Details

analyze1.5s (16.4%)

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
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 (1.3%)

Algorithm

1×

intervals

Results

48.0ms	78×	body	1024	invalid
30.0ms	246×	body	128	valid
12.0ms	31×	body	512	invalid
3.0ms	5×	body	1024	valid
3.0ms	12×	body	256	invalid
1.0ms	5×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify233.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune12.0ms (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 146 to 76 computations (47.9% saved)

localize24.0ms (0.3%)

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)))

rewrite35.0ms (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:

14.0ms	(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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

series516.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

374.0ms	(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)))
50.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
49.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5167	1251

prune149.0ms (1.7%)

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 3866 to 1406 computations (63.6% saved)

localize19.0ms (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` `cancel-sign-sub-inv_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 66

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)

series505.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(-.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))
141.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
54.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
50.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4958	1662
1	4958	1662

prune127.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Merged error: 3.2b

Counts

82 → 6

Compiler

Compiled 2720 to 1461 computations (46.3% 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)

rewrite24.0ms (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` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `log-pow_binary64` `exp-diff_binary64` `flip--_binary64`

Counts

4 → 64

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

series459.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
167.0ms	(exp.f64 (-.f64 (.f64 (log.f64 (neg.f64 x.re)) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
75.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
49.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify108.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4987	1395
1	4987	1395

prune102.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	7	82

Merged error: 3.2b

Counts

82 → 7

Compiler

Compiled 2280 to 970 computations (57.5% 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)

rewrite40.0ms (0.4%)

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:

8.0ms	(/.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)

series355.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
57.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
44.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
41.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify105.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4987	3671
1	4987	3671

prune170.0ms (1.9%)

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)

regimes334.0ms (3.7%)

Compiler: Compiled 2027 to 1375 computations (32.2% saved)

bsearch161.0ms (1.8%)

Steps

Iters	Range		Point
9	-3.3717620368255286e-301	1.3885635823988996e-307	-2.9795338187053e-310
8	-2.6633705815960678	-7.624617286107797e-05	-0.00016347183500136866

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	80	96
1	80	96

end0.0ms (0%)

sample3.7s (41.5%)

Algorithm

1×

intervals

Results

1.3s	2332×	body	1024	invalid
878.0ms	7601×	body	128	valid
336.0ms	901×	body	512	invalid
107.0ms	405×	body	256	invalid
94.0ms	166×	body	1024	valid
67.0ms	555×	body	128	invalid
49.0ms	124×	body	512	valid
31.0ms	34×	body	2048	invalid
23.0ms	95×	body	256	valid
16.0ms	14×	body	2048	valid

Compiler

Compiled 476 to 314 computations (34% saved)

Details

analyze1.5s (16.4%)

sample119.0ms (1.3%)

simplify233.0ms (2.6%)

prune12.0ms (0.1%)

localize24.0ms (0.3%)

rewrite35.0ms (0.4%)

series516.0ms (5.7%)

simplify82.0ms (0.9%)

prune149.0ms (1.7%)

localize19.0ms (0.2%)

rewrite25.0ms (0.3%)

series505.0ms (5.6%)

simplify63.0ms (0.7%)

prune127.0ms (1.4%)

localize12.0ms (0.1%)

rewrite24.0ms (0.3%)

series459.0ms (5.1%)

simplify108.0ms (1.2%)

prune102.0ms (1.1%)

localize17.0ms (0.2%)

rewrite40.0ms (0.4%)

series355.0ms (3.9%)

simplify105.0ms (1.2%)

prune170.0ms (1.9%)

regimes334.0ms (3.7%)

bsearch161.0ms (1.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.7s (41.5%)

Profiling