Metrics for sintan (problem 3.4.5)

analyze369.0ms (2.8%)

Memory

18.3MiB live, 437.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.9%	50.1%	0%	0%	0%	0
0%	0%	49.9%	50.1%	0%	0%	0%	1
0%	0%	49.9%	50.1%	0%	0%	0%	2
0%	0%	49.9%	50.1%	0%	0%	0%	3
0%	0%	49.9%	50.1%	0%	0%	0%	4
0%	0%	49.9%	50.1%	0%	0%	0%	5
0%	0%	49.9%	50.1%	0%	0%	0%	6
0%	0%	49.9%	50.1%	0%	0%	0%	7
0%	0%	49.9%	50.1%	0%	0%	0%	8
0%	0%	49.9%	50.1%	0%	0%	0%	9
0%	0%	49.9%	50.1%	0%	0%	0%	10
0%	0%	49.9%	50.1%	0%	0%	0%	11
0%	0%	49.9%	50.1%	0%	0%	0%	12

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample9.4s (71.5%)

Memory

80.5MiB live, 10 715.0MiB allocated

Samples

6.9s	4 546×	2	valid
1.1s	1 156×	3	valid
849.0ms	2 419×	1	valid
13.0ms	135×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.5s

ival-tan: 5.0s (58.8% of total)

ival-sin: 2.3s (26.7% of total)

ival-sub: 416.0ms (4.9% of total)

adjust: 351.0ms (4.1% of total)

const: 268.0ms (3.1% of total)

ival-div: 137.0ms (1.6% of total)

ival-<=: 50.0ms (0.6% of total)

ival-and: 12.0ms (0.1% of total)

ival-assert: 3.0ms (0% of total)

Bogosity

preprocess66.0ms (0.5%)

Memory

12.1MiB live, 89.9MiB allocated

Algorithm

1×	egg-herbie

Rules

320×	`lower-fma.f64`
320×	`lower-fma.f32`
192×	`lower-*.f64`
192×	`lower-*.f32`
144×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Outputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Symmetry

(abs eps)

explain657.0ms (5%)

Memory

-45.4MiB live, 457.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
160	-	3	(9.573614971533866e-105)	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
99	-	0	-	`(-.f64 eps (tan.f64 eps))`
99	-	0	-	`(-.f64 eps (sin.f64 eps))`
0	-	0	-	`(tan.f64 eps)`
0	-	0	-	`eps`
0	-	0	-	`(sin.f64 eps)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`	u/u	157	0
↳	`(-.f64 eps (sin.f64 eps))`	underflow	157
↳	`(-.f64 eps (tan.f64 eps))`	underflow	157
`-.f64`	`(-.f64 eps (sin.f64 eps))`	cancellation	99	0
`-.f64`	`(-.f64 eps (tan.f64 eps))`	cancellation	99	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	157
2	99

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

306.0ms	268×	2	valid
85.0ms	172×	1	valid
56.0ms	64×	3	valid
1.0ms	8×	0	valid

Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 423.0ms

ival-tan: 213.0ms (50.3% of total)

ival-sin: 100.0ms (23.6% of total)

ival-div: 61.0ms (14.4% of total)

adjust: 35.0ms (8.3% of total)

ival-sub: 13.0ms (3.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.9%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify38.0ms (0.3%)

Memory

8.3MiB live, 44.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 eps (tan.f64 eps))
✓	cost-diff	(sin.f64 eps)
✓	cost-diff	(-.f64 eps (sin.f64 eps))
✓	cost-diff	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Rules

320×	`lower-fma.f64`
320×	`lower-fma.f32`
192×	`lower-*.f64`
192×	`lower-*.f32`
144×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
eps
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

Outputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
eps
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

localize249.0ms (1.9%)

Memory

24.4MiB live, 185.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	65.9%	(-.f64 eps (sin.f64 eps))
✓	accuracy	65.9%	(-.f64 eps (tan.f64 eps))
✓	accuracy	38.5%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Samples

203.0ms	134×	2	valid
21.0ms	32×	3	valid
15.0ms	86×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 24 to 8 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 227.0ms

ival-tan: 126.0ms (55.6% of total)

ival-sin: 64.0ms (28.2% of total)

adjust: 26.0ms (11.5% of total)

ival-sub: 6.0ms (2.6% of total)

ival-div: 3.0ms (1.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series5.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))>
#<alt (-.f64 eps (sin.f64 eps))>
#<alt (sin.f64 eps)>
#<alt (-.f64 eps (tan.f64 eps))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	-inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	0	(/ (- eps (sin eps)) (- eps (tan eps)))
0.0ms	eps	@	inf	(- eps (tan eps))
0.0ms	eps	@	-inf	(- eps (tan eps))

rewrite353.0ms (2.7%)

Memory

-11.7MiB live, 429.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 318×	`lower-*.f64`
4 318×	`lower-*.f32`
3 264×	`lower-/.f32`
3 262×	`lower-/.f64`
2 758×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	11	19
1	51	19
2	408	19
3	5947	19
0	8258	19

