Details

analyze472.0ms (7.3%)

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
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)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	172×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify228.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

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: 35.0b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize13.0ms (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))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite40.0ms (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))
10.0ms	(+.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)))

series519.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
120.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5223	1826

prune413.0ms (6.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 7.0b

Counts

83 → 7

Compiler

Compiled 8239 to 5536 computations (32.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.5b	(/.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))
9.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite71.0ms (1.1%)

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:

20.0ms	(/.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))))

series999.0ms (15.5%)

Counts

4 → 12

Calls

4 calls:

406.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
319.0ms	(/.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))
142.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify102.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4971	4138
1	4971	4138

prune264.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	137	7	144

Merged error: 6.9b

Counts

144 → 7

Compiler

Compiled 5767 to 3357 computations (41.8% 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))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite46.0ms (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:

13.0ms	(/.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)))

series667.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

349.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
125.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4959	2860
1	4959	2860

prune144.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	107	7	114

Merged error: 6.9b

Counts

114 → 7

Compiler

Compiled 3378 to 1882 computations (44.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
13.6b	(/.f64 a (.f64 (.f64 a c) 2))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.0ms	(/.f64 a (.f64 (.f64 a c) 2))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series342.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
16.0ms	(/.f64 a (.f64 (.f64 a c) 2))

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4995	1466
1	4995	1466

prune111.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Merged error: 6.9b

Counts

92 → 7

Compiler

Compiled 2643 to 1441 computations (45.5% saved)

regimes141.0ms (2.2%)

Compiler: Compiled 447 to 336 computations (24.8% saved)

bsearch114.0ms (1.8%)

Steps

Iters	Range	Point
8	5.047843856159705e+79	3.275486995190224e+82	2.2382631606544506e+82
11	-1.860825766371501e-278	-9.262240264721869e-302	-3.316085297718727e-287
9	-3.141987374119816e+97	-1.5578411367101382e+89	-2.3585860632819396e+97

Iters

Range

Point

5.047843856159705e+79

3.275486995190224e+82

2.2382631606544506e+82

-1.860825766371501e-278

-9.262240264721869e-302

-3.316085297718727e-287

-3.141987374119816e+97

-1.5578411367101382e+89

-2.3585860632819396e+97

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	121	84
1	121	84

end0.0ms (0%)

sample1.4s (22%)

Algorithm

1×

intervals

Results

288.0ms	1134×	body	2048	valid
274.0ms	5060×	body	128	valid
161.0ms	792×	body	1024	valid
135.0ms	417×	body	4096	valid
59.0ms	403×	body	512	valid
33.0ms	666×	body	128	nan
22.0ms	380×	body	128	invalid
20.0ms	194×	body	256	valid

Compiler

Compiled 263 to 186 computations (29.3% saved)

Details

analyze472.0ms (7.3%)

sample40.0ms (0.6%)

simplify228.0ms (3.5%)

prune8.0ms (0.1%)

localize13.0ms (0.2%)

rewrite40.0ms (0.6%)

series519.0ms (8.1%)

simplify58.0ms (0.9%)

prune413.0ms (6.4%)

localize14.0ms (0.2%)

rewrite71.0ms (1.1%)

series999.0ms (15.5%)

simplify102.0ms (1.6%)

prune264.0ms (4.1%)

localize14.0ms (0.2%)

rewrite46.0ms (0.7%)

series667.0ms (10.3%)

simplify89.0ms (1.4%)

prune144.0ms (2.2%)

localize18.0ms (0.3%)

rewrite34.0ms (0.5%)

series342.0ms (5.3%)

simplify57.0ms (0.9%)

prune111.0ms (1.7%)

regimes141.0ms (2.2%)

bsearch114.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (22%)

Profiling