Details

analyze521.0ms (11.5%)

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)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify411.0ms (9.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (241.0ms)

Iter	Nodes	Cost
0	5127	30

prune2.0ms (0.1%)

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: 26.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.8b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1109` `*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
9×	`times-frac_binary64_1094`
7×	`add-log-exp_binary64_1124`
5×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
3×	`associate-/r_binary64_1034` `pow1_binary64_1146` `associate-/l_binary64_1035`
2×	`flip3--_binary64_1092` `associate-/l/_binary64_1037` `flip--_binary64_1063` `associate-/r/_binary64_1036` `flip-+_binary64_1062` `flip3-+_binary64_1091`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `sub-neg_binary64_1081` `sum-log_binary64_1176` `div-exp_binary64_1136` `div-sub_binary64_1093` `+-commutative_binary64_1020` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

3 → 54

Calls

3 calls:

12.0ms	(/.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))

series322.0ms (7.1%)

Counts

3 → 9

Calls

3 calls:

197.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
87.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
38.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5716	1814

prune94.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	7	64

Merged error: 25.5b

Counts

64 → 7

Compiler

Compiled 1628 to 667 computations (59% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.6b	(/.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))))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1088`
28×	`sqrt-prod_binary64_1103`
25×	`add-sqr-sqrt_binary64_1109`
24×	`times-frac_binary64_1094`
23×	`add-cube-cbrt_binary64_1120`
10×	`unpow-prod-down_binary64_1164` `distribute-lft-out_binary64_1041`
8×	`associate-/r*_binary64_1034`
6×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `sqrt-div_binary64_1104` `add-log-exp_binary64_1124` `pow1_binary64_1146`
3×	`flip-+_binary64_1062` `flip3-+_binary64_1091` `associate-/l*_binary64_1035`
2×	`rem-sqrt-square_binary64_1101` `flip3--_binary64_1092` `associate-/l/_binary64_1037` `flip--_binary64_1063` `associate-/r/_binary64_1036` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `sub-neg_binary64_1081` `div-exp_binary64_1136` `div-sub_binary64_1093` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

4 → 95

Calls

4 calls:

17.0ms	(/.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))))
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 x.im y.re) (.f64 x.re y.im))

series430.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(/.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))))
93.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
49.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
42.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5185	3239

prune150.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	104	10	114

Merged error: 23.1b

Counts

114 → 10

Compiler

Compiled 3703 to 1560 computations (57.9% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.7b	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite52.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_1088`
36×	`add-sqr-sqrt_binary64_1109`
30×	`associate-r_binary64_1030`
28×	`times-frac_binary64_1094`
25×	`sqrt-prod_binary64_1103`
22×	`add-cube-cbrt_binary64_1120`
13×	`add-exp-log_binary64_1123`
9×	`add-cbrt-cube_binary64_1121`
8×	`unpow-prod-down_binary64_1164` `pow1_binary64_1146` `distribute-lft-out_binary64_1041`
6×	`sqrt-div_binary64_1104` `add-log-exp_binary64_1124`
5×	`unswap-sqr_binary64_1056`
4×	`prod-exp_binary64_1134`
3×	`flip3--_binary64_1092` `flip--_binary64_1063` `associate-l_binary64_1031` `flip-+_binary64_1062` `flip3-+_binary64_1091`
2×	`rem-sqrt-square_binary64_1101` `associate-*l/_binary64_1033` `cbrt-unprod_binary64_1118` `frac-times_binary64_1098` `associate-/r/_binary64_1036` `div-exp_binary64_1136` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`-commutative_binary64_1021` `sub-neg_binary64_1081` `rec-exp_binary64_1135` `un-div-inv_binary64_1086` `1-exp_binary64_1129` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `pow-prod-down_binary64_1156` `associate-r/_binary64_1032` `div-inv_binary64_1085`

Counts

4 → 102

Calls

4 calls:

23.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (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 x.im y.re) (.f64 x.re y.im))

series413.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
76.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
46.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
46.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5192	2914

prune159.0ms (3.5%)

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

Merged error: 23.1b

Counts

124 → 10

Compiler

Compiled 3967 to 1856 computations (53.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.7b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.6b	(.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))))

rewrite56.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64_1088`
32×	`times-frac_binary64_1094`
31×	`add-sqr-sqrt_binary64_1109`
24×	`add-cube-cbrt_binary64_1120`
21×	`associate-r_binary64_1030`
17×	`add-exp-log_binary64_1123`
16×	`unpow-prod-down_binary64_1164` `distribute-lft-out_binary64_1041`
11×	`add-cbrt-cube_binary64_1121`
8×	`add-log-exp_binary64_1124`
7×	`pow1_binary64_1146`
5×	`associate-/r*_binary64_1034`
4×	`associate-/r/_binary64_1036` `div-exp_binary64_1136` `prod-exp_binary64_1134`
3×	`unswap-sqr_binary64_1056` `flip3--_binary64_1092` `flip--_binary64_1063` `associate-l_binary64_1031` `flip-+_binary64_1062` `flip3-+_binary64_1091` `associate-/l*_binary64_1035`
2×	`associate-*l/_binary64_1033` `cbrt-unprod_binary64_1118` `frac-times_binary64_1098` `rec-exp_binary64_1135` `1-exp_binary64_1129` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`
1×	`-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `inv-pow_binary64_1170` `sub-neg_binary64_1081` `sum-log_binary64_1176` `un-div-inv_binary64_1086` `+-commutative_binary64_1020` `diff-log_binary64_1177` `pow-prod-down_binary64_1156` `pow-flip_binary64_1159` `associate-r/_binary64_1032`

Counts

4 → 113

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))))
11.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
10.0ms	(/.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))

series352.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(.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))))
78.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
46.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
35.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5226	2881

prune135.0ms (3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	125	10	135

Merged error: 23.1b

Counts

135 → 10

Compiler

Compiled 2868 to 1538 computations (46.4% saved)

regimes105.0ms (2.3%)

Compiler: Compiled 840 to 684 computations (18.6% saved)

bsearch18.0ms (0.4%)

Steps

Iters	Range		Point
7	8.552798055396875e+67	1.631459502626628e+69	3.641078765129503e+68

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	77
1	63	77

end0.0ms (0%)

sample841.0ms (18.6%)

Algorithm

1×

intervals

Results

344.0ms	8000×	body	128	valid
20.0ms	490×	body	128	invalid

Compiler

Compiled 264 to 203 computations (23.1% saved)

Details

analyze521.0ms (11.5%)

sample30.0ms (0.7%)

simplify411.0ms (9.1%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite25.0ms (0.6%)

series322.0ms (7.1%)

simplify74.0ms (1.6%)

prune94.0ms (2.1%)

localize17.0ms (0.4%)

rewrite45.0ms (1%)

series430.0ms (9.5%)

simplify68.0ms (1.5%)

prune150.0ms (3.3%)

localize21.0ms (0.5%)

rewrite52.0ms (1.2%)

series413.0ms (9.1%)

simplify77.0ms (1.7%)

prune159.0ms (3.5%)

localize12.0ms (0.3%)

rewrite56.0ms (1.2%)

series352.0ms (7.8%)

simplify80.0ms (1.8%)

prune135.0ms (3%)

regimes105.0ms (2.3%)

bsearch18.0ms (0.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample841.0ms (18.6%)

Profiling