Details

analyze1.5s (16%)

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)

sample117.0ms (1.3%)

Algorithm

1×

intervals

Results

44.0ms	77×	body	1024	invalid
34.0ms	248×	body	128	valid
12.0ms	28×	body	512	invalid
3.0ms	10×	body	256	invalid
2.0ms	18×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	4×	body	256	valid
1.0ms	2×	body	512	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify231.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

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

Merged error: 31.6b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.7b	(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)))

rewrite31.0ms (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:

10.0ms	(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.im)

series507.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

373.0ms	(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)))
47.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
42.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify116.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4863	1251
1	4863	1251

prune111.0ms (1.2%)

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: 16.6b

Counts

69 → 4

Compiler

Compiled 3000 to 836 computations (72.1% saved)

localize16.0ms (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)
29.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite28.0ms (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:

7.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
6.0ms	(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)))
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.im)

series479.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(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)))
141.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
45.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
44.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4953	1596
1	4953	1596

prune104.0ms (1.1%)

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

Merged error: 2.6b

Counts

85 → 7

Compiler

Compiled 2194 to 1045 computations (52.4% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
40×	`unpow-prod-down_binary64`
38×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`associate-/l*_binary64`
12×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`neg-mul-1_binary64` `sqr-pow_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `exp-to-pow_binary64` `pow-exp_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

3 → 101

Calls

3 calls:

11.0ms	(/.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)
2.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))

series328.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

223.0ms	(/.f64 (pow.f64 (neg.f64 x.re) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im)))
60.0ms	(exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))
45.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5007	3324

prune105.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	109	8	117

Merged error: 2.6b

Counts

117 → 8

Compiler

Compiled 2622 to 740 computations (71.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (neg.f64 x.re))
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)

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-neg-in_binary64` `unswap-sqr_binary64` `distribute-rgt-neg-in_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`pow1/3_binary64` `neg-mul-1_binary64`

Counts

4 → 72

Calls

4 calls:

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)
2.0ms	(cbrt.f64 (neg.f64 x.re))

series309.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt.f64 (neg.f64 x.re))
48.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
43.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
42.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4864	1004
1	4864	1004

prune108.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	84	8	92

Merged error: 2.6b

Counts

92 → 8

Compiler

Compiled 3767 to 557 computations (85.2% saved)

regimes382.0ms (4.1%)

Compiler: Compiled 3217 to 2110 computations (34.4% saved)

bsearch355.0ms (3.8%)

Steps

Iters	Range		Point
9	2.0127026023608453e-80	7.0794449952514586e-71	2.3965001777473233e-78
9	1.663723895030559e-195	5.312962113335841e-190	4.850736462389239e-194
9	-6.139068561378969e-303	3.979131364867758e-308	3.92947659999936e-310
5	-1.6115313855752777e-43	-6.423227623683697e-44	-8.430888126662982e-44
5	-5.958152191737171e+18	-1.9166237221040312e+18	-1.9459793054640932e+18

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	203
1	101	203

end0.0ms (0%)

sample4.0s (43.7%)

Algorithm

1×

intervals

Results

1.4s	2414×	body	1024	invalid
867.0ms	7552×	body	128	valid
355.0ms	970×	body	512	invalid
104.0ms	416×	body	256	invalid
102.0ms	183×	body	1024	valid
70.0ms	581×	body	128	invalid
57.0ms	151×	body	512	valid
35.0ms	37×	body	2048	invalid
26.0ms	106×	body	256	valid
11.0ms	8×	body	2048	valid

Compiler

Compiled 769 to 476 computations (38.1% saved)

Details

analyze1.5s (16%)

sample117.0ms (1.3%)

simplify231.0ms (2.5%)

prune14.0ms (0.2%)

localize24.0ms (0.3%)

rewrite31.0ms (0.3%)

series507.0ms (5.5%)

simplify116.0ms (1.3%)

prune111.0ms (1.2%)

localize16.0ms (0.2%)

rewrite28.0ms (0.3%)

series479.0ms (5.2%)

simplify85.0ms (0.9%)

prune104.0ms (1.1%)

localize11.0ms (0.1%)

rewrite28.0ms (0.3%)

series328.0ms (3.6%)

simplify103.0ms (1.1%)

prune105.0ms (1.1%)

localize20.0ms (0.2%)

rewrite25.0ms (0.3%)

series309.0ms (3.4%)

simplify75.0ms (0.8%)

prune108.0ms (1.2%)

regimes382.0ms (4.1%)

bsearch355.0ms (3.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample4.0s (43.7%)

Profiling