Stop Event

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

Counts

4 → 419

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (-.f64 eps (sin.f64 eps)))) #s(literal -1 binary64)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (sin.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (sin.f64 eps))) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps))
(+.f64 (.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(+.f64 (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 (/.f64 (.f64 eps eps) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))))
(-.f64 (/.f64 (.f64 eps eps) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 eps eps)))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))))
(-.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps))) (.f64 (.f64 eps eps) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal -2 binary64))))) (/.f64 (pow.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps))) (.f64 (.f64 eps eps) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal -2 binary64))))))
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(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (+.f64 (fma.f64 eps (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (pow.f64 (.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))) #s(literal 1 binary64)))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))))
(*.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(*.f64 (+.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
(.f64 (+.f64 eps (tan.f64 eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))))
(*.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps))
(.f64 (neg.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps)))))
(.f64 (+.f64 (neg.f64 (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 eps (tan.f64 eps)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) eps) (.f64 eps eps)))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 eps (tan.f64 eps)))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (.f64 eps eps)) (.f64 eps (.f64 eps (*.f64 eps eps)))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))

simplify403.0ms (3.1%)

Memory

-1.5MiB live, 627.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 288×	`lower-fma.f64`
12 288×	`lower-fma.f32`
6 122×	`lower-*.f64`
6 122×	`lower-*.f32`
1 424×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 43

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 (.f64 eps eps) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) eps)) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps) #s(literal -1 binary64)) (sin.f64 eps)) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps) (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps))
(* 1/6 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* -1/3 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/3 binary64))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -2/15 binary64)) #s(literal -1/3 binary64))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -17/315 binary64)) #s(literal -2/15 binary64)) #s(literal -1/3 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -62/2835 binary64) #s(literal -17/315 binary64)) #s(literal -2/15 binary64))) #s(literal -1/3 binary64))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))

eval72.0ms (0.5%)

Memory: 5.0MiB live, 116.6MiB allocated
Compiler: Compiled 12 434 to 1 225 computations (90.1% saved)

prune82.0ms (0.6%)

Memory

13.7MiB live, 136.5MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	458	4	462
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	459	4	463

Accuracy

100.0%

Counts

463 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
▶	99.9%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
▶	99.8%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
▶	99.0%	#s(literal -1/2 binary64)

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify21.0ms (0.2%)

Memory

7.4MiB live, 46.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Program
✓	cost-diff	(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
✓	cost-diff	(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
✓	cost-diff	(*.f64 eps eps)
✓	cost-diff	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	(*.f64 eps #s(literal -27/2800 binary64))
✓	cost-diff	(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
✓	cost-diff	(*.f64 eps eps)
✓	cost-diff	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	(*.f64 eps eps)
✓	cost-diff	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Rules

672×	`lower-fma.f32`
660×	`lower-fma.f64`
242×	`lower-*.f32`
234×	`lower-*.f64`
162×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	92
0	31	92
1	70	92
2	157	92
3	312	92
4	526	92
5	596	92
6	597	92
0	597	92

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 9/40 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(*.f64 eps #s(literal 27/112000 binary64))
#s(literal 27/112000 binary64)
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 9/40 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(*.f64 eps #s(literal 27/112000 binary64))
#s(literal 27/112000 binary64)
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)

localize71.0ms (0.5%)

Memory

-14.0MiB live, 176.3MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
✓	accuracy	100.0%	(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
✓	accuracy	100.0%	(*.f64 eps #s(literal 27/112000 binary64))
✓	accuracy	99.4%	(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
✓	accuracy	100.0%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
✓	accuracy	99.4%	(*.f64 eps #s(literal -27/2800 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)

Samples

48.0ms

256×

valid

Compiler

Compiled 105 to 23 computations (78.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 17.0ms (46.7% of total)

const: 12.0ms (32.9% of total)

ival-add: 7.0ms (19.2% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

-4.0MiB live, 33.9MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))>
#<alt (*.f64 eps eps)>
#<alt (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))>
#<alt (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))>
#<alt (*.f64 eps #s(literal -27/2800 binary64))>
#<alt (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))>
#<alt (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))>
#<alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))>
#<alt (*.f64 eps #s(literal 27/112000 binary64))>
#<alt (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))>
#<alt (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* -27/2800 eps)>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* 27/112000 (pow eps 3))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt -27/2800>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(* eps 27/112000)
1.0ms	eps	@	0	(+ (* 9/40 (* eps eps)) -1/2)
1.0ms	eps	@	-inf	(* eps (+ (* eps (* eps 27/112000)) -27/2800))
0.0ms	eps	@	inf	(* eps (+ (* eps (* eps 27/112000)) -27/2800))
0.0ms	eps	@	inf	(+ (* (* eps eps) (+ (* eps (* eps -27/2800)) 9/40)) -1/2)

rewrite394.0ms (3%)

Memory

21.3MiB live, 856.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 174×	`lower-fma.f32`
7 162×	`lower-fma.f64`
5 010×	`lower-*.f32`
5 002×	`lower-*.f64`
4 046×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	73
0	31	73
1	145	73
2	1084	73
0	8205	73

