Details

analyze115.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
31.2%	50%	18.8%	7
40.6%	37.5%	22%	8
45.3%	26.5%	28.2%	9
46.8%	19.5%	33.7%	10
48.8%	14%	37.2%	11
51.7%	10.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	5.1%	41.6%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 39 to 25 computations (35.9% saved)

simplify241.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4956	20
1	4956	20

prune4.0ms (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

Error

8.8b

Counts

2 → 2

Compiler

Compiled 41 to 29 computations (29.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))
0.1b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
8.3b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

rewrite36.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-*l/_binary64_3090` `add-sqr-sqrt_binary64_3169`
8×	`*-un-lft-identity_binary64_3147` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
7×	`associate-l_binary64_3088`
6×	`associate-r_binary64_3087`
4×	`flip--_binary64_3122` `flip-+_binary64_3121` `flip3--_binary64_3151` `flip3-+_binary64_3150` `frac-sub_binary64_3156`
2×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
1×	`cancel-sign-sub-inv_binary64_3113` `sub-neg_binary64_3140` `+-commutative_binary64_3077` `difference-of-squares_binary64_3116` `diff-log_binary64_3239` `sum-log_binary64_3238`

Counts

4 → 68

Calls

4 calls:

10.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
8.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
7.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
4.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

series125.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
37.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
29.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
18.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

simplify48.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4685	1737
1	4685	1737

prune97.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	75	7	82

Error

0.1b

Counts

82 → 7

Compiler

Compiled 2090 to 893 computations (57.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x.re (-.f64 x.re x.im))
0.1b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.2b	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))

rewrite64.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097`
31×	`cancel-sign-sub-inv_binary64_3113`
26×	`associate-*r/_binary64_3089`
25×	`add-sqr-sqrt_binary64_3169`
24×	`associate-*l/_binary64_3090`
23×	`*-un-lft-identity_binary64_3147`
19×	`add-cube-cbrt_binary64_3182`
18×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
16×	`associate--l+_binary64_3084` `frac-sub_binary64_3156`
13×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
12×	`frac-times_binary64_3157`
11×	`flip--_binary64_3122` `flip3--_binary64_3151` `sub-neg_binary64_3140`
10×	`associate-l_binary64_3088`
9×	`associate-r_binary64_3087`
6×	`add-log-exp_binary64_3186`
5×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
3×	`*-commutative_binary64_3078`
2×	`unswap-sqr_binary64_3115`
1×	`distribute-lft-out_binary64_3098` `distribute-lft-out--_binary64_3099` `difference-of-squares_binary64_3116` `diff-log_binary64_3239`

Counts

4 → 137

Calls

4 calls:

17.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
12.0ms	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))
9.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
8.0ms	(*.f64 x.re (-.f64 x.re x.im))

series135.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
38.0ms	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))
28.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
27.0ms	(*.f64 x.re (-.f64 x.re x.im))

simplify103.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4702	3820
1	4702	3820

prune343.0ms (9.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	148	8	156

Error

0.0b

Counts

156 → 8

Compiler

Compiled 3932 to 1396 computations (64.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 x.re x.re) (+.f64 x.re x.im)) (.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (.f64 x.re x.im)))))
0.2b	(+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (*.f64 x.re x.im)))
0.2b	(.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (.f64 x.re x.im))))
5.7b	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))

rewrite56.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_3169` `associate-*r/_binary64_3089`
11×	`-un-lft-identity_binary64_3147` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `associate-l*_binary64_3088`
9×	`add-cube-cbrt_binary64_3182`
8×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `add-log-exp_binary64_3186`
7×	`associate-r_binary64_3087`
5×	`distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097`
4×	`frac-add_binary64_3155` `pow-prod-down_binary64_3218` `associate-+l+_binary64_3080` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
3×	`distribute-lft-neg-in_binary64_3104` `distribute-rgt-neg-in_binary64_3105`
2×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `+-commutative_binary64_3077` `associate-+r+_binary64_3079` `distribute-lft-neg-out_binary64_3106` `sum-log_binary64_3238`
1×	`unsub-neg_binary64_3141` `neg-mul-1_binary64_3143` `distribute-lft-out_binary64_3098`

Counts

4 → 87

Calls

4 calls:

