Details

analyze1.5s (17.2%)

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
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample119.0ms (1.4%)

Algorithm

1×

intervals

Results

46.0ms	78×	body	1024	invalid
29.0ms	246×	body	128	valid
12.0ms	31×	body	512	invalid
3.0ms	5×	body	1024	valid
3.0ms	12×	body	256	invalid
1.0ms	10×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify239.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4949	72
1	4949	72

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.2b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 (atan2.f64 x.im x.re) y.re)
30.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.6b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series513.0ms (6%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
51.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
43.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
43.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify114.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4809	1251
1	4809	1251

prune109.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 19.1b

Counts

69 → 4

Compiler

Compiled 2982 to 826 computations (72.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 65

Calls

4 calls:

6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series499.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
152.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
50.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
47.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4910	1650
1	4910	1650

prune98.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	75	6	81

Merged error: 3.2b

Counts

81 → 6

Compiler

Compiled 2116 to 1038 computations (50.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.0b	(exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
0.2b	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`associate-r_binary64`
3×	`exp-prod_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `log-pow_binary64` `exp-diff_binary64` `exp-sum_binary64` `flip--_binary64`

Counts

4 → 62

Calls

4 calls:

5.0ms	(exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
4.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
4.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series477.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
161.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
86.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
59.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5018	1367

prune66.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	73	7	80

Merged error: 3.2b

Counts

80 → 7

Compiler

Compiled 1601 to 514 computations (67.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
40×	`unpow-prod-down_binary64`
14×	`associate-/l*_binary64`
12×	`add-exp-log_binary64` `distribute-lft-neg-in_binary64` `add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `neg-mul-1_binary64` `sqr-pow_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 127

Calls

4 calls:

9.0ms	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

series345.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
51.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
46.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
42.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4955	3671
1	4955	3671

prune166.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	139	7	146

Merged error: 3.2b

Counts

146 → 7

Compiler

Compiled 6618 to 899 computations (86.4% saved)

regimes186.0ms (2.2%)

Compiler: Compiled 948 to 656 computations (30.8% saved)

bsearch155.0ms (1.8%)

Steps

Iters	Range		Point
9	-3.3717620368255286e-301	1.3885635823988996e-307	8.064492694088511e-308
9	-4.831977407349566e+44	-2.979728947696884e+39	-3.0256129117146835e+39

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	96
1	80	96

end0.0ms (0%)

sample3.5s (41.1%)

Algorithm

1×

intervals

Results

1.3s	2332×	body	1024	invalid
857.0ms	7601×	body	128	valid
325.0ms	901×	body	512	invalid
98.0ms	405×	body	256	invalid
96.0ms	166×	body	1024	valid
66.0ms	555×	body	128	invalid
45.0ms	124×	body	512	valid
30.0ms	34×	body	2048	invalid
22.0ms	95×	body	256	valid
14.0ms	14×	body	2048	valid

Compiler

Compiled 322 to 209 computations (35.1% saved)

Details

analyze1.5s (17.2%)

sample119.0ms (1.4%)

simplify239.0ms (2.8%)

prune8.0ms (0.1%)

localize30.0ms (0.4%)

rewrite30.0ms (0.4%)

series513.0ms (6%)

simplify114.0ms (1.3%)

prune109.0ms (1.3%)

localize15.0ms (0.2%)

rewrite25.0ms (0.3%)

series499.0ms (5.9%)

simplify75.0ms (0.9%)

prune98.0ms (1.2%)

localize12.0ms (0.1%)

rewrite22.0ms (0.3%)

series477.0ms (5.6%)

simplify67.0ms (0.8%)

prune66.0ms (0.8%)

localize17.0ms (0.2%)

rewrite41.0ms (0.5%)

series345.0ms (4.1%)

simplify115.0ms (1.3%)

prune166.0ms (2%)

regimes186.0ms (2.2%)

bsearch155.0ms (1.8%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.5s (41.1%)

Profiling