (+.f64 (log.f64 #s(literal 1/8 binary64)) (.f64 #s(literal -3 binary64) (log.f64 x))) (.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (.f64 (*.f64 x x) #s(literal -8 binary64))))))
(+ (log 1/8) (+ (* -3 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -64/3 (pow x 2)) 8)) 4))))
(+.f64 (+.f64 (log.f64 #s(literal 1/8 binary64)) (.f64 #s(literal -3 binary64) (log.f64 x))) (.f64 (.f64 x x) (+.f64 #s(literal -4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -8 binary64) (.f64 (*.f64 x x) #s(literal -64/3 binary64)))))))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) (log.f64 x)))
(+ (log -1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x)) (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 x x))) (.f64 x x)))
(- (+ (log -1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal -1/32 binary64) (/.f64 #s(literal -1/192 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) (log.f64 x))))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(+ (log 1/2) (+ (log (/ -1 x)) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 x x))) (.f64 x x)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (+.f64 (/.f64 (+.f64 #s(literal -1/32 binary64) (/.f64 #s(literal -1/192 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (.f64 x x)))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (.f64 x x)))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (.f64 x (.f64 x x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(+ (log -1/16) (* -5 (log x)))
(+.f64 (log.f64 #s(literal -1/16 binary64)) (*.f64 (log.f64 x) #s(literal -5 binary64)))
(+ (log -1/16) (+ (* -5 (log x)) (* -2 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/16 binary64)) (+.f64 (.f64 (log.f64 x) #s(literal -5 binary64)) (.f64 x (*.f64 x #s(literal -2 binary64)))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* 6 (pow x 2)) 2))))
(+.f64 (log.f64 #s(literal -1/16 binary64)) (+.f64 (.f64 (log.f64 x) #s(literal -5 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -2 binary64) (.f64 x (*.f64 x #s(literal 6 binary64)))))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* (pow x 2) (+ 6 (* 40/3 (pow x 2)))) 2))))
(+.f64 (.f64 (log.f64 x) #s(literal -5 binary64)) (+.f64 (log.f64 #s(literal -1/16 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 6 binary64) (.f64 (*.f64 x x) #s(literal 40/3 binary64))))))))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) (log.f64 x)))
(- (+ (log -1/2) (+ (log (/ 1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (log.f64 x))))
(- (+ (log -1/2) (+ (log (/ 1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (+.f64 (log.f64 #s(literal -1/2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (log.f64 x))) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 5/192 binary64) (pow.f64 x #s(literal 6 binary64)))))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 5/192 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/ -1/16 (pow x 5))
(/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 5 binary64)))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 5))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (pow.f64 x #s(literal 5 binary64)))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (pow.f64 x #s(literal 5 binary64)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (.f64 x (.f64 x (*.f64 x x))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x))))))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x))))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x))))))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x))))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

eval107.0ms (1.4%)

Compiler: Compiled 14827 to 2341 computations (84.2% saved)

prune175.0ms (2.3%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	781	1	782
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	782	7	789

Accuracy

100.0%

Counts

789 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
▶	28.8%	(log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))
✓	29.3%	(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
✓	28.6%	(log.f64 (/.f64 #s(literal -1/2 binary64) x))
✓	2.3%	(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
✓	30.5%	(log.f64 (+.f64 x x))
✓	44.5%	x

Compiler

Compiled 59 to 40 computations (32.2% saved)

simplify207.0ms (2.7%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x))
✓	cost-diff	(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))
✓	cost-diff	(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x)
✓	cost-diff	(log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))

Rules

3390×	`sum3-define`
2500×	`fma-lowering-fma.f32`
2500×	`fma-lowering-fma.f64`
2478×	`fmm-def`
1976×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	63
1	23	63
2	39	63
3	76	63
4	128	63
5	225	63
6	457	63
7	885	63
8	1798	63
9	4440	63
10	6534	63
11	7475	63
12	7741	63
13	7794	63
14	7824	63
0	8813	63

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(log (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x))
(/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x)
(+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2)
(/ (- (/ -1/16 (* x x)) -1/8) (* x x))
(- (/ -1/16 (* x x)) -1/8)
(/ -1/16 (* x x))
-1/16
(* x x)
x
-1/8
-1/2

