Details

analyze733.0ms (7.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample23.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	11×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify221.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5232	30

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

25.8b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.7b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.3b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite83.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

25.6b

Rules

11×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
7×	`add-log-exp_binary64_1481`
5×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`pow1_binary64_1503` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `flip3-+_binary64_1445` `associate-/r/_binary64_1388` `flip-+_binary64_1416`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

3 → 55

Calls

3 calls:

9.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1509 to 201 computations (86.7% saved)

series622.0ms (6.7%)

Error

4.2b

Counts

3 → 69

Calls

3 calls:

346.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
134.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
92.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 2499 to 1601 computations (35.9% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4991	2974
1	4991	2974

prune124.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Error

4.1b

Counts

125 → 12

Compiler

Compiled 2545 to 989 computations (61.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
15.7b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
26.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.4b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite164.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

43×	`*-un-lft-identity_binary64_1442`
28×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
10×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
8×	`associate-/r*_binary64_1386`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l*_binary64_1387`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 3624 to 1413 computations (61% saved)

series957.0ms (10.3%)

Error

4.1b

Counts

4 → 96

Calls

4 calls:

426.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
167.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
138.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
131.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6048 to 3830 computations (36.7% saved)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5094	5035

prune244.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	193	11	204

Error

4.1b

Counts

204 → 11

Compiler

Compiled 5918 to 2440 computations (58.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
15.7b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
26.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.4b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite183.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

43×	`*-un-lft-identity_binary64_1442`
28×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
10×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
8×	`associate-/l*_binary64_1387`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/r*_binary64_1386`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `associate-/r/_binary64_1388` `flip--_binary64_1417`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 95

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 3780 to 1587 computations (58% saved)

series912.0ms (9.8%)

Error

4.1b

Counts

4 → 92

Calls

4 calls:

358.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
173.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
134.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
130.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 7206 to 4881 computations (32.3% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5143	5115

prune252.0ms (2.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	187	11	198

Error

4.0b

Counts

198 → 11

Compiler

Compiled 6290 to 2911 computations (53.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.7b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
1.1b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
24.6b	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite198.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

57×	`*-un-lft-identity_binary64_1442`
32×	`times-frac_binary64_1448`
31×	`add-sqr-sqrt_binary64_1464`
24×	`add-cube-cbrt_binary64_1477`
21×	`associate-r_binary64_1382`
17×	`add-exp-log_binary64_1480`
16×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
11×	`add-cbrt-cube_binary64_1478`
8×	`add-log-exp_binary64_1481`
7×	`pow1_binary64_1503`
5×	`associate-/r*_binary64_1386`
4×	`div-exp_binary64_1493` `prod-exp_binary64_1491` `associate-/r/_binary64_1388`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `unswap-sqr_binary64_1410` `associate-l_binary64_1383` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l*_binary64_1387`
2×	`1-exp_binary64_1486` `rec-exp_binary64_1492` `cbrt-unprod_binary64_1475` `cbrt-undiv_binary64_1476` `frac-times_binary64_1452` `associate-*l/_binary64_1385` `div-inv_binary64_1439`
1×	`pow-prod-down_binary64_1513` `un-div-inv_binary64_1440` `associate-r/_binary64_1384` `-commutative_binary64_1373` `inv-pow_binary64_1527` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 114

Calls

4 calls:

19.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
15.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 3152 to 1744 computations (44.7% saved)

series725.0ms (7.8%)

Error

4.0b

Counts

4 → 81

Calls

4 calls:

338.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
152.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
89.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
82.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3261 to 2406 computations (26.2% saved)

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5048	4216

prune194.0ms (2.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	195	11	206

Error

4.0b

Counts

206 → 11

Compiler

Compiled 3975 to 2082 computations (47.6% saved)

regimes1.2s (13.2%)

Accuracy

Total 9.7b remaining (67.6%)

Threshold costs 0b (0%)

Compiler

Compiled 8844 to 5603 computations (36.6% saved)

bsearch89.0ms (1%)

Steps

Iters	Range		Point
7	3.290682121393716e+152	2.422979362772352e+154	1.4163261492702185e+153
9	1.1684044936491682e-157	2.605506511486811e-150	5.980746905707731e-154
10	-4.998751043810138e-102	-1.1251155016854812e-112	-1.2031460365109471e-102
7	-2.846347883263074e+54	-4.362918788324185e+52	-2.6657023148269232e+54

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	156
1	89	156

end0.0ms (0%)

sample1.9s (20.7%)

Algorithm

1×

intervals

Results

349.0ms	8000×	body	128	valid
18.0ms	453×	body	128	invalid

Compiler

Compiled 1824 to 1154 computations (36.7% saved)

Details

analyze733.0ms (7.9%)

sample23.0ms (0.2%)

simplify221.0ms (2.4%)

prune2.0ms (0%)

localize14.0ms (0.1%)

rewrite83.0ms (0.9%)

series622.0ms (6.7%)

simplify77.0ms (0.8%)

prune124.0ms (1.3%)

localize17.0ms (0.2%)

rewrite164.0ms (1.8%)

series957.0ms (10.3%)

simplify94.0ms (1%)

prune244.0ms (2.6%)

localize20.0ms (0.2%)

rewrite183.0ms (2%)

series912.0ms (9.8%)

simplify92.0ms (1%)

prune252.0ms (2.7%)

localize11.0ms (0.1%)

rewrite198.0ms (2.1%)

series725.0ms (7.8%)

simplify100.0ms (1.1%)

prune194.0ms (2.1%)

regimes1.2s (13.2%)

bsearch89.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.9s (20.7%)

Profiling