Details

analyze1.1s (15.1%)

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)

sample3.6s (48.9%)

Results

2.2s	4083×	body	2048	valid
828.0ms	2082×	body	1024	valid
321.0ms	1087×	body	512	valid
100.0ms	507×	body	256	valid
61.0ms	497×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify129.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

686×	`div-sub_binary64`
546×	`sub-neg_binary64`
397×	`neg-mul-1_binary64`
344×	`neg-sub0_binary64`
311×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	72	17
3	203	17
4	532	17
5	1340	17
6	2710	17
7	3748	17
8	4643	17
9	4981	17

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

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(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))
✓	0.6b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series5.0ms (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)))

rewrite55.0ms (0.7%)

Algorithm

2×	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`

Counts

2 → 67

Calls

2 calls:

53.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
53.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	199	32
2	2277	32
3	5491	32
0	0	0
1	0	0

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Rules

649×	`cancel-sign-sub-inv_binary64`
494×	`fma-def_binary64`
460×	`sub-neg_binary64`
309×	`distribute-rgt-out_binary64`
286×	`unswap-sqr_binary64`

Counts

91 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	380
1	113	362
2	316	359
3	829	359
4	2262	359
5	4207	359
6	4609	359
7	4995	359

prune88.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Error

0.6b

Counts

84 → 5

Alt Table

Status	Error	Program
	2.5b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 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))))))))
	2.1b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 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)))
▶	0.6b	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.8b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	1.6b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))

Compiler

Compiled 2765 to 2025 computations (26.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.0b	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.0b	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.6b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series463.0ms (6.2%)

Counts

2 → 24

Calls

2 calls:

461.0ms	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
2.0ms	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite57.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

2 → 69

Calls

2 calls:

55.0ms	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
55.0ms	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	215	36
2	2448	36
3	4925	36
0	0	0
1	0	0

simplify126.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
850×	`unsub-neg_binary64`
557×	`sub-neg_binary64`
476×	`distribute-neg-in_binary64`
388×	`neg-sub0_binary64`

Counts

93 → 72

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	432
1	18	432
2	25	432
3	34	432
4	52	432
5	79	432
6	134	432
7	270	432
8	527	432
9	1633	432
10	2720	432
11	3905	432
12	4474	432
13	4642	432
14	4925	432
15	4845	432

prune143.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	156	4	160

Error

0.6b

Counts

160 → 4

Alt Table

Status	Error	Program
▶	1.0b	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
	2.5b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) 2) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2))))
	2.1b	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))
	3.1b	(exp.f64 (pow.f64 (cbrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))) 3))

Compiler

Compiled 4720 to 3517 computations (25.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1)))
✓	0.0b	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
✓	0.6b	(acos.f64 (fma.f64 4 (*.f64 v v) -1))

series401.0ms (5.4%)

Counts

3 → 36

Calls

3 calls:

397.0ms	(log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1)))
2.0ms	(acos.f64 (fma.f64 4 (*.f64 v v) -1))
2.0ms	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))

rewrite111.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

614×	`log1p-expm1-u_binary64`
614×	`expm1-log1p-u_binary64`
295×	`log-prod_binary64`
132×	`pow3_binary64`
130×	`expm1-udef_binary64`

Counts

3 → 94

Calls

3 calls:

105.0ms	(log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1)))
105.0ms	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
105.0ms	(acos.f64 (fma.f64 4 (*.f64 v v) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	155	32
2	1593	32
3	4964	32
4	4995	32
5	4931	32
0	0	0
1	0	0

simplify173.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
434×	`unswap-sqr_binary64`

Counts

130 → 64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	384
1	16	384
2	26	384
3	45	384
4	91	384
5	223	384
6	706	384
7	1167	384
8	1174	384
9	1322	384
10	1492	384
11	1674	384
12	1897	384
13	2182	384
14	2601	384
15	3166	384
16	3852	384
17	4070	384
18	4314	384
19	4396	384
20	4429	384
21	4450	384
22	5019	384

prune46.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Error

0.6b

Counts

68 → 4

Alt Table

Status	Error	Program
✓	1.0b	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
	2.5b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) 2) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2))))
	3.5b	(exp.f64 (pow.f64 (cbrt.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1)))) 3))
▶	2.1b	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))

Compiler

Compiled 1434 to 1048 computations (26.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))
	0.6b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
✓	1.0b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))
✓	1.0b	(pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)

series18.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

13.0ms

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

2.0ms

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

2.0ms

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

rewrite73.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

542×	`log-prod_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
187×	`log-pow_binary64`
124×	`add-sqr-sqrt_binary64`

Counts

3 → 115

Calls

3 calls:

69.0ms

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

69.0ms

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

69.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	261	54
2	2877	54
3	4873	54
0	0	0
1	0	0

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-neg_binary64`
623×	`unsub-neg_binary64`
363×	`distribute-neg-in_binary64`
362×	`unswap-sqr_binary64`
323×	`fma-def_binary64`

Counts

151 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	648
1	27	648
2	39	648
3	57	648
4	95	648
5	175	648
6	405	648
7	840	648
8	1087	648
9	2311	648
10	3383	648
11	4319	648
12	4756	648
13	4801	648

prune116.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Error

0.6b

Counts

114 → 4

Alt Table

Status	Error	Program
✓	1.0b	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
	2.5b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) 2) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2))))
	3.5b	(exp.f64 (pow.f64 (cbrt.f64 (log.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1)))) 3))
✓	2.1b	(exp.f64 (log.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))

Compiler

Compiled 4290 to 3213 computations (25.1% saved)

regimes317.0ms (4.3%)

Accuracy

Total 0.0b remaining (1.3%)

Threshold costs 0.0b (1.3%)

Counts

69 → 1

Compiler

Compiled 7196 to 5429 computations (24.6% 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	14	25
1	17	25
2	16	25

end121.0ms (1.6%)

Compiler: Compiled 177 to 136 computations (23.2% saved)

Details

analyze1.1s (15.1%)

sample3.6s (48.9%)

simplify129.0ms (1.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series5.0ms (0.1%)

rewrite55.0ms (0.7%)

simplify75.0ms (1%)

prune88.0ms (1.2%)

localize10.0ms (0.1%)

series463.0ms (6.2%)

rewrite57.0ms (0.8%)

simplify126.0ms (1.7%)

prune143.0ms (1.9%)

localize9.0ms (0.1%)

series401.0ms (5.4%)

rewrite111.0ms (1.5%)

simplify173.0ms (2.3%)

prune46.0ms (0.6%)

localize15.0ms (0.2%)

series18.0ms (0.2%)

rewrite73.0ms (1%)

simplify112.0ms (1.5%)

prune116.0ms (1.6%)

regimes317.0ms (4.3%)

simplify2.0ms (0%)

end121.0ms (1.6%)

Profiling