Outputs
(log (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x))
(log.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))
(/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x)
(+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2)
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))
(/ (- (/ -1/16 (* x x)) -1/8) (* x x))
(/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x))
(- (/ -1/16 (* x x)) -1/8)
(+.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64))
(/ -1/16 (* x x))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
-1/16
#s(literal -1/16 binary64)
(* x x)
(*.f64 x x)
x
-1/8
#s(literal -1/8 binary64)
-1/2
#s(literal -1/2 binary64)

localize110.0ms (1.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x)
✓	accuracy	99.7%	(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x))
✓	accuracy	99.7%	(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
✓	accuracy	82.2%	(log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))

Results

42.0ms	130×	0	valid
16.0ms	126×	0	invalid

Compiler

Compiled 76 to 12 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 6.0ms (43.7% of total)

ival-sub: 2.0ms (14.6% of total)

ival-log: 2.0ms (14.6% of total)

ival-mult: 2.0ms (14.6% of total)

ival-add: 1.0ms (7.3% of total)

const: 1.0ms (7.3% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0%)

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (log (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x))>
#<alt (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x)>
#<alt (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2)>
#<alt (/ (- (/ -1/16 (* x x)) -1/8) (* x x))>
#<alt (/ -1/16 (* x x))>

Outputs
#<alt (+ (log -1/16) (* -5 (log x)))>
#<alt (+ (log -1/16) (+ (* -5 (log x)) (* -2 (pow x 2))))>
#<alt (+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* 6 (pow x 2)) 2))))>
#<alt (+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* (pow x 2) (+ 6 (* 40/3 (pow x 2)))) 2))))>
#<alt (+ (log -1/2) (log (/ 1 x)))>
#<alt (- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log -1/2) (+ (log (/ 1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log -1/2) (+ (log (/ 1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (log (/ -1 x)))>
#<alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ (log 1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (/ -1/16 (pow x 5))>
#<alt (/ (- (* 1/8 (pow x 2)) 1/16) (pow x 5))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)>
#<alt (/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))>
#<alt (/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))>
#<alt -1/2>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt -1/2>
#<alt (- (* 1/8 (/ 1 (pow x 2))) 1/2)>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))>
#<alt (/ -1/16 (pow x 4))>
#<alt (/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))>
#<alt (/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))>
#<alt (/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ 1/8 (pow x 2))>
#<alt (/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ -1/16 (pow x 2))>

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(log (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x))
0.0ms	x	@	0	(/ (- (/ -1/16 (* x x)) -1/8) (* x x))
0.0ms	x	@	inf	(log (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x))
0.0ms	x	@	-inf	(log (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x))
0.0ms	x	@	0	(/ -1/16 (* x x))

rewrite313.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2750×	`-lowering-.f32`
2750×	`-lowering-.f64`
2668×	`/-lowering-/.f32`
2668×	`/-lowering-/.f64`
1136×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	49	51
2	224	51
3	1412	51
0	9205	51

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 672

Calls

Call 1

Inputs
(log (/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x))
(/ (+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2) x)
(+ (/ (- (/ -1/16 (* x x)) -1/8) (* x x)) -1/2)
(/ (- (/ -1/16 (* x x)) -1/8) (* x x))
(/ -1/16 (* x x))

