Details

analyze160.0ms (0.8%)

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 17 to 17 computations (0% saved)

sample29.0ms (0.1%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	17×	body	128	nan

Compiler

Compiled 33 to 35 computations (-6.1% saved)

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	54	23
1	54	23

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 1.0b

Counts

2 → 2

Compiler

Compiled 44 to 44 computations (0% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0b	(+.f64 (/.f64 (*.f64 2 PI.f64) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
1.0b	(cos.f64 (+.f64 (/.f64 (*.f64 2 PI.f64) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0b	(/.f64 (*.f64 2 PI.f64) 3)

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_3488`
14×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523`
12×	`times-frac_binary64_3494`
11×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
6×	`associate-/r*_binary64_3432` `add-log-exp_binary64_3527` `div-sub_binary64_3493`
4×	`associate-/l*_binary64_3433` `associate-+r-_binary64_3422` `pow1_binary64_3549` `div-inv_binary64_3485`
3×	`acos-neg_binary64_3671` `div-exp_binary64_3539` `distribute-frac-neg_binary64_3451` `cbrt-undiv_binary64_3522` `acos-asin_binary64_3669`
2×	`clear-num_binary64_3487` `cos-diff_binary64_3625` `frac-2neg_binary64_3499`
1×	`distribute-rgt-out_binary64_3441` `distribute-lft-out_binary64_3439` `frac-add_binary64_3496` `flip-+_binary64_3462` `flip3-+_binary64_3491` `cbrt-unprod_binary64_3521` `+-commutative_binary64_3418` `sum-log_binary64_3579` `cos-sum_binary64_3622` `prod-exp_binary64_3537`

Counts

4 → 76

Calls

4 calls:

11.0ms	(cos.f64 (+.f64 (/.f64 (*.f64 2 PI.f64) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
11.0ms	(+.f64 (/.f64 (*.f64 2 PI.f64) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
5.0ms	(/.f64 (*.f64 2 PI.f64) 3)
3.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

series111.0ms (0.5%)

Counts

4 → 10

Calls

4 calls:

76.0ms	(cos.f64 (+.f64 (/.f64 (*.f64 2 PI.f64) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
22.0ms	(+.f64 (/.f64 (*.f64 2 PI.f64) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
14.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
0.0ms	(/.f64 (*.f64 2 PI.f64) 3)

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4839	1582
1	4839	1582

prune338.0ms (1.6%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	59	27	86
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	28	88

Merged error: 0.0b

Counts

88 → 28

Compiler

Compiled 2269 to 1553 computations (31.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3))
1.0b	(/.f64 PI.f64 3)
1.0b	(/.f64 PI.f64 3)
62.9b	(sin.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3)))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
18×	`times-frac_binary64_3494`
8×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
6×	`associate-/r_binary64_3432` `associate-/l_binary64_3433` `add-log-exp_binary64_3527`
4×	`pow1_binary64_3549`
3×	`div-inv_binary64_3485`
2×	`clear-num_binary64_3487` `frac-2neg_binary64_3499` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
1×	`distribute-lft-out_binary64_3439` `flip-+_binary64_3462` `sin-sum_binary64_3621` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `sum-log_binary64_3579`

Counts

4 → 74

Calls

4 calls:

7.0ms	(sin.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3)))
6.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3))
3.0ms	(/.f64 PI.f64 3)
3.0ms	(/.f64 PI.f64 3)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(sin.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3)))
0.0ms	(/.f64 PI.f64 3)
0.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3))
0.0ms	(/.f64 PI.f64 3)

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4752	814
1	4752	814

prune633.0ms (3%)

Pruning

41 alts after pruning (40 fresh and 1 done)

	Pruned	Kept	Total
New	60	18	78
Fresh	5	22	27
Picked	0	1	1
Done	0	0	0
Total	65	41	106

Merged error: 0b

Counts

106 → 41

Compiler

Compiled 3696 to 2650 computations (28.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 PI.f64 3)
1.0b	(+.f64 (*.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (/.f64 PI.f64 3) 3)))
1.6b	(pow.f64 (/.f64 PI.f64 3) 3)
62.9b	(sin.f64 (+.f64 (*.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (/.f64 PI.f64 3) 3))))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_3510` `times-frac_binary64_3494` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
13×	`unpow-prod-down_binary64_3567` `cube-prod_binary64_3516`
9×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
6×	`add-log-exp_binary64_3527`
5×	`pow1_binary64_3549`
3×	`associate-/r_binary64_3432` `associate-/l_binary64_3433` `pow-unpow_binary64_3565` `div-inv_binary64_3485`
2×	`pow-exp_binary64_3556` `rem-cube-cbrt_binary64_3511` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
1×	`unpow3_binary64_3554` `clear-num_binary64_3487` `flip-+_binary64_3462` `sin-sum_binary64_3621` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `pow-to-exp_binary64_3557` `cube-div_binary64_3517` `frac-2neg_binary64_3499` `sqr-pow_binary64_3460` `cube-mult_binary64_3518` `sum-log_binary64_3579` `pow-pow_binary64_3560`

Counts

4 → 92

Calls

4 calls:

