Details

analyze462.0ms (8%)

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 (0.7%)

Algorithm

1×

intervals

Results

9.0ms	39×	body	2048	valid
8.0ms	161×	body	128	valid
5.0ms	27×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	18×	body	128	nan
1.0ms	16×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify231.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_767`
15×	`add-sqr-sqrt_binary64_789`
14×	`add-cube-cbrt_binary64_802`
12×	`times-frac_binary64_773`
8×	`add-log-exp_binary64_806`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`distribute-lft-out_binary64_718` `pow1_binary64_828`
4×	`associate-/l*_binary64_712`
3×	`associate-/r*_binary64_711` `sqrt-prod_binary64_783`
2×	`associate-/l/_binary64_714` `flip-+_binary64_741` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(+.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)))

series454.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5101	2019

prune445.0ms (7.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	9	85

Merged error: 4.0b

Counts

85 → 9

Compiler

Compiled 8579 to 5793 computations (32.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_789`
18×	`*-un-lft-identity_binary64_767`
13×	`associate-r_binary64_707` `add-exp-log_binary64_805` `add-cube-cbrt_binary64_802`
11×	`times-frac_binary64_773`
9×	`add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806`
7×	`pow1_binary64_828`
4×	`associate-l_binary64_708` `prod-exp_binary64_816`
3×	`unswap-sqr_binary64_735` `flip-+_binary64_741` `sqrt-prod_binary64_783` `flip3-+_binary64_770`
2×	`frac-times_binary64_777` `distribute-lft-out_binary64_718` `cbrt-unprod_binary64_800` `associate-*l/_binary64_710` `flip--_binary64_742` `div-exp_binary64_818` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `-commutative_binary64_698` `1-exp_binary64_811` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `associate-r/_binary64_709` `rec-exp_binary64_817` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `un-div-inv_binary64_765` `div-inv_binary64_764`

Counts

4 → 80

Calls

4 calls:

15.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series442.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
129.0ms	(+.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))))
58.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify89.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4920	2059
1	4920	2059

prune152.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 4.0b

Counts

101 → 8

Compiler

Compiled 3184 to 1996 computations (37.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
12.7b	(/.f64 (.f64 4 (.f64 a c)) a)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
7.0ms	(/.f64 (.f64 4 (.f64 a c)) a)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series347.0ms (6%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(-.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))))
72.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
18.0ms	(/.f64 (.f64 4 (.f64 a c)) a)

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4982	1372
1	4982	1372

prune151.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	83	7	90

Merged error: 4.0b

Counts

90 → 7

Compiler

Compiled 3130 to 1951 computations (37.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
0.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_789`
15×	`*-un-lft-identity_binary64_767`
9×	`add-exp-log_binary64_805` `sqrt-prod_binary64_783` `add-cbrt-cube_binary64_803` `add-cube-cbrt_binary64_802`
8×	`add-log-exp_binary64_806`
7×	`cancel-sign-sub-inv_binary64_733`
6×	`associate-/r*_binary64_711` `times-frac_binary64_773` `difference-of-squares_binary64_736`
5×	`pow1_binary64_828`
4×	`flip--_binary64_742` `flip3--_binary64_771`
3×	`distribute-lft-out--_binary64_719`
2×	`cbrt-undiv_binary64_801` `associate-/r/_binary64_713` `sub-neg_binary64_760` `diff-log_binary64_859` `div-exp_binary64_818` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `associate-/l*_binary64_712` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 76

Calls

4 calls:

11.0ms	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
8.0ms	(-.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)))

series733.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

400.0ms	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
135.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4935	2059
1	4935	2059

prune164.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	87	8	95

Merged error: 4.0b

Counts

95 → 8

Compiler

Compiled 3146 to 2053 computations (34.7% saved)

regimes178.0ms (3.1%)

Compiler: Compiled 387 to 345 computations (10.9% saved)

bsearch101.0ms (1.7%)

Steps

Iters	Range	Point
8	2.1950977032473466e+77	6.31439153101362e+81	1.2594828022150501e+81
10	-1.1878171559580877e-247	-9.821703124247129e-266	-1.0003654787895762e-265
7	-9.955055632374411e+154	-6.078197847532872e+152	-6.199403977267283e+152

Iters

Range

Point

2.1950977032473466e+77

6.31439153101362e+81

1.2594828022150501e+81

-1.1878171559580877e-247

-9.821703124247129e-266

-1.0003654787895762e-265

-9.955055632374411e+154

-6.078197847532872e+152

-6.199403977267283e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	89
1	95	89

end0.0ms (0%)

sample1.4s (24.2%)

Algorithm

1×

intervals

Results

297.0ms	1206×	body	2048	valid
268.0ms	5101×	body	128	valid
146.0ms	737×	body	1024	valid
120.0ms	385×	body	4096	valid
53.0ms	377×	body	512	valid
37.0ms	661×	body	128	nan
21.0ms	415×	body	128	invalid
19.0ms	194×	body	256	valid

Compiler

Compiled 247 to 196 computations (20.6% saved)

Details

analyze462.0ms (8%)

sample40.0ms (0.7%)

simplify231.0ms (4%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite33.0ms (0.6%)

series454.0ms (7.9%)

simplify76.0ms (1.3%)

prune445.0ms (7.7%)

localize12.0ms (0.2%)

rewrite43.0ms (0.7%)

series442.0ms (7.6%)

simplify89.0ms (1.5%)

prune152.0ms (2.6%)

localize12.0ms (0.2%)

rewrite32.0ms (0.5%)

series347.0ms (6%)

simplify56.0ms (1%)

prune151.0ms (2.6%)

localize12.0ms (0.2%)

rewrite35.0ms (0.6%)

series733.0ms (12.7%)

simplify64.0ms (1.1%)

prune164.0ms (2.8%)

regimes178.0ms (3.1%)

bsearch101.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (24.2%)

Profiling