Details

analyze318.0ms (5.3%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	199×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	18×	body	4096	valid
2.0ms	10×	body	1024	valid
0.0ms	3×	body	512	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0%)

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

39.0b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_3208`
6×	`*-un-lft-identity_binary64_3147`
5×	`add-sqr-sqrt_binary64_3169` `add-log-exp_binary64_3186`
4×	`add-cube-cbrt_binary64_3182` `sqrt-div_binary64_3164` `sqrt-prod_binary64_3163`
3×	`add-exp-log_binary64_3185` `flip-+_binary64_3121` `add-cbrt-cube_binary64_3183` `flip3-+_binary64_3150` `sqrt-pow1_binary64_3165`
2×	`pow1/2_binary64_3227` `associate-*r/_binary64_3089`
1×	`pow-prod-down_binary64_3218` `distribute-lft-out_binary64_3098` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `sum-log_binary64_3238`

Counts

3 → 40

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series279.0ms (4.6%)

Counts

3 → 37

Calls

3 calls:

99.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
93.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
86.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 1011 to 921 computations (8.9% saved)

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4930	1192
1	4930	1192

prune95.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	10	78

Error

7.7b

Counts

78 → 10

Compiler

Compiled 1446 to 761 computations (47.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.0b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
30.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3169`
18×	`sqrt-prod_binary64_3163`
16×	`*-un-lft-identity_binary64_3147`
10×	`pow1_binary64_3208` `add-cube-cbrt_binary64_3182`
7×	`associate-r_binary64_3087`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186` `associate-l_binary64_3088` `sqrt-div_binary64_3164`
4×	`unswap-sqr_binary64_3115` `flip-+_binary64_3121` `flip3-+_binary64_3150` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
3×	`pow-prod-down_binary64_3218` `distribute-lft-out_binary64_3098`
2×	`rem-sqrt-square_binary64_3160` `associate-*r/_binary64_3089`
1×	`*-commutative_binary64_3078` `sqrt-unprod_binary64_3167` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `sum-log_binary64_3238`

Counts

4 → 76

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
6.0ms	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series325.0ms (5.4%)

Counts

4 → 45

Calls

4 calls:

92.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
86.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
84.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
63.0ms	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))

Compiler

Compiled 1304 to 1203 computations (7.7% saved)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5080	2183

prune116.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	120	11	131

Error

7.7b

Counts

131 → 11

Compiler

Compiled 2499 to 1167 computations (53.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.7b	(sqrt.f64 (.f64 (.f64 im im) 2))
30.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_3169`
50×	`sqrt-prod_binary64_3163`
38×	`*-un-lft-identity_binary64_3147`
36×	`times-frac_binary64_3153`
26×	`add-cube-cbrt_binary64_3182`
12×	`difference-of-squares_binary64_3116`
11×	`pow1_binary64_3208`
9×	`associate-/r*_binary64_3091`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `distribute-lft-out--_binary64_3099` `add-log-exp_binary64_3186`
4×	`sqrt-pow1_binary64_3165` `associate-/l*_binary64_3092` `sqrt-div_binary64_3164`
3×	`cancel-sign-sub-inv_binary64_3113` `pow-prod-down_binary64_3218`
2×	`flip--_binary64_3122` `flip3--_binary64_3151` `pow1/2_binary64_3227` `associate-/r/_binary64_3093`
1×	`clear-num_binary64_3146` `flip-+_binary64_3121` `sqrt-undiv_binary64_3168` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `sub-neg_binary64_3140` `rem-sqrt-square_binary64_3160` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239` `div-inv_binary64_3144`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series341.0ms (5.7%)

Counts

4 → 38

Calls

4 calls:

124.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
116.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
73.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

Compiler

Compiled 1287 to 1094 computations (15% saved)