Outputs
(log.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))
(+.f64 (log.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x)) #s(literal 0 binary64))
(+.f64 (log.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 x)))
(+.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x)))) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x)))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))) x)))
(+.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x)))))))
(+.f64 (log.f64 #s(literal -1 binary64)) (+.f64 (log.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (log.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))) (log.f64 (-.f64 #s(literal 0 binary64) x))))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (log.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (.f64 (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (*.f64 x x))))) #s(literal -1 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x)))))))
(+.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (*.f64 x x)))))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x)))))
(+.f64 (+.f64 #s(literal 0 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))))) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(-.f64 (log.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))) (log.f64 x))
(-.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x)))) (log.f64 (-.f64 #s(literal 0 binary64) x)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))))))
(-.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))))))
(-.f64 (+.f64 #s(literal 0 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))))) (log.f64 (-.f64 #s(literal 0 binary64) x)))
(-.f64 (+.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64))) (log.f64 (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))))))
(-.f64 (-.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x)))) (log.f64 #s(literal -1 binary64))) (log.f64 x))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (log.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64))))
(neg.f64 (log.f64 (/.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)))))
(neg.f64 (.f64 (log.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)) x)) #s(literal -1 binary64)))
(.f64 (log.f64 (/.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (log.f64 (/.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))
(+.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))
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(.f64 (-.f64 (.f64 #s(literal -1/16 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) x)))
(.f64 (-.f64 (.f64 #s(literal 1/16 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (*.f64 x x))) x))))
(.f64 (-.f64 #s(literal -1/16 binary64) (/.f64 (.f64 x (.f64 x x)) (/.f64 x #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (.f64 x x) (/.f64 #s(literal -1/8 binary64) (.f64 x x))))))
(.f64 (+.f64 (.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) x) (/.f64 (.f64 x x) (/.f64 x #s(literal -1/8 binary64)))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x))
(.f64 (-.f64 (.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) (.f64 x x)) (.f64 x #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(.f64 (-.f64 (.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x #s(literal 1/8 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x))
(.f64 (-.f64 (.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) x) (/.f64 x (/.f64 x #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) x))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (-.f64 (.f64 #s(literal -1/16 binary64) (/.f64 x #s(literal -1/8 binary64))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))))
(.f64 (-.f64 (.f64 (.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -8 binary64)) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))))
(.f64 (.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) x))
(.f64 (.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/16 binary64) (*.f64 x x)))
(exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 #s(literal -1/16 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal 1/16 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -1/16 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal -1/16 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -16 binary64))
(/.f64 (/.f64 #s(literal -1/16 binary64) x) x)
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(literal 1/16 binary64) x)))
(/.f64 (/.f64 #s(literal 1/16 binary64) x) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 16 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 x #s(literal 1/16 binary64)))
(pow.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal 1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal -1/16 binary64) x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 x (/.f64 #s(literal -1/16 binary64) x)))) #s(literal -1 binary64))
(.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/16 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/16 binary64))
(*.f64 (/.f64 #s(literal -1/16 binary64) x) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1/16 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1/16 binary64) x))

simplify247.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

2226×	`+-lowering-+.f64`
2226×	`+-lowering-+.f32`
1928×	`fma-lowering-fma.f32`
1928×	`fma-lowering-fma.f64`
1574×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	600
1	263	519
2	762	507
3	2160	507
4	6236	507
0	8300	507

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(+ (log -1/16) (* -5 (log x)))
(+ (log -1/16) (+ (* -5 (log x)) (* -2 (pow x 2))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* 6 (pow x 2)) 2))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* (pow x 2) (+ 6 (* 40/3 (pow x 2)))) 2))))
(+ (log -1/2) (log (/ 1 x)))
(- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log -1/2) (+ (log (/ 1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log -1/2) (+ (log (/ 1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 1/2) (log (/ -1 x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(/ -1/16 (pow x 5))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 5))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/ -1/2 x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/ -1/16 (pow x 4))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(/ -1/16 (pow x 4))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/ 1/8 (pow x 2))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/ 1/8 (pow x 2))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))
(/ -1/16 (pow x 2))

Outputs
(+ (log -1/16) (* -5 (log x)))
(+.f64 (log.f64 #s(literal -1/16 binary64)) (*.f64 #s(literal -5 binary64) (log.f64 x)))
(+ (log -1/16) (+ (* -5 (log x)) (* -2 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/16 binary64)) (+.f64 (.f64 #s(literal -5 binary64) (log.f64 x)) (.f64 #s(literal -2 binary64) (*.f64 x x))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* 6 (pow x 2)) 2))))
(+.f64 (.f64 #s(literal -5 binary64) (log.f64 x)) (+.f64 (log.f64 #s(literal -1/16 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -2 binary64) (.f64 (*.f64 x x) #s(literal 6 binary64))))))
(+ (log -1/16) (+ (* -5 (log x)) (* (pow x 2) (- (* (pow x 2) (+ 6 (* 40/3 (pow x 2)))) 2))))
(+.f64 (.f64 #s(literal -5 binary64) (log.f64 x)) (+.f64 (log.f64 #s(literal -1/16 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 6 binary64) (.f64 (*.f64 x x) #s(literal 40/3 binary64)))))))))
(+ (log -1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(- (+ (log -1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) (log.f64 x)))
(- (+ (log -1/2) (+ (log (/ 1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (log.f64 x))))
(- (+ (log -1/2) (+ (log (/ 1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 5/192 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (log.f64 x)))))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (log.f64 #s(literal 1/2 binary64)) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 5/192 (/ 1 (pow x 6)))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (/.f64 #s(literal 5/192 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (.f64 x x))))))
(/ -1/16 (pow x 5))
(/.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x)))) x)
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 5))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 5))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x))) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4)))) x)
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x))) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x))) x)
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* (pow x 2) (+ 1/8 (* -1/2 (pow x 2)))) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))) (.f64 x (.f64 x (*.f64 x x))))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)))
(- (* 1/8 (/ 1 (pow x 2))) (+ 1/2 (/ 1/16 (pow x 4))))
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)))
(/ -1/16 (pow x 4))
(/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 x (.f64 x (*.f64 x x))))
(/ (- (* 1/8 (pow x 2)) 1/16) (pow x 4))
(/.f64 (+.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 x (.f64 x (*.f64 x x))))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x x))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x x))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x x))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x x))
(/ (- 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))

