Details

analyze1.6s (18.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5006	504
0	4	4
1	4	4

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)

sample110.0ms (1.3%)

Algorithm

1×

intervals

Results

34.0ms	68×	body	1024	invalid
27.0ms	242×	body	128	valid
11.0ms	33×	body	512	invalid
8.0ms	7×	body	1024	valid
3.0ms	12×	body	256	invalid
2.0ms	19×	body	128	invalid
2.0ms	2×	body	2048	valid
2.0ms	5×	body	512	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	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: 30.5b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
31.4b	(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)))

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:

8.0ms	(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.im)

series292.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(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)))
25.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
23.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
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 (101.0ms)

Iter	Nodes	Cost
0	4863	1251
1	4863	1251

prune113.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 19.7b

Counts

69 → 5

Compiler

Compiled 3039 to 864 computations (71.6% saved)

localize16.0ms (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)
2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite23.0ms (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:

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

series238.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(-.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))
74.0ms	(.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)
22.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4958	1662
1	4958	1662

prune99.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 3.3b

Counts

83 → 8

Compiler

Compiled 2207 to 1090 computations (50.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
0.0b	(-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
0.2b	(*.f64 (log.f64 x.re) y.re)
2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite23.0ms (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:

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

series232.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(exp.f64 (-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
82.0ms	(-.f64 (.f64 (log.f64 x.re) y.re) (.f64 (atan2.f64 x.im x.re) y.im))
38.0ms	(*.f64 (log.f64 x.re) y.re)
27.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5201	1277

prune71.0ms (0.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Merged error: 3.3b

Counts

84 → 10

Compiler

Compiled 1611 to 568 computations (64.7% saved)

localize14.0ms (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)))))
2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
2.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
2.7b	(*.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:

34.0ms	(.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)

series456.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(.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)))))
31.0ms	(*.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 (69.0ms)

Iter	Nodes	Cost
0	4932	8966
1	4932	8966

prune222.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	196	10	206

Merged error: 3.3b

Counts

206 → 10

Compiler

Compiled 9580 to 1445 computations (84.9% saved)

regimes469.0ms (5.6%)

Compiler: Compiled 3192 to 2170 computations (32% saved)

bsearch86.0ms (1%)

Steps

Iters	Range		Point
10	-1.3438403193467702e-297	1.5520194723550723e-306	7.0491519677833e-311

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	53
1	63	53

end0.0ms (0%)

sample3.7s (44.4%)

Algorithm

1×

intervals

Results

1.2s	2341×	body	1024	invalid
835.0ms	7593×	body	128	valid
327.0ms	954×	body	512	invalid
104.0ms	444×	body	256	invalid
88.0ms	175×	body	1024	valid
63.0ms	548×	body	128	invalid
49.0ms	142×	body	512	valid
31.0ms	42×	body	2048	invalid
18.0ms	79×	body	256	valid
9.0ms	11×	body	2048	valid

Compiler

Compiled 687 to 462 computations (32.8% saved)

Details

analyze1.6s (18.8%)

sample110.0ms (1.3%)

simplify66.0ms (0.8%)

prune8.0ms (0.1%)

localize24.0ms (0.3%)

rewrite28.0ms (0.3%)

series292.0ms (3.5%)

simplify119.0ms (1.4%)

prune113.0ms (1.4%)

localize16.0ms (0.2%)

rewrite23.0ms (0.3%)

series238.0ms (2.9%)

simplify65.0ms (0.8%)

prune99.0ms (1.2%)

localize11.0ms (0.1%)

rewrite23.0ms (0.3%)

series232.0ms (2.8%)

simplify47.0ms (0.6%)

prune71.0ms (0.9%)

localize14.0ms (0.2%)

rewrite76.0ms (0.9%)

series456.0ms (5.5%)

simplify152.0ms (1.8%)

prune222.0ms (2.7%)

regimes469.0ms (5.6%)

bsearch86.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.7s (44.4%)

Profiling