Details

analyze1.5s (12.7%)

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample117.0ms (1%)

Algorithm

1×

intervals

Results

42.0ms	65×	body	1024	invalid
29.0ms	244×	body	128	valid
10.0ms	25×	body	512	invalid
8.0ms	14×	body	256	invalid
3.0ms	2×	body	2048	invalid
2.0ms	6×	body	512	valid
2.0ms	15×	body	128	invalid
2.0ms	3×	body	1024	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify242.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 32.8b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.3b	(sin.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 (0.3%)

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(sin.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)))
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)

series508.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(sin.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)))
44.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
43.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
39.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4884	1270
1	4884	1270

prune116.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 17.7b

Counts

70 → 6

Compiler

Compiled 3096 to 890 computations (71.3% saved)

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
35.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
35.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) 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)))

series1.1s (9.2%)

Counts

4 → 12

Calls

4 calls:

360.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
346.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
332.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
40.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5056	1579

prune184.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Merged error: 17.7b

Counts

57 → 7

Compiler

Compiled 4552 to 2359 computations (48.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

rewrite27.0ms (0.2%)

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` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
5.0ms	(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)

series488.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

353.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
48.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
45.0ms	(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)))

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4884	1270
1	4884	1270

prune105.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 17.7b

Counts

75 → 7

Compiler

Compiled 2995 to 841 computations (71.9% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

10.9b	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))) 3))
29.7b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
6×	`pow1_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cube-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`rem-cbrt-cube_binary64` `pow1/3_binary64` `sin-sum_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 61

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))) 3))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

series754.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

340.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
327.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re))) 3))
47.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
40.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5157	2116

prune134.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	72	8	80

Merged error: 17.7b

Counts

80 → 8

Compiler

Compiled 3323 to 1447 computations (56.5% saved)

regimes823.0ms (7%)

Compiler: Compiled 8042 to 5420 computations (32.6% saved)

bsearch102.0ms (0.9%)

Steps

Iters	Range		Point
9	-6.462275146886427e-300	3.979131364867758e-308	2.14883129594067e-310

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	74	129
1	74	129

end0.0ms (0%)

sample4.9s (42.3%)

Algorithm

1×

intervals

Results

1.5s	2485×	body	1024	invalid
892.0ms	7559×	body	128	valid
352.0ms	903×	body	512	invalid
207.0ms	171×	body	2048	invalid
92.0ms	160×	body	1024	valid
87.0ms	356×	body	256	invalid
60.0ms	488×	body	128	invalid
59.0ms	158×	body	512	valid
27.0ms	109×	body	256	valid
16.0ms	14×	body	2048	valid

Compiler

Compiled 1695 to 1123 computations (33.7% saved)

Details

analyze1.5s (12.7%)

sample117.0ms (1%)

simplify242.0ms (2.1%)

prune9.0ms (0.1%)

localize24.0ms (0.2%)

rewrite30.0ms (0.3%)

series508.0ms (4.3%)

simplify102.0ms (0.9%)

prune116.0ms (1%)

localize41.0ms (0.3%)

rewrite35.0ms (0.3%)

series1.1s (9.2%)

simplify75.0ms (0.6%)

prune184.0ms (1.6%)

localize23.0ms (0.2%)

rewrite27.0ms (0.2%)

series488.0ms (4.2%)

simplify102.0ms (0.9%)

prune105.0ms (0.9%)

localize35.0ms (0.3%)

rewrite36.0ms (0.3%)

series754.0ms (6.4%)

simplify78.0ms (0.7%)

prune134.0ms (1.1%)

regimes823.0ms (7%)

bsearch102.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.9s (42.3%)

Profiling