Details

analyze458.0ms (7%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
8.0ms	34×	body	2048	valid
6.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	24×	body	128	nan
1.0ms	7×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify234.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 34.4b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_767`
10×	`add-log-exp_binary64_806`
9×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
8×	`add-sqr-sqrt_binary64_789`
7×	`add-cube-cbrt_binary64_802`
6×	`distribute-lft-out_binary64_718`
5×	`pow1_binary64_828` `times-frac_binary64_773` `associate-/l*_binary64_712`
3×	`sqrt-prod_binary64_783` `distribute-rgt-neg-in_binary64_725`
2×	`associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `neg-sub0_binary64_762` `flip-+_binary64_741` `sum-log_binary64_858` `flip3-+_binary64_770` `flip--_binary64_742` `div-exp_binary64_818` `flip3--_binary64_771` `sqrt-div_binary64_784` `associate-+l-_binary64_702`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800` `sub-neg_binary64_760` `prod-exp_binary64_816` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `neg-log_binary64_860` `+-commutative_binary64_697` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `div-sub_binary64_772` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series525.0ms (8%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
118.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
69.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5223	1826

prune461.0ms (7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 5.3b

Counts

83 → 8

Compiler

Compiled 8864 to 6013 computations (32.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.4b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
8.1b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite67.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
34×	`times-frac_binary64_773` `add-sqr-sqrt_binary64_789`
33×	`*-un-lft-identity_binary64_767`
17×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
14×	`associate-/l*_binary64_712`
13×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816` `add-cube-cbrt_binary64_802`
11×	`sqrt-prod_binary64_783`
10×	`distribute-lft-out--_binary64_719` `difference-of-squares_binary64_736`
8×	`associate-/r*_binary64_711` `add-log-exp_binary64_806`
6×	`associate-/r/_binary64_713` `cancel-sign-sub-inv_binary64_733`
5×	`pow1_binary64_828` `distribute-rgt-neg-in_binary64_725` `flip--_binary64_742` `flip3--_binary64_771`
4×	`div-inv_binary64_764`
2×	`frac-2neg_binary64_778` `diff-log_binary64_859` `clear-num_binary64_766` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `sub-neg_binary64_760` `neg-sub0_binary64_762` `neg-log_binary64_860` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `associate--l-_binary64_705`

Counts

4 → 125

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
16.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series981.0ms (14.9%)

Counts

4 → 12

Calls

4 calls:

401.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
321.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
135.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4971	4138
1	4971	4138

prune224.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	138	7	145

Merged error: 5.2b

Counts

145 → 7

Compiler

Compiled 4929 to 2801 computations (43.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_789`
39×	`*-un-lft-identity_binary64_767`
21×	`times-frac_binary64_773`
19×	`add-cube-cbrt_binary64_802`
11×	`sqrt-prod_binary64_783`
10×	`add-log-exp_binary64_806` `distribute-lft-out--_binary64_719` `difference-of-squares_binary64_736`
7×	`associate-/r*_binary64_711` `cancel-sign-sub-inv_binary64_733`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`pow1_binary64_828` `distribute-rgt-neg-in_binary64_725`
4×	`flip--_binary64_742` `flip3--_binary64_771`
3×	`associate-/l*_binary64_712` `diff-log_binary64_859`
2×	`associate-/r/_binary64_713` `sub-neg_binary64_760` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `neg-sub0_binary64_762` `neg-log_binary64_860` `pow1/2_binary64_847` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `div-inv_binary64_764` `associate--l-_binary64_705`

Counts

4 → 95

Calls

4 calls:

12.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series662.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

341.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
143.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4959	2860
1	4959	2860

prune139.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	107	7	114

Merged error: 5.2b

Counts

114 → 7

Compiler

Compiled 3076 to 1681 computations (45.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1/2 a))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_767`
19×	`add-sqr-sqrt_binary64_789`
13×	`associate-r_binary64_707` `add-cube-cbrt_binary64_802`
10×	`times-frac_binary64_773` `add-log-exp_binary64_806`
9×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
7×	`pow1_binary64_828`
5×	`associate-l_binary64_708`
4×	`distribute-lft-out_binary64_718`
3×	`flip-+_binary64_741` `sqrt-prod_binary64_783` `flip3-+_binary64_770`
2×	`frac-times_binary64_777` `unswap-sqr_binary64_735` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `sum-log_binary64_858` `associate-*l/_binary64_710` `distribute-rgt-neg-in_binary64_725` `flip--_binary64_742` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `neg-sub0_binary64_762` `-commutative_binary64_698` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `neg-log_binary64_860` `+-commutative_binary64_697` `pow1/2_binary64_847` `associate-r/_binary64_709` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `div-inv_binary64_764` `associate-+l-_binary64_702`

Counts

4 → 80

Calls

4 calls:

20.0ms	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1/2 a))
9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series549.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1/2 a))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
130.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5106	2137

prune102.0ms (1.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	92	7	99

Merged error: 5.2b

Counts

99 → 7

Compiler

Compiled 2248 to 1220 computations (45.7% saved)

regimes164.0ms (2.5%)

Compiler: Compiled 440 to 378 computations (14.1% saved)

bsearch103.0ms (1.6%)

Steps

Iters	Range	Point
8	6.787489049073195e+118	7.133955408180205e+122	5.525835260688754e+121
9	2.173626231849138e-227	1.6620553427918547e-219	7.131198222427231e-227
8	-1.6407368404235515e+56	-3.3624292403433257e+53	-1.5894887112160012e+56

Iters

Range

Point

6.787489049073195e+118

7.133955408180205e+122

5.525835260688754e+121

2.173626231849138e-227

1.6620553427918547e-219

7.131198222427231e-227

-1.6407368404235515e+56

-3.3624292403433257e+53

-1.5894887112160012e+56

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	120	84
1	120	84

end0.0ms (0%)

sample1.3s (20.5%)

Algorithm

1×

intervals

Results

283.0ms	5258×	body	128	valid
273.0ms	1104×	body	2048	valid
135.0ms	682×	body	1024	valid
123.0ms	398×	body	4096	valid
54.0ms	372×	body	512	valid
32.0ms	662×	body	128	nan
23.0ms	360×	body	128	invalid
18.0ms	186×	body	256	valid

Compiler

Compiled 216 to 163 computations (24.5% saved)

Details

analyze458.0ms (7%)

sample39.0ms (0.6%)

simplify234.0ms (3.6%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite39.0ms (0.6%)

series525.0ms (8%)

simplify55.0ms (0.8%)

prune461.0ms (7%)

localize14.0ms (0.2%)

rewrite67.0ms (1%)

series981.0ms (14.9%)

simplify104.0ms (1.6%)

prune224.0ms (3.4%)

localize14.0ms (0.2%)

rewrite47.0ms (0.7%)

series662.0ms (10.1%)

simplify95.0ms (1.5%)

prune139.0ms (2.1%)

localize12.0ms (0.2%)

rewrite47.0ms (0.7%)

series549.0ms (8.4%)

simplify69.0ms (1.1%)

prune102.0ms (1.6%)

regimes164.0ms (2.5%)

bsearch103.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (20.5%)

Profiling