eval94.0ms (1.2%)

Compiler: Compiled 19326 to 3521 computations (81.8% saved)

prune139.0ms (1.8%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	732	0	732
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	732	7	739

Accuracy

100.0%

Counts

739 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
✓	28.8%	(log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))
✓	29.3%	(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
✓	28.6%	(log.f64 (/.f64 #s(literal -1/2 binary64) x))
✓	2.3%	(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
✓	30.5%	(log.f64 (+.f64 x x))
✓	44.5%	x

Compiler

Compiled 147 to 82 computations (44.2% saved)

regimes11.0ms (0.1%)

Counts

10 → 3

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(log.f64 (+.f64 x x))
(log.f64 (/.f64 #s(literal -1/2 binary64) x))
(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x))
(log.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x))
(log.f64 (+.f64 x (hypot.f64 #s(literal 1 binary64) x)))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Outputs

(log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)) x))

(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))

(log.f64 (+.f64 x x))

Calls

3 calls:

4.0ms	x
3.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
100.0%	3	`x`
86.8%	3	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
86.8%	3	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes3.0ms (0%)

Counts

6 → 3

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(log.f64 (+.f64 x x))
(log.f64 (/.f64 #s(literal -1/2 binary64) x))
(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))
(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))

Outputs

(log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))

(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))

(log.f64 (+.f64 x x))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.9%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes44.0ms (0.6%)

Counts

5 → 3

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(log.f64 (+.f64 x x))
(log.f64 (/.f64 #s(literal -1/2 binary64) x))
(log.f64 (+.f64 x (-.f64 (/.f64 #s(literal -1/2 binary64) x) x)))

Outputs
(log.f64 (/.f64 #s(literal -1/2 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(log.f64 (+.f64 x x))

Calls

1 calls:

44.0ms

Results

Accuracy	Segments	Branch
99.6%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 2

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(log.f64 (+.f64 x x))

Outputs
x
(log.f64 (+.f64 x x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
73.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -1.7b remaining (-4.8%)

Threshold costs -1.7b (-4.8%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
44.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch61.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
43.0ms	1.9044263881525242e-13	1493295198523868700.0
15.0ms	-965.1801619298202	-5.140046935629366e-7

Results

22.0ms

320×

valid

Compiler

Compiled 462 to 322 computations (30.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-add: 3.0ms (24.2% of total)

ival-log: 3.0ms (24.2% of total)

ival-mult: 3.0ms (24.2% of total)

ival-sqrt: 2.0ms (16.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch60.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
42.0ms	1.9044263881525242e-13	1493295198523868700.0
15.0ms	-965.1801619298202	-5.140046935629366e-7

Results

22.0ms

320×

valid

Compiler

Compiled 408 to 295 computations (27.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-add: 3.0ms (23.5% of total)

ival-log: 3.0ms (23.5% of total)

ival-mult: 3.0ms (23.5% of total)

ival-sqrt: 3.0ms (23.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch60.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
18.0ms	1.9044263881525242e-13	1493295198523868700.0
20.0ms	-965.1801619298202	-5.140046935629366e-7

Results

27.0ms

320×

valid

Compiler

Compiled 354 to 259 computations (26.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-add: 3.0ms (23.5% of total)

ival-log: 3.0ms (23.5% of total)

ival-mult: 3.0ms (23.5% of total)

ival-sqrt: 3.0ms (23.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch20.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	1.9044263881525242e-13	1493295198523868700.0

Results

12.0ms

176×

valid

Compiler

Compiled 113 to 76 computations (32.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 2.0ms (28.9% of total)

ival-log: 2.0ms (28.9% of total)

ival-mult: 2.0ms (28.9% of total)

ival-sqrt: 1.0ms (14.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	103
1	50	103
2	53	103
3	55	103
4	56	103

