Details

analyze264.0ms (4.9%)

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
0%	99.9%	0.1%	5
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample42.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	48×	body	1024	valid
10.0ms	155×	body	128	valid
7.0ms	35×	body	512	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	159	14
1	159	14

prune2.0ms (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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.1b	(*.f64 x (cos.f64 y))
0.1b	(*.f64 z (sin.f64 y))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(*.f64 x (cos.f64 y))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_5556`
7×	`*-un-lft-identity_binary64_5534` `add-cbrt-cube_binary64_5570` `add-exp-log_binary64_5572` `add-cube-cbrt_binary64_5569` `pow1_binary64_5595`
6×	`associate-l_binary64_5475` `associate-r_binary64_5474`
5×	`add-log-exp_binary64_5573`
2×	`cbrt-unprod_binary64_5567` `*-commutative_binary64_5465` `unswap-sqr_binary64_5502` `prod-exp_binary64_5583` `pow-prod-down_binary64_5605`
1×	`diff-log_binary64_5626` `cancel-sign-sub-inv_binary64_5500` `flip--_binary64_5509` `flip3--_binary64_5538` `sub-neg_binary64_5527`

Counts

3 → 48

Calls

6 calls:

4.0ms	(*.f64 z (sin.f64 y))
4.0ms	(*.f64 x (cos.f64 y))
4.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
0.0ms	(*.f64 z (sin.f64 y))

series351.0ms (6.5%)

Counts

3 → 33

Calls

3 calls:

212.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
72.0ms	(*.f64 x (cos.f64 y))
67.0ms	(*.f64 z (sin.f64 y))

Compiler

Compiled 514 to 459 computations (10.7% saved)

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5076	896

prune84.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Error

0.0b

Counts

82 → 9

Compiler

Compiled 1109 to 293 computations (73.6% saved)

localize15.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (.f64 x (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
0.1b	(.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
0.1b	(*.f64 z (sin.f64 y))
0.0b	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))
0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
0.3b	(cbrt.f64 (cos.f64 y))
0.3b	(cbrt.f64 (cos.f64 y))
0.3b	(cbrt.f64 (cos.f64 y))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_5565`
23×	`add-sqr-sqrt_binary64_5556`
15×	`*-un-lft-identity_binary64_5534` `add-cube-cbrt_binary64_5569`
11×	`pow1_binary64_5595`
9×	`pow1/3_binary64_5616`
6×	`associate-l_binary64_5475` `swap-sqr_binary64_5501` `add-exp-log_binary64_5572` `associate-r_binary64_5474`
4×	`add-cbrt-cube_binary64_5570` `add-log-exp_binary64_5573` `unswap-sqr_binary64_5502`
2×	`pow-sqr_binary64_5507` `pow-prod-up_binary64_5604` `pow-prod-down_binary64_5605`
1×	`cbrt-unprod_binary64_5567` `pow-plus_binary64_5597` `*-commutative_binary64_5465` `pow2_binary64_5615` `prod-exp_binary64_5583`

Counts

4 → 73

Calls

8 calls:

7.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))
1.0ms	(cbrt.f64 (cos.f64 y))
1.0ms	(cbrt.f64 (cos.f64 y))
0.0ms	(-.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (.f64 z (sin.f64 y)))

series287.0ms (5.3%)

Counts

4 → 16

Calls

4 calls:

92.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
70.0ms	(cbrt.f64 (cos.f64 y))
65.0ms	(cbrt.f64 (cos.f64 y))
59.0ms	(cbrt.f64 (cos.f64 y))

Compiler

Compiled 548 to 413 computations (24.6% saved)

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4872	740
1	4872	740

prune94.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	88	10	98

Error

0.0b

Counts

98 → 10

Compiler

Compiled 1947 to 541 computations (72.2% saved)

localize16.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
0.1b	(*.f64 z (sin.f64 y))
0.1b	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
0.0b	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
0.1b	(*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
0.1b	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
0.3b	(pow.f64 (cos.f64 y) 2)
0.3b	(cbrt.f64 (cos.f64 y))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_5572`
22×	`add-sqr-sqrt_binary64_5556`
19×	`unpow-prod-down_binary64_5613`
18×	`associate-r_binary64_5474`
16×	`prod-exp_binary64_5583`
13×	`*-un-lft-identity_binary64_5534` `add-cube-cbrt_binary64_5569`
11×	`add-cbrt-cube_binary64_5570`
9×	`pow-exp_binary64_5602`
7×	`cbrt-unprod_binary64_5567` `pow1_binary64_5595`
6×	`cbrt-prod_binary64_5565` `unswap-sqr_binary64_5502`
5×	`pow-to-exp_binary64_5603` `sqr-pow_binary64_5506`
4×	`associate-l_binary64_5475` `add-log-exp_binary64_5573`
3×	`unpow2_binary64_5599` `pow-unpow_binary64_5611`
2×	`*-commutative_binary64_5465` `unpow1/3_binary64_5601`
1×	`pow-pow_binary64_5606` `pow1/3_binary64_5616` `pow-prod-down_binary64_5605`

Counts

4 → 90

Calls

8 calls:

11.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
9.0ms	(*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
2.0ms	(pow.f64 (cos.f64 y) 2)
1.0ms	(cbrt.f64 (cos.f64 y))
0.0ms	(-.f64 (.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))

series425.0ms (7.9%)

Counts

4 → 24

Calls

4 calls:

250.0ms	(*.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
77.0ms	(.f64 (.f64 x (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
73.0ms	(cbrt.f64 (cos.f64 y))
26.0ms	(pow.f64 (cos.f64 y) 2)

Compiler

Compiled 675 to 574 computations (15% saved)