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5159	3910

prune167.0ms (2.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	141	16	157

Error

2.0b

Counts

157 → 16

Compiler

Compiled 4174 to 1625 computations (61.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (fabs.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(*.f64 (fabs.f64 im) (sqrt.f64 2))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_3169`
22×	`sqrt-prod_binary64_3163`
19×	`*-un-lft-identity_binary64_3147`
13×	`add-cube-cbrt_binary64_3182`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
9×	`times-frac_binary64_3153` `associate-/r*_binary64_3091`
7×	`pow1_binary64_3208`
6×	`associate-r_binary64_3087` `difference-of-squares_binary64_3116` `add-log-exp_binary64_3186`
4×	`sqrt-div_binary64_3164`
3×	`cancel-sign-sub-inv_binary64_3113` `distribute-lft-out--_binary64_3099` `associate-l_binary64_3088`
2×	`flip--_binary64_3122` `unswap-sqr_binary64_3115` `flip3--_binary64_3151` `prod-exp_binary64_3196` `cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `associate-/r/_binary64_3093`
1×	`-commutative_binary64_3078` `clear-num_binary64_3146` `flip-+_binary64_3121` `pow-prod-down_binary64_3218` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `sub-neg_binary64_3140` `rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `diff-log_binary64_3239` `associate-/l_binary64_3092` `div-inv_binary64_3144`

Counts

4 → 89

Calls

4 calls:

13.0ms	(/.f64 (.f64 (fabs.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(*.f64 (fabs.f64 im) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series430.0ms (7.1%)

Counts

4 → 43

Calls

4 calls:

183.0ms	(/.f64 (.f64 (fabs.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
129.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
89.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.0ms	(*.f64 (fabs.f64 im) (sqrt.f64 2))

Compiler

Compiled 1622 to 1377 computations (15.1% saved)

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5075	2601

prune139.0ms (2.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	5	8	13
Picked	1	0	1
Done	0	2	2
Total	135	13	148

Error

0.4b

Counts

148 → 13

Compiler

Compiled 3155 to 1320 computations (58.2% saved)

regimes1.1s (18.6%)

Accuracy

Total 22.4b remaining (98.9%)

Threshold costs 0b (0%)

Compiler

Compiled 8239 to 5712 computations (30.7% saved)

bsearch205.0ms (3.4%)

Steps

Iters	Range		Point
7	4.543590596204842e+68	3.7097476619738605e+70	3.641911564658625e+70
4	2.1829006900380296e-44	3.4169489057150076e-44	2.4066168209035574e-44
8	1.4118472738795398e-124	1.280676852016625e-121	1.4299984141510836e-124
8	1.8204460167394784e-150	7.406352386087152e-146	3.24503967386611e-149
10	1.2561215238385132e-187	2.8447327710513945e-173	8.572356981549358e-176
9	-1.3637319715462841e-186	-1.8635257871352885e-194	-1.1367816435235204e-191
9	-2.2005257271496646e-156	-1.3049993673254402e-163	-3.4993194957776107e-161
7	-3.266032139050482e+31	-5.860941657435586e+29	-1.8027506436573165e+31

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	205
1	101	205

end0.0ms (0%)

sample1.9s (31.3%)

Algorithm

1×

intervals

Results

291.0ms	6081×	body	128	valid
148.0ms	528×	body	4096	valid
146.0ms	625×	body	2048	valid
79.0ms	437×	body	1024	valid
31.0ms	220×	body	512	valid
10.0ms	109×	body	256	valid

Compiler

Compiled 1282 to 885 computations (31% saved)

Details

analyze318.0ms (5.3%)

sample30.0ms (0.5%)

simplify100.0ms (1.7%)

prune3.0ms (0%)

localize14.0ms (0.2%)

rewrite23.0ms (0.4%)

series279.0ms (4.6%)

simplify61.0ms (1%)

prune95.0ms (1.6%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series325.0ms (5.4%)

simplify75.0ms (1.2%)

prune116.0ms (1.9%)

localize12.0ms (0.2%)

rewrite44.0ms (0.7%)

series341.0ms (5.7%)

simplify78.0ms (1.3%)

prune167.0ms (2.8%)

localize15.0ms (0.3%)

rewrite39.0ms (0.6%)

series430.0ms (7.1%)

simplify70.0ms (1.2%)

prune139.0ms (2.3%)

regimes1.1s (18.6%)

bsearch205.0ms (3.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.9s (31.3%)

Profiling