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal -1 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x)) (if (<=.f64 x #s(literal 5/4 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))) (log.f64 (+.f64 x x))))
(if (<=.f64 x #s(literal -2476979795053773/2251799813685248 binary64)) (log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x)) (if (<=.f64 x #s(literal 5/4 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (log.f64 (+.f64 x x))))
(if (<=.f64 x #s(literal -5854679515581645/4503599627370496 binary64)) (log.f64 (/.f64 #s(literal -1/2 binary64) x)) (if (<=.f64 x #s(literal 5/4 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))) (log.f64 (+.f64 x x))))
(if (<=.f64 x #s(literal 5/4 binary64)) x (log.f64 (+.f64 x x)))
x

Outputs
(if (<=.f64 x #s(literal -1 binary64)) (log.f64 (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal -1/2 binary64)) x)) (if (<=.f64 x #s(literal 5/4 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))) (log.f64 (+.f64 x x))))
(if (<=.f64 x #s(literal -2476979795053773/2251799813685248 binary64)) (log.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x)) (if (<=.f64 x #s(literal 5/4 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))) (log.f64 (+.f64 x x))))
(if (<=.f64 x #s(literal -5854679515581645/4503599627370496 binary64)) (log.f64 (/.f64 #s(literal -1/2 binary64) x)) (if (<=.f64 x #s(literal 5/4 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))) (log.f64 (+.f64 x x))))
(if (<=.f64 x #s(literal 5/4 binary64)) x (log.f64 (+.f64 x x)))
x

soundness864.0ms (11.3%)

Rules

3490×	`+-lowering-+.f64`
3490×	`+-lowering-+.f32`
2540×	`/-lowering-/.f32`
2540×	`/-lowering-/.f64`
2464×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	122	434
1	355	365
2	1103	351
3	3794	340
0	8358	340
0	15	91
1	65	78
2	284	78
3	2393	78
0	8577	78
0	7	8
1	13	6
2	14	6
3	15	6
0	15	6

Stop Event

1×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 276 to 158 computations (42.8% saved)

preprocess103.0ms (1.4%)

Compiler: Compiled 278 to 120 computations (56.8% saved)

Iter	Nodes	Cost
0	14	27
1	34	19
2	62	19
3	109	19
4	249	19
5	451	19
6	652	19
7	795	19
8	826	19
0	7	8
1	13	6
2	14	6
3	15	6
0	15	6

Iter	Nodes	Cost
0	14	27
1	34	19
2	62	19
3	109	19
4	249	19
5	451	19
6	652	19
7	795	19
8	826	19
0	7	8
1	13	6
2	14	6
3	15	6
0	15	6

analyze122.0ms (1.6%)

sample2.6s (33.7%)

preprocess24.0ms (0.3%)

explain215.0ms (2.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize153.0ms (2%)

series4.0ms (0%)

rewrite29.0ms (0.4%)

simplify241.0ms (3.2%)

eval5.0ms (0.1%)

prune10.0ms (0.1%)

simplify151.0ms (2%)

localize130.0ms (1.7%)

series121.0ms (1.6%)

rewrite239.0ms (3.1%)

simplify165.0ms (2.2%)

eval122.0ms (1.6%)

prune95.0ms (1.2%)

simplify7.0ms (0.1%)

localize135.0ms (1.8%)

series22.0ms (0.3%)

rewrite203.0ms (2.6%)

simplify240.0ms (3.1%)

eval107.0ms (1.4%)

prune175.0ms (2.3%)

simplify207.0ms (2.7%)

localize110.0ms (1.4%)

series3.0ms (0%)

rewrite313.0ms (4.1%)

simplify247.0ms (3.2%)

eval94.0ms (1.2%)

prune139.0ms (1.8%)

regimes11.0ms (0.1%)

regimes3.0ms (0%)

regimes44.0ms (0.6%)

regimes2.0ms (0%)

regimes2.0ms (0%)

bsearch61.0ms (0.8%)

bsearch60.0ms (0.8%)

bsearch60.0ms (0.8%)

bsearch20.0ms (0.3%)

simplify9.0ms (0.1%)

soundness864.0ms (11.3%)

preprocess103.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	27
1	34	19
2	62	19
3	109	19
4	249	19
5	451	19
6	652	19
7	795	19
8	826	19
0	7	8
1	13	6
2	14	6
3	15	6
0	15	6