Details

analyze1.4s (16.8%)

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)

sample118.0ms (1.4%)

Algorithm

1×

intervals

Results

47.0ms	81×	body	1024	invalid
28.0ms	244×	body	128	valid
14.0ms	39×	body	512	invalid
3.0ms	12×	body	256	invalid
3.0ms	5×	body	1024	valid
2.0ms	6×	body	512	valid
2.0ms	18×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify158.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune14.0ms (0.2%)

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

Error

37.2b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
31.0b	(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)))
34.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite28.0ms (0.3%)

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:

7.0ms	(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)))
6.0ms	(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.im)

series294.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(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)))
34.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify119.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4863	1251
1	4863	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

Error

21.0b

Counts

69 → 4

Compiler

Compiled 3000 to 828 computations (72.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.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)
34.1b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
6×	`associate-r_binary64`
3×	`log-pow_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 69

Calls

4 calls:

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

series257.0ms (3%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(exp.f64 (-.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)))
71.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
27.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
23.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4953	1596
1	4953	1596

prune99.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

3.4b

Counts

85 → 7

Compiler

Compiled 2194 to 1037 computations (52.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (pow.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)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `sqr-pow_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

2 → 63

Calls

2 calls:

5.0ms	(/.f64 (pow.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)

series142.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

116.0ms	(/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
26.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5032	1852

prune63.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Error

3.4b

Counts

76 → 8

Compiler

Compiled 1586 to 502 computations (68.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (cbrt.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) (cbrt.f64 (/.f64 (pow.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)

rewrite76.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`add-sqr-sqrt_binary64`
140×	`cbrt-prod_binary64`
114×	`times-frac_binary64`
70×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
46×	`unpow-prod-down_binary64`
37×	`associate-r_binary64` `associate-l_binary64`
28×	`swap-sqr_binary64` `unswap-sqr_binary64`
22×	`sqr-pow_binary64`
17×	`pow1_binary64`
12×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
6×	`pow1/3_binary64`
5×	`pow-prod-down_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64` `*-commutative_binary64`
2×	`pow-prod-up_binary64` `pow-sqr_binary64`
1×	`associate-r/_binary64` `pow-plus_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64`

Counts

4 → 184

Calls

4 calls:

32.0ms	(.f64 (cbrt.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) (cbrt.f64 (/.f64 (pow.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)

series459.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

377.0ms	(.f64 (cbrt.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im)))) (cbrt.f64 (/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))))
32.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
25.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
24.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify152.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4932	8966
1	4932	8966

prune242.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	196	8	204

Error

3.4b

Counts

204 → 8

Compiler

Compiled 9580 to 1445 computations (84.9% saved)

regimes506.0ms (5.9%)

Accuracy

Total 5.2b remaining (61.5%)

Threshold costs 0b (0%)

Compiler

Compiled 4337 to 2485 computations (42.7% saved)

bsearch262.0ms (3.1%)

Steps

Iters	Range	Point
10	-1.580981949934583e-298	5.542257536724659e-307	-3.27886602974523e-310
9	-6.288966763378732e-158	-5.625656401323206e-163	-1.4463420928420722e-158
10	-1.2234419803510532e-24	-3.4194638415434316e-40	-2.9631297454697988e-33

Iters

Range

Point

-1.580981949934583e-298

5.542257536724659e-307

-3.27886602974523e-310

-6.288966763378732e-158

-5.625656401323206e-163

-1.4463420928420722e-158

-1.2234419803510532e-24

-3.4194638415434316e-40

-2.9631297454697988e-33

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	127
1	83	127

end0.0ms (0%)

sample3.8s (44.1%)

Algorithm

1×

intervals

Results

1.2s	2450×	body	1024	invalid
838.0ms	7614×	body	128	valid
337.0ms	999×	body	512	invalid
98.0ms	433×	body	256	invalid
82.0ms	161×	body	1024	valid
66.0ms	568×	body	128	invalid
47.0ms	139×	body	512	valid
20.0ms	77×	body	256	valid
18.0ms	25×	body	2048	invalid
7.0ms	9×	body	2048	valid

Compiler

Compiled 954 to 539 computations (43.5% saved)

Details

analyze1.4s (16.8%)

sample118.0ms (1.4%)

simplify158.0ms (1.8%)

prune14.0ms (0.2%)

localize23.0ms (0.3%)

rewrite28.0ms (0.3%)

series294.0ms (3.4%)

simplify119.0ms (1.4%)

prune109.0ms (1.3%)

localize19.0ms (0.2%)

rewrite24.0ms (0.3%)

series257.0ms (3%)

simplify83.0ms (1%)

prune99.0ms (1.2%)

localize10.0ms (0.1%)

rewrite14.0ms (0.2%)

series142.0ms (1.7%)

simplify67.0ms (0.8%)

prune63.0ms (0.7%)

localize13.0ms (0.2%)

rewrite76.0ms (0.9%)

series459.0ms (5.3%)

simplify152.0ms (1.8%)

prune242.0ms (2.8%)

regimes506.0ms (5.9%)

bsearch262.0ms (3.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.8s (44.1%)

Profiling