Stop Event

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

Counts

10 → 357

Calls

Call 1

Inputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(*.f64 eps #s(literal 27/112000 binary64))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))

Outputs
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal -9/40 binary64)))) (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal -9/40 binary64)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 #s(literal 9/40 binary64) eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 9/40 binary64) eps) eps #s(literal -1/2 binary64))
(neg.f64 (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)) (neg.f64 (+.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal 9/80 binary64))))))
(neg.f64 (/.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64))) (+.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal 9/80 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -1/4 binary64))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)) (+.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal 9/80 binary64))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (.f64 (.f64 eps eps) #s(literal 9/80 binary64)))))
(/.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -1/4 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal 9/80 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (.f64 (.f64 eps eps) #s(literal 9/80 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (.f64 (.f64 eps eps) #s(literal 9/80 binary64)))) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
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(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64)) #s(literal -19683/21952000000 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 729/12544000000 binary64)) #s(literal 729/7840000 binary64)) (.f64 (*.f64 eps eps) #s(literal 729/313600000 binary64)))))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64)) #s(literal -19683/21952000000 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 729/7840000 binary64) (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 729/12544000000 binary64)) (.f64 (*.f64 eps eps) #s(literal 729/313600000 binary64))))))
(.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 729/12544000000 binary64)) #s(literal -729/7840000 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal 27/2800 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64)) #s(literal -19683/21952000000 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 729/12544000000 binary64)) #s(literal 729/7840000 binary64)) (.f64 (*.f64 eps eps) #s(literal 729/313600000 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 729/12544000000 binary64)) #s(literal -729/7840000 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) #s(literal -27/112000 binary64) #s(literal -27/2800 binary64))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)))
(.f64 (-.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 729/12544000000 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal -27/112000 binary64)))))

simplify376.0ms (2.9%)

Memory

-5.2MiB live, 685.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 106×	`lower-fma.f64`
13 106×	`lower-fma.f32`
4 108×	`lower-*.f64`
4 108×	`lower-*.f32`
1 350×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	812
1	157	812
2	410	812
3	1090	812
4	3145	804
5	6078	804
0	8284	730

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* -27/2800 eps)
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* 27/112000 (pow eps 3))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
-27/2800
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 eps (.f64 eps #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 eps (.f64 eps #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* 27/112000 (pow eps 6))
(.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (.f64 eps eps))))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (*.f64 eps eps))))) #s(literal -1/2 binary64))
(* 27/112000 (pow eps 6))
(.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (.f64 eps eps))))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (*.f64 eps eps))))) #s(literal -1/2 binary64))
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* 27/112000 (pow eps 4))
(.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* 27/112000 (pow eps 4))
(.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* 27/112000 (pow eps 3))
(.f64 eps (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* 27/112000 (pow eps 3))
(.f64 eps (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
-27/2800
#s(literal -27/2800 binary64)
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))

eval75.0ms (0.6%)

Memory: 12.4MiB live, 204.6MiB allocated
Compiler: Compiled 17 532 to 1 354 computations (92.3% saved)

prune45.0ms (0.3%)

Memory

-17.8MiB live, 143.3MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	513	0	513
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	513	4	517

Accuracy

100.0%

Counts

517 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.9%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.8%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
✓	99.0%	#s(literal -1/2 binary64)

Compiler

Compiled 82 to 46 computations (43.9% saved)

regimes4.0ms (0%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
2.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
100.0%	1	`eps`
100.0%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes3.0ms (0%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(literal -1/2 binary64)

(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.9%	1	`eps`
99.9%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes4.0ms (0%)

Memory

-30.4MiB live, 8.8MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Outputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.8%	1	`eps`
99.8%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes2.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)

Calls

2 calls:

1.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.0%	1	`eps`
99.0%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify5.0ms (0%)

Memory

12.2MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	18	34

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

soundness346.0ms (2.6%)

Memory

-21.1MiB live, 225.9MiB allocated

Rules

12 288×	`lower-fma.f64`
12 288×	`lower-fma.f32`
6 122×	`lower-*.f64`
6 122×	`lower-*.f32`
1 424×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 73 to 41 computations (43.8% saved)

preprocess83.0ms (0.6%)

Memory: 2.6MiB live, 118.1MiB allocated
Remove: (abs eps)
Compiler: Compiled 216 to 120 computations (44.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

analyze369.0ms (2.8%)

sample9.4s (71.5%)

preprocess66.0ms (0.5%)

explain657.0ms (5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify38.0ms (0.3%)

localize249.0ms (1.9%)

series5.0ms (0%)

rewrite353.0ms (2.7%)

simplify403.0ms (3.1%)

eval72.0ms (0.5%)

prune82.0ms (0.6%)

simplify21.0ms (0.2%)

localize71.0ms (0.5%)

series13.0ms (0.1%)

rewrite394.0ms (3%)

simplify376.0ms (2.9%)

eval75.0ms (0.6%)

prune45.0ms (0.3%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes4.0ms (0%)

regimes2.0ms (0%)

simplify5.0ms (0%)

soundness346.0ms (2.6%)

preprocess83.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22