Details

analyze235.0ms (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	68.7%	6.3%	5
25%	65.6%	9.5%	6
37.5%	39%	23.5%	7
37.5%	36.7%	25.9%	8
43.7%	20.7%	35.6%	9
43.7%	19.3%	37%	10
46.8%	10.6%	42.5%	11
46.8%	9.9%	43.3%	12
48.4%	5.4%	46.2%	13
48.4%	5%	46.6%	14

Compiler

Compiled 19 to 17 computations (10.5% saved)

sample1.6s (14.6%)

Results

1.5s	8256×	body	128	valid
79.0ms	524×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	26	23
2	40	21
3	49	21
4	56	21
5	63	21
6	74	21
7	73	21
8	62	21

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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
✓	0.9b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series41.0ms (0.4%)

Counts

3 → 72

Calls

3 calls:

24.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
9.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
7.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

2.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
0.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))

simplify132.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

516×	`distribute-rgt-in_binary64`
515×	`fma-neg_binary64`
508×	`associate-/l/_binary64`
495×	`distribute-lft-in_binary64`
420×	`distribute-rgt-out_binary64`

Counts

123 → 97

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	105	2186
1	150	2070
2	246	2070
3	411	2070
4	874	2070
5	2199	2070
6	4684	2070
7	5109	2070

prune113.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Error

0.9b

Counts

98 → 4

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))
	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2215 to 1263 computations (43% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))
✓	0.0b	(fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))
✓	0.9b	(cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))

series4.9s (45.1%)

Counts

4 → 96

Calls

4 calls:

1.5s	(cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))
1.3s	(fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))
1.3s	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))
706.0ms	(cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`log-prod_binary64`
6×	`cbrt-prod_binary64`

Counts

4 → 55

Calls

4 calls:

2.0ms	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))
1.0ms	(cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))
0.0ms	(fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))

simplify135.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

513×	`log-prod_binary64`
447×	`distribute-rgt-out_binary64`
375×	`unswap-sqr_binary64`
318×	`fma-def_binary64`
306×	`distribute-rgt-in_binary64`

Counts

151 → 96

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	97	2668
1	114	2531
2	151	2505
3	241	2412
4	546	2400
5	2045	2338
6	4748	2338
7	5340	2338

prune107.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Error

0.9b

Counts

100 → 4

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))
	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
▶	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2168 to 1049 computations (51.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
	0.9b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
✓	1.0b	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

series48.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
21.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
0.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

simplify242.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1392×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
592×	`cube-prod_binary64`
500×	`fabs-mul_binary64`
470×	`pow-sqr_binary64`

Counts

70 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	1455
1	59	1377
2	74	1377
3	87	1377
4	100	1377
5	122	1377
6	170	1377
7	270	1377
8	614	1377
9	1210	1377
10	1349	1377
11	1612	1377
12	1917	1377
13	2211	1377
14	2613	1377
15	2967	1377
16	3150	1377
17	3407	1377
18	3546	1377
19	3625	1377
20	3705	1377
21	4463	1377
22	4855	1377

prune128.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Error

0.9b

Counts

123 → 4

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))
▶	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2850 to 1724 computations (39.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
	0.9b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series2.1s (19.3%)

Counts

2 → 48

Calls

2 calls:

1.1s

(*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

937.0ms

(cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

5.0ms

(*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

1.0ms

(cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

simplify142.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-def_binary64`
461×	`unswap-sqr_binary64`
368×	`sqr-pow_binary64`
277×	`*-commutative_binary64`
256×	`associate-+l+_binary64`

Counts

103 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	3140
1	108	3106
2	225	2632
3	451	2584
4	809	2307
5	1396	2307
6	2653	2307
7	4646	2307
8	5156	2307

prune308.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	358	1	359
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	358	5	363

Error

Counts

363 → 5

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))
✓	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	0.1b	(.f64 2 (.f64 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 2)) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 17285 to 9648 computations (44.2% saved)

regimes377.0ms (3.5%)

Accuracy

Total 0.0b remaining (78.6%)

Threshold costs 0.0b (78.6%)

Counts

34 → 1

Compiler

Compiled 8856 to 7290 computations (17.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	48
1	33	48
2	37	48
3	39	48
4	39	48

end165.0ms (1.5%)

Compiler: Compiled 208 to 155 computations (25.5% saved)

Details

analyze235.0ms (2.2%)

sample1.6s (14.6%)

simplify11.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series41.0ms (0.4%)

rewrite9.0ms (0.1%)

simplify132.0ms (1.2%)

prune113.0ms (1%)

localize13.0ms (0.1%)

series4.9s (45.1%)

rewrite7.0ms (0.1%)

simplify135.0ms (1.2%)

prune107.0ms (1%)

localize13.0ms (0.1%)

series48.0ms (0.4%)

rewrite2.0ms (0%)

simplify242.0ms (2.2%)

prune128.0ms (1.2%)

localize15.0ms (0.1%)

series2.1s (19.3%)

rewrite12.0ms (0.1%)

simplify142.0ms (1.3%)

prune308.0ms (2.8%)

regimes377.0ms (3.5%)

simplify3.0ms (0%)

end165.0ms (1.5%)

Profiling