Details

analyze225.0ms (5.3%)

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)

sample57.0ms (1.3%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
1.0ms	16×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify9.0ms (0.2%)

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 (0.1%)

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)

localize11.0ms (0.3%)

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))
✓	1.0b	(/.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)))

series134.0ms (3.2%)

Counts

3 → 72

Calls

3 calls:

119.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
9.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
5.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite6.0ms (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))

simplify134.0ms (3.2%)

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

prune105.0ms (2.5%)

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 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
▶	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))))
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2127 to 1223 computations (42.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series244.0ms (5.8%)

Counts

4 → 96

Calls

4 calls:

93.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))))
70.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))
63.0ms	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
17.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
156×	`add-cube-cbrt_binary64`
144×	`sqrt-prod_binary64`

Counts

4 → 242

Calls

4 calls:

9.0ms	(/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))
3.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3))))
0.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))

simplify330.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

692×	`distribute-rgt-in_binary64`
495×	`associate-/l/_binary64`
371×	`fma-def_binary64`
308×	`*-commutative_binary64`
304×	`fma-neg_binary64`

Counts

338 → 323

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	264	9313
1	501	9003
2	900	8721
3	1849	8607
4	2330	8600
5	3649	8388
6	4997	8388

prune402.0ms (9.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	323	4	327

Error

0.9b

Counts

327 → 4

Alt Table

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

Compiler

Compiled 9417 to 5928 computations (37.1% saved)

localize16.0ms (0.4%)

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))))
	1.0b	(/.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)))))
	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series54.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
23.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

rewrite2.0ms (0.1%)

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:

1.0ms	(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))))

simplify256.0ms (6.1%)

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

prune127.0ms (3%)

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 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)) (sqrt.f64 3)))))
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
▶	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2759 to 1681 computations (39.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

23.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-pow_binary64`
3×	`log-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`exp-prod_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

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

simplify140.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

813×	`log-prod_binary64`
451×	`exp-to-pow_binary64`
376×	`times-frac_binary64`
372×	`unswap-sqr_binary64`
368×	`log-pow_binary64`

Counts

42 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	936
1	76	878
2	110	878
3	149	878
4	243	878
5	504	878
6	1156	878
7	2811	878
8	4708	878
9	4941	878
10	4995	878
11	4970	878
12	4980	878

prune90.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	131	4	135

Error

0.0b

Counts

135 → 4

Alt Table

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

Compiler

Compiled 3093 to 1863 computations (39.8% saved)

regimes505.0ms (12%)

Accuracy

Total 0.1b remaining (78.3%)

Threshold costs 0.1b (78.3%)

Counts

45 → 1

Compiler

Compiled 11658 to 9317 computations (20.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-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	19	56
1	28	56
2	32	56
3	35	56
4	36	56
5	36	56

end1.0ms (0%)

Compiler: Compiled 35 to 27 computations (22.9% saved)

sample1.3s (30.2%)

Algorithm

1×

intervals

Results

857.0ms	8000×	body	128	valid
51.0ms	583×	body	128	nan

Compiler

Compiled 143 to 119 computations (16.8% saved)

Details

analyze225.0ms (5.3%)

sample57.0ms (1.3%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

series134.0ms (3.2%)

rewrite6.0ms (0.1%)

simplify134.0ms (3.2%)

prune105.0ms (2.5%)

localize13.0ms (0.3%)

series244.0ms (5.8%)

rewrite41.0ms (1%)

simplify330.0ms (7.8%)

prune402.0ms (9.5%)

localize16.0ms (0.4%)

series54.0ms (1.3%)

rewrite2.0ms (0.1%)

simplify256.0ms (6.1%)

prune127.0ms (3%)

localize14.0ms (0.3%)

series23.0ms (0.5%)

rewrite3.0ms (0.1%)

simplify140.0ms (3.3%)

prune90.0ms (2.1%)

regimes505.0ms (12%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.3s (30.2%)

Profiling