Details

analyze518.0ms (6.4%)

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)

sample20.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify217.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

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

26.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
26.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `cancel-sign-sub-inv_binary64_1067` `div-sub_binary64_1106`

Counts

2 → 44

Calls

2 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 x.im y.re) (.f64 x.re y.im))

series472.0ms (5.9%)

Counts

2 → 51

Calls

2 calls:

320.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
152.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1161 to 954 computations (17.8% saved)

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	6016	2391

prune108.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	87	8	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	8	96

Error

3.1b

Counts

96 → 8

Compiler

Compiled 1936 to 680 computations (64.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
17.5b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
28.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1101`
30×	`sqrt-prod_binary64_1117`
25×	`add-sqr-sqrt_binary64_1123`
24×	`times-frac_binary64_1107`
23×	`add-cube-cbrt_binary64_1136`
12×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
8×	`associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
3×	`flip3-+_binary64_1104` `associate-/l*_binary64_1046` `flip-+_binary64_1075`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `pow1/2_binary64_1181`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `div-sub_binary64_1106`

Counts

4 → 98

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series822.0ms (10.2%)

Counts

4 → 91

Calls

4 calls:

429.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
164.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
117.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
111.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3618 to 3078 computations (14.9% saved)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4983	4883
1	4983	4883

prune312.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	189	8	197

Error

3.1b

Counts

197 → 8

Compiler

Compiled 6143 to 3696 computations (39.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.4b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.4b	(.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))))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1101`
32×	`times-frac_binary64_1107`
30×	`add-sqr-sqrt_binary64_1123`
23×	`add-cube-cbrt_binary64_1136`
21×	`associate-r_binary64_1041`
16×	`add-exp-log_binary64_1139`
14×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
10×	`add-cbrt-cube_binary64_1137`
6×	`pow1_binary64_1162`
5×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045`
4×	`prod-exp_binary64_1150` `associate-/r/_binary64_1047` `div-exp_binary64_1152`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l_binary64_1046` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`
2×	`1-exp_binary64_1145` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `flip3-+_binary64_1104` `div-inv_binary64_1098` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `associate-*l/_binary64_1044`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `cancel-sign-sub-inv_binary64_1067` `pow-flip_binary64_1175` `un-div-inv_binary64_1099`

Counts

3 → 101

Calls

3 calls:

21.0ms	(.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))))
9.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series581.0ms (7.2%)

Counts

3 → 63

Calls

3 calls:

328.0ms	(.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))))
166.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
87.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 1635 to 1440 computations (11.9% saved)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5155	3653

prune162.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	164	8	172

Error

3.1b

Counts

172 → 8

Compiler

Compiled 3498 to 1864 computations (46.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.2b	(cbrt.f64 (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
26.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite78.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64_1101`
60×	`times-frac_binary64_1107`
43×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
30×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
21×	`cbrt-prod_binary64_1132`
15×	`associate-/r*_binary64_1045`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`associate-/l*_binary64_1046`
8×	`associate-/r/_binary64_1047`
6×	`associate-/l/_binary64_1048`
4×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `div-sub_binary64_1106`
1×	`pow1/3_binary64_1183` `cbrt-div_binary64_1133`

Counts

4 → 150

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
12.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
11.0ms	(cbrt.f64 (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

series1.5s (18.9%)

Counts

4 → 103

Calls

4 calls:

444.0ms	(cbrt.f64 (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
365.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
357.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
351.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 8721 to 5978 computations (31.5% saved)

simplify130.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5006	8980

prune679.0ms (8.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	253	8	261

Error

3.1b

Counts

261 → 8

Compiler

Compiled 14285 to 6706 computations (53.1% saved)

regimes651.0ms (8.1%)

Accuracy

Total 9.4b remaining (65.6%)

Threshold costs 0b (0%)

Compiler

Compiled 4028 to 2929 computations (27.3% saved)

bsearch69.0ms (0.9%)

Steps

Iters	Range		Point
9	2.449785227828945e+136	4.180276525269703e+142	3.237823215092107e+141
5	9.185935165691043e-122	2.705138498078679e-121	2.0246643543322144e-121
5	-6.317464190349449e-132	-2.7867758429039275e-132	-5.1209567346932005e-132
9	-1.751636783636788e+25	-9.910630632959035e+19	-1.7351387155195298e+25

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	174
1	88	174

end0.0ms (0%)

sample1.3s (16%)

Algorithm

1×

intervals

Results

336.0ms	8000×	body	128	valid
19.0ms	477×	body	128	invalid

Compiler

Compiled 906 to 642 computations (29.1% saved)

Details

analyze518.0ms (6.4%)

sample20.0ms (0.2%)

simplify217.0ms (2.7%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite16.0ms (0.2%)

series472.0ms (5.9%)

simplify85.0ms (1%)

prune108.0ms (1.3%)

localize13.0ms (0.2%)

rewrite45.0ms (0.6%)

series822.0ms (10.2%)

simplify92.0ms (1.1%)

prune312.0ms (3.9%)

localize11.0ms (0.1%)

rewrite43.0ms (0.5%)

series581.0ms (7.2%)

simplify92.0ms (1.1%)

prune162.0ms (2%)

localize16.0ms (0.2%)

rewrite78.0ms (1%)

series1.5s (18.9%)

simplify130.0ms (1.6%)

prune679.0ms (8.4%)

regimes651.0ms (8.1%)

bsearch69.0ms (0.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (16%)

Profiling