Details

analyze1.2s (15.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample3.7s (49.3%)

Results

2.3s	4147×	body	2048	valid
830.0ms	2005×	body	1024	valid
310.0ms	1017×	body	512	valid
118.0ms	552×	body	256	valid
68.0ms	535×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

685×	`div-sub_binary64`
303×	`associate-/r*_binary64`
302×	`fma-def_binary64`
296×	`fma-neg_binary64`
220×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	76	17
3	215	17
4	640	17
5	1828	17
6	4394	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
2.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite63.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

891×	`log1p-expm1-u_binary64`
891×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`
91×	`add-cbrt-cube_binary64`
90×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	199	32
2	2345	32

Stop Event

1×	node limit

Counts

2 → 67

Calls

2 calls:

62.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
61.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

649×	`cancel-sign-sub-inv_binary64`
494×	`fma-def_binary64`
285×	`unswap-sqr_binary64`
207×	`distribute-neg-frac_binary64`
189×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	380
1	114	362
2	326	359
3	976	359
4	3116	359

Stop Event

1×	node limit

Counts

91 → 83

prune91.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	6	84

Error

0.7b

Counts

84 → 6

Alt Table

Status	Error	Program
	2.2b	(.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2))
	1.0b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	2.2b	(+.f64 (fma.f64 (sqrt.f64 (.f64 (PI.f64) 1/2)) (sqrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
	2.6b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
	2.2b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 1))) (fma.f64 (neg.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 1 (.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 1)))
▶	0.7b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 3065 to 2244 computations (26.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.0b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series330.0ms (4.4%)

Counts

2 → 24

Calls

2 calls:

328.0ms	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
2.0ms	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite51.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

471×	`log-prod_binary64`
272×	`pow2_binary64`
190×	`pow1/3_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	220	36
2	2553	36

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

50.0ms	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
50.0ms	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
335×	`fma-def_binary64`
328×	`div-sub_binary64`
246×	`sub-neg_binary64`
207×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	432
1	21	432
2	28	432
3	37	432
4	55	432
5	96	432
6	178	432
7	388	432
8	786	432
9	2475	432
10	4590	432

Stop Event

1×	node limit

Counts

90 → 69

prune194.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	153	5	158

Error

0.7b

Counts

158 → 5

Alt Table

Status	Error	Program
▶	0.7b	(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)))
	3.3b	(expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) 3))
	2.2b	(expm1.f64 (-.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 2) (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))))
	2.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) 2) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	1.0b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Compiler

Compiled 4650 to 3471 computations (25.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)))
✓	0.0b	(pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)
	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
✓	1.0b	(pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)

series812.0ms (10.9%)

Counts

3 → 36

Calls

3 calls:

421.0ms

(pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)

380.0ms

(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)))

11.0ms

(pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)

rewrite70.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log-prod_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
197×	`log-pow_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	54
1	297	54
2	3252	54

Stop Event

1×	node limit

Counts

3 → 120

Calls

3 calls:

66.0ms

(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)))

66.0ms

(pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)

66.0ms

(pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
362×	`unswap-sqr_binary64`
323×	`fma-def_binary64`
245×	`sub-neg_binary64`
217×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	648
1	27	648
2	39	648
3	57	648
4	96	648
5	211	648
6	653	648
7	1515	648
8	1967	648
9	3787	648

Stop Event

1×	node limit

Counts

156 → 78

prune125.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Error

0.7b

Counts

119 → 5

Alt Table

Status	Error	Program
✓	0.7b	(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)))
	3.3b	(expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) 3))
	2.2b	(expm1.f64 (-.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 2) (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))))
	2.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) 2) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
▶	1.0b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Compiler

Compiled 4595 to 3459 computations (24.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series2.0ms (0%)

Counts

1 → 0

Calls

1 calls:

2.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`log1p-expm1-u_binary64`
667×	`expm1-log1p-u_binary64`
152×	`prod-diff_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	164	14
2	1805	14

Stop Event

1×	node limit

Counts

1 → 35

Calls

1 calls:

39.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

35 → 35

prune51.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	34	6	40

Error

0.7b

Counts

40 → 6

Alt Table

Status	Error	Program
✓	0.7b	(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3) 1/3)))
	3.3b	(expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) 3))
	62.2b	(/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (fma.f64 (PI.f64) 1/2 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	2.2b	(expm1.f64 (-.f64 (log1p.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 2) (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))))
	2.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) 2) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.4b	(+.f64 (fma.f64 (PI.f64) 1/2 (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))))

Compiler

Compiled 1435 to 1085 computations (24.4% saved)

regimes351.0ms (4.7%)

Accuracy

Total 0.0b remaining (3%)

Threshold costs 0.0b (3%)

Counts

91 → 1

Compiler

Compiled 9289 to 7064 computations (24% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	4294967295
1	19	4294967295

Stop Event

1×

saturated

end216.0ms (2.9%)

Compiler: Compiled 304 to 233 computations (23.4% saved)

Details

analyze1.2s (15.7%)

sample3.7s (49.3%)

simplify29.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series4.0ms (0.1%)

rewrite63.0ms (0.9%)

simplify29.0ms (0.4%)

prune91.0ms (1.2%)

localize10.0ms (0.1%)

series330.0ms (4.4%)

rewrite51.0ms (0.7%)

simplify46.0ms (0.6%)

prune194.0ms (2.6%)

localize16.0ms (0.2%)

series812.0ms (10.9%)

rewrite70.0ms (0.9%)

simplify51.0ms (0.7%)

prune125.0ms (1.7%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite40.0ms (0.5%)

simplify6.0ms (0.1%)

prune51.0ms (0.7%)

regimes351.0ms (4.7%)

simplify2.0ms (0%)

end216.0ms (2.9%)

Profiling