13.0ms	(+.f64 (.f64 (.f64 x.re x.re) (+.f64 x.re x.im)) (.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (.f64 x.re x.im)))))
13.0ms	(.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (.f64 x.re x.im))))
9.0ms	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))
8.0ms	(+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (*.f64 x.re x.im)))

series143.0ms (4%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (.f64 x.re x.im))))
40.0ms	(+.f64 (.f64 (.f64 x.re x.re) (+.f64 x.re x.im)) (.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (.f64 x.re x.im)))))
27.0ms	(+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (*.f64 x.re x.im)))
26.0ms	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))

simplify86.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5011	2769

prune116.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	100	7	107

Error

0.0b

Counts

107 → 7

Compiler

Compiled 2916 to 1251 computations (57.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 x.re x.re) (+.f64 x.re x.im)) (neg.f64 (.f64 x.im (.f64 x.re (+.f64 x.re (*.f64 x.im 3))))))
0.2b	(.f64 x.re (+.f64 x.re (.f64 x.im 3)))
0.2b	(.f64 x.im (.f64 x.re (+.f64 x.re (*.f64 x.im 3))))
5.7b	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))

rewrite45.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/_binary64_3089`
16×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
11×	`add-sqr-sqrt_binary64_3169` `distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097`
10×	`*-un-lft-identity_binary64_3147`
8×	`flip-+_binary64_3121` `associate-r_binary64_3087` `flip3-+_binary64_3150` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
7×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `associate-l_binary64_3088`
4×	`frac-add_binary64_3155` `distribute-neg-frac_binary64_3111` `associate-+r+_binary64_3079` `distribute-neg-in_binary64_3108`
3×	`*-commutative_binary64_3078`
2×	`unswap-sqr_binary64_3115` `associate-+l+_binary64_3080` `sum-log_binary64_3238`
1×	`unsub-neg_binary64_3141` `associate-+r-_binary64_3081` `distribute-lft-out_binary64_3098` `+-commutative_binary64_3077` `neg-sub0_binary64_3142` `neg-log_binary64_3240`

Counts

4 → 94

Calls

4 calls:

12.0ms	(+.f64 (.f64 (.f64 x.re x.re) (+.f64 x.re x.im)) (neg.f64 (.f64 x.im (.f64 x.re (+.f64 x.re (*.f64 x.im 3))))))
9.0ms	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))
8.0ms	(.f64 x.im (.f64 x.re (+.f64 x.re (*.f64 x.im 3))))
6.0ms	(.f64 x.re (+.f64 x.re (.f64 x.im 3)))

series132.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 x.im (.f64 x.re (+.f64 x.re (*.f64 x.im 3))))
39.0ms	(+.f64 (.f64 (.f64 x.re x.re) (+.f64 x.re x.im)) (neg.f64 (.f64 x.im (.f64 x.re (+.f64 x.re (*.f64 x.im 3))))))
27.0ms	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))
25.0ms	(.f64 x.re (+.f64 x.re (.f64 x.im 3)))

simplify79.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5095	2291

prune107.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	106	7	113

Error

Counts

113 → 7

Compiler

Compiled 2478 to 1337 computations (46% saved)

regimes230.0ms (6.4%)

Accuracy

Total 0.2b remaining (98.4%)

Threshold costs 0.2b (98.4%)

Compiler

Compiled 3006 to 1887 computations (37.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	20
1	66	20

end0.0ms (0%)

sample1.2s (34.3%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	128	valid
20.0ms	404×	body	128	invalid

Compiler

Compiled 1036 to 653 computations (37% saved)

Details

analyze115.0ms (3.2%)

sample18.0ms (0.5%)

simplify241.0ms (6.7%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

rewrite36.0ms (1%)

series125.0ms (3.5%)

simplify48.0ms (1.3%)

prune97.0ms (2.7%)

localize11.0ms (0.3%)

rewrite64.0ms (1.8%)

series135.0ms (3.7%)

simplify103.0ms (2.9%)

prune343.0ms (9.5%)

localize12.0ms (0.3%)

rewrite56.0ms (1.6%)

series143.0ms (4%)

simplify86.0ms (2.4%)

prune116.0ms (3.2%)

localize11.0ms (0.3%)

rewrite45.0ms (1.2%)

series132.0ms (3.7%)

simplify79.0ms (2.2%)

prune107.0ms (3%)

regimes230.0ms (6.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (34.3%)

Profiling