Details

analyze258.0ms (3.1%)

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)

sample39.0ms (0.5%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify9.0ms (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)

localize12.0ms (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)))

series38.0ms (0.5%)

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)))
8.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
6.0ms	(/.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))

simplify137.0ms (1.6%)

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

prune107.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

0.9b

Counts

98 → 3

Alt Table

Status	Error	Program
	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))))))
▶	1.0b	(*.f64 2 (log.f64 (exp.f64 (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 2137 to 1213 computations (43.2% saved)

localize15.0ms (0.2%)

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))
	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)))

series24.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

24.0ms

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

rewrite3.0ms (0%)

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)))))

simplify143.0ms (1.7%)

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

prune85.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	129	5	134

Error

Counts

134 → 5

Alt Table

Status	Error	Program
	1.0b	(*.f64 2 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))) (log.f64 (sqrt.f64 (exp.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))))))))
	1.5b	(.f64 2 (.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (log.f64 (exp.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)))))))))
✓	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))))))
	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 3281 to 1999 computations (39.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series3.7s (44.3%)

Counts

4 → 96

Calls

4 calls:

2.5s	(log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3))))))
1.2s	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))))
24.0ms	(cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))
6.0ms	(/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64`

Counts

4 → 74

Calls

4 calls:

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

simplify144.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-+l+_binary64`
345×	`associate-/l/_binary64`
280×	`distribute-rgt-out_binary64`
266×	`unswap-sqr_binary64`
250×	`associate-/l*_binary64`

Counts

170 → 129

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	3774
1	190	3619
2	289	3559
3	433	3520
4	857	3508
5	1881	3508
6	4804	3508

prune275.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	259	4	263

Error

Counts

263 → 4

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 2 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))) (log.f64 (sqrt.f64 (exp.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))))))))
	1.5b	(.f64 2 (+.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 g h))) 3)))) 1/3)) 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 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 10908 to 6932 computations (36.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 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)))
✓	1.0b	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

series1.2s (14.6%)

Counts

1 → 24

Calls

1 calls:

1.2s	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
6×	`log-pow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 23

Calls

1 calls:

3.0ms

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

simplify137.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-/l*_binary64`
570×	`log-prod_binary64`
444×	`unswap-sqr_binary64`
375×	`exp-sum_binary64`
365×	`fma-def_binary64`

Counts

47 → 41

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	75	1347
1	95	1275
2	125	1275
3	160	1275
4	244	1275
5	439	1269
6	953	1269
7	2112	1269
8	4275	1269
9	4898	1269
10	4989	1269
11	5197	1269

prune220.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	276	4	280

Error

Counts

280 → 4

Alt Table

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

Compiler

Compiled 10971 to 6713 computations (38.8% saved)

regimes405.0ms (4.8%)

Accuracy

Total 0.0b remaining (75.2%)

Threshold costs 0.0b (75.2%)

Counts

32 → 1

Compiler

Compiled 10181 to 8068 computations (20.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	24	53
1	35	53
2	39	53
3	42	53
4	43	53
5	43	53

end1.0ms (0%)

Compiler: Compiled 34 to 26 computations (23.5% saved)

sample1.3s (15.9%)

Algorithm

1×

intervals

Results

873.0ms	8000×	body	128	valid
48.0ms	559×	body	128	nan

Compiler

Compiled 176 to 140 computations (20.5% saved)

Details

analyze258.0ms (3.1%)

sample39.0ms (0.5%)

simplify9.0ms (0.1%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series38.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify137.0ms (1.6%)

prune107.0ms (1.3%)

localize15.0ms (0.2%)

series24.0ms (0.3%)

rewrite3.0ms (0%)

simplify143.0ms (1.7%)

prune85.0ms (1%)

localize18.0ms (0.2%)

series3.7s (44.3%)

rewrite11.0ms (0.1%)

simplify144.0ms (1.7%)

prune275.0ms (3.3%)

localize16.0ms (0.2%)

series1.2s (14.6%)

rewrite4.0ms (0.1%)

simplify137.0ms (1.6%)

prune220.0ms (2.6%)

regimes405.0ms (4.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.3s (15.9%)

Profiling