14.0ms	(sin.f64 (+.f64 (*.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (/.f64 PI.f64 3) 3))))
11.0ms	(+.f64 (*.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (/.f64 PI.f64 3) 3)))
6.0ms	(pow.f64 (/.f64 PI.f64 3) 3)
3.0ms	(/.f64 PI.f64 3)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(sin.f64 (+.f64 (*.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (/.f64 PI.f64 3) 3))))
0.0ms	(pow.f64 (/.f64 PI.f64 3) 3)
0.0ms	(+.f64 (*.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (/.f64 PI.f64 3) 3)))
0.0ms	(/.f64 PI.f64 3)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5017	1410

prune754.0ms (3.6%)

Pruning

47 alts after pruning (45 fresh and 2 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	6	33	39
Picked	0	1	1
Done	0	1	1
Total	90	47	137

Merged error: 0b

Counts

137 → 47

Compiler

Compiled 4146 to 3080 computations (25.7% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 PI.f64 2/3)
1.0b	(+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3))
1.6b	(pow.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 PI.f64 (cbrt.f64 3))) 3)
62.9b	(sin.f64 (+.f64 (.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 PI.f64 (cbrt.f64 3))) 3))))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-exp-log_binary64_3526`
21×	`add-cbrt-cube_binary64_3524` `prod-exp_binary64_3537`
15×	`pow-exp_binary64_3556` `div-exp_binary64_3539`
9×	`add-sqr-sqrt_binary64_3510` `cbrt-unprod_binary64_3521` `pow1_binary64_3549`
7×	`rem-cube-cbrt_binary64_3511` `add-cube-cbrt_binary64_3523` `cbrt-undiv_binary64_3522` `*-un-lft-identity_binary64_3488`
6×	`add-log-exp_binary64_3527`
4×	`1-exp_binary64_3532` `rec-exp_binary64_3538`
3×	`associate-l_binary64_3429` `associate-r_binary64_3428` `pow-unpow_binary64_3565` `cube-div_binary64_3517`
2×	`pow-prod-down_binary64_3559` `pow-pow_binary64_3560`
1×	`unpow3_binary64_3554` `associate-l/_binary64_3431` `distribute-lft-out_binary64_3439` `unswap-sqr_binary64_3456` `flip-+_binary64_3462` `sin-sum_binary64_3621` `flip3-+_binary64_3491` `unpow-prod-down_binary64_3567` `+-commutative_binary64_3418` `pow-to-exp_binary64_3557` `frac-times_binary64_3498` `cube-prod_binary64_3516` `associate-r/_binary64_3430` `sqr-pow_binary64_3460` `cube-mult_binary64_3518` `*-commutative_binary64_3419` `sum-log_binary64_3579` `div-inv_binary64_3485`

Counts

4 → 81

Calls

4 calls:

14.0ms	(pow.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 PI.f64 (cbrt.f64 3))) 3)
9.0ms	(sin.f64 (+.f64 (.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 PI.f64 (cbrt.f64 3))) 3))))
6.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3))
4.0ms	(*.f64 PI.f64 2/3)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(sin.f64 (+.f64 (.f64 PI.f64 2/3) (cbrt.f64 (pow.f64 (.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 PI.f64 (cbrt.f64 3))) 3))))
0.0ms	(pow.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 PI.f64 (cbrt.f64 3))) 3)
0.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 PI.f64 3))
0.0ms	(*.f64 PI.f64 2/3)

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4919	880
1	4919	880

prune769.0ms (3.7%)

Pruning

57 alts after pruning (54 fresh and 3 done)

	Pruned	Kept	Total
New	68	17	85
Fresh	7	37	44
Picked	0	1	1
Done	0	2	2
Total	75	57	132

Merged error: 0b

Counts

132 → 57

Compiler

Compiled 2834 to 2103 computations (25.8% saved)

regimes5.1s (24.3%)

Compiler: Compiled 77522 to 64931 computations (16.2% saved)

bsearch4.3s (20.8%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	67
1	37	67

end0.0ms (0%)

sample8.0s (38.3%)

Algorithm

1×

intervals

Results

627.0ms	8000×	body	128	valid
33.0ms	518×	body	128	nan

Compiler

Compiled 8140 to 6782 computations (16.7% saved)

Pareto

Details

analyze160.0ms (0.8%)

sample29.0ms (0.1%)

simplify101.0ms (0.5%)

prune5.0ms (0%)

localize12.0ms (0.1%)

rewrite36.0ms (0.2%)

series111.0ms (0.5%)

simplify84.0ms (0.4%)

prune338.0ms (1.6%)

localize26.0ms (0.1%)

rewrite26.0ms (0.1%)

series0.0ms (0%)

simplify112.0ms (0.5%)

prune633.0ms (3%)

localize28.0ms (0.1%)

rewrite44.0ms (0.2%)

series0.0ms (0%)

simplify50.0ms (0.2%)

prune754.0ms (3.6%)

localize32.0ms (0.2%)

rewrite45.0ms (0.2%)

series0.0ms (0%)

simplify73.0ms (0.4%)

prune769.0ms (3.7%)

regimes5.1s (24.3%)

bsearch4.3s (20.8%)

simplify5.0ms (0%)

end0.0ms (0%)

sample8.0s (38.3%)

Profiling