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5178	1077

prune98.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	114	10	124

Error

0.0b

Counts

124 → 10

Compiler

Compiled 2167 to 851 computations (60.7% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y)))
0.2b	(.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))))
0.1b	(*.f64 x (cos.f64 y))
0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
0.6b	(cbrt.f64 (sin.f64 y))
0.6b	(cbrt.f64 (sin.f64 y))
0.6b	(cbrt.f64 (sin.f64 y))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_5565`
23×	`add-sqr-sqrt_binary64_5556`
15×	`*-un-lft-identity_binary64_5534` `add-cube-cbrt_binary64_5569`
11×	`pow1_binary64_5595`
9×	`pow1/3_binary64_5616`
6×	`associate-l_binary64_5475` `swap-sqr_binary64_5501` `add-exp-log_binary64_5572` `associate-r_binary64_5474`
4×	`add-cbrt-cube_binary64_5570` `add-log-exp_binary64_5573` `unswap-sqr_binary64_5502`
2×	`pow-sqr_binary64_5507` `pow-prod-up_binary64_5604` `pow-prod-down_binary64_5605`
1×	`cbrt-unprod_binary64_5567` `pow-plus_binary64_5597` `*-commutative_binary64_5465` `pow2_binary64_5615` `prod-exp_binary64_5583`

Counts

4 → 73

Calls

8 calls:

7.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
1.0ms	(cbrt.f64 (sin.f64 y))
1.0ms	(cbrt.f64 (sin.f64 y))
1.0ms	(cbrt.f64 (sin.f64 y))
0.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 z (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))

series290.0ms (5.4%)

Counts

4 → 16

Calls

4 calls:

87.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
70.0ms	(cbrt.f64 (sin.f64 y))
70.0ms	(cbrt.f64 (sin.f64 y))
62.0ms	(cbrt.f64 (sin.f64 y))

Compiler

Compiled 602 to 455 computations (24.4% saved)

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4890	770
1	4890	770

prune93.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	89	10	99

Error

0.0b

Counts

99 → 10

Compiler

Compiled 1821 to 449 computations (75.3% saved)

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	623	690
1	623	690

regimes214.0ms (3.9%)

Compiler: Compiled 1744 to 1322 computations (24.2% saved)

bsearch0.0ms (0%)

regimes107.0ms (2%)

Compiler: Compiled 177 to 210 computations (-18.6% saved)

bsearch43.0ms (0.8%)

Steps

Iters	Range		Point
6	1.3827063248774922e+73	9.826545263290659e+73	1.566947469422516e+73
6	-1.2622681149058688e+62	-2.3896334660428343e+61	-5.110291561466219e+61

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes126.0ms (2.3%)

Compiler: Compiled 93 to 138 computations (-48.4% saved)

bsearch96.0ms (1.8%)

Steps

Iters	Range		Point
9	0.00012771932569782867	148216.87020837155	0.035175556323187133
7	-0.00031753722337157916	-1.9211000390631178e-05	-0.0003136828338515734
9	-5.076605944694576e+175	-2.0820810656550475e+169	-2.277340817064507e+172

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes90.0ms (1.7%)

Compiler: Compiled 78 to 120 computations (-53.8% saved)

bsearch46.0ms (0.9%)

Steps

Iters	Range		Point
10	5.4100461032050636e+20	3.1066890732198254e+31	5.461493382191782e+20
7	-0.00031753722337157916	-1.9211000390631178e-05	-0.0003136828338515734

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes34.0ms (0.6%)

Compiler: Compiled 66 to 105 computations (-59.1% saved)

bsearch0.0ms (0%)

regimes29.0ms (0.5%)

Compiler: Compiled 18 to 63 computations (-250% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.5%)

Compiler: Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.4%)

Accuracy

Total 0.1b remaining (73.5%)

Threshold costs 0.1b (73.5%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 103 to 78 computations (24.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	147	145
1	147	145

end0.0ms (0%)

sample2.0s (37.1%)

Algorithm

1×

intervals

Results

544.0ms	1993×	body	1024	valid
315.0ms	4488×	body	128	valid
197.0ms	1011×	body	512	valid
70.0ms	504×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 537 to 414 computations (22.9% saved)

Pareto

0.45336195961660536

Details

analyze264.0ms (4.9%)

sample42.0ms (0.8%)

simplify105.0ms (1.9%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite16.0ms (0.3%)

series351.0ms (6.5%)

simplify69.0ms (1.3%)

prune84.0ms (1.6%)

localize15.0ms (0.3%)

rewrite17.0ms (0.3%)

series287.0ms (5.3%)

simplify80.0ms (1.5%)

prune94.0ms (1.7%)

localize16.0ms (0.3%)

rewrite31.0ms (0.6%)

series425.0ms (7.9%)

simplify68.0ms (1.3%)

prune98.0ms (1.8%)

localize13.0ms (0.2%)

rewrite17.0ms (0.3%)

series290.0ms (5.4%)

simplify60.0ms (1.1%)

prune93.0ms (1.7%)

simplify19.0ms (0.3%)

regimes214.0ms (3.9%)

bsearch0.0ms (0%)

regimes107.0ms (2%)

bsearch43.0ms (0.8%)

regimes126.0ms (2.3%)

bsearch96.0ms (1.8%)

regimes90.0ms (1.7%)

bsearch46.0ms (0.9%)

regimes34.0ms (0.6%)

bsearch0.0ms (0%)

regimes29.0ms (0.5%)

bsearch0.0ms (0%)

regimes26.0ms (0.5%)

bsearch0.0ms (0%)

regimes22.0ms (0.4%)

bsearch6.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.0s (37.1%)

Profiling