Details

analyze457.0ms (7.9%)

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)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	185×	body	128	valid
8.0ms	26×	body	2048	valid
3.0ms	17×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	27×	body	128	nan
1.0ms	17×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify228.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

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

Merged error: 31.5b

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)
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (0.5%)

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)
6.0ms	(+.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))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series446.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
118.0ms	(+.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))))
68.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5101	2019

prune497.0ms (8.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 6.4b

Counts

85 → 10

Compiler

Compiled 9499 to 6416 computations (32.5% saved)

localize13.0ms (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))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (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))
6.0ms	(+.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)))

series477.0ms (8.2%)

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))
136.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
134.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4920	2059
1	4920	2059

prune148.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 6.4b

Counts

102 → 9

Compiler

Compiled 2972 to 1817 computations (38.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
15.0b	(/.f64 (.f64 4 (.f64 a c)) a)
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series329.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
60.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.0ms	(/.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

prune159.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	5	6
Picked	1	0	1
Done	1	1	2
Total	83	8	91

Merged error: 6.3b

Counts

91 → 8

Compiler

Compiled 3271 to 2046 computations (37.5% 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))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(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))))))
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)))

series738.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

404.0ms	(/.f64 (.f64 4 c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
142.0ms	(-.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))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4935	2059
1	4935	2059

prune152.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 6.3b

Counts

96 → 8

Compiler

Compiled 2985 to 1885 computations (36.9% saved)

regimes168.0ms (2.9%)

Compiler: Compiled 420 to 354 computations (15.7% saved)

bsearch84.0ms (1.4%)

Steps

Iters	Range		Point
8	1.926398635008391e+97	1.2558611526501326e+101	7.922796939806533e+99
7	-9.131643782654936e-299	-6.405261263554672e-301	-6.510183985272386e-301
6	-6.201624392123495e+73	-6.987174791110545e+72	-6.063829179971075e+73

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	98	92
1	98	92

end0.0ms (0%)

sample1.4s (24.2%)

Algorithm

1×

intervals

Results

277.0ms	5197×	body	128	valid
274.0ms	1111×	body	2048	valid
148.0ms	725×	body	1024	valid
117.0ms	380×	body	4096	valid
54.0ms	376×	body	512	valid
34.0ms	695×	body	128	nan
21.0ms	374×	body	128	invalid
20.0ms	211×	body	256	valid

Compiler

Compiled 260 to 201 computations (22.7% saved)

Details

analyze457.0ms (7.9%)

sample38.0ms (0.7%)

simplify228.0ms (3.9%)

prune8.0ms (0.1%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series446.0ms (7.7%)

simplify74.0ms (1.3%)

prune497.0ms (8.6%)

localize13.0ms (0.2%)

rewrite38.0ms (0.7%)

series477.0ms (8.2%)

simplify90.0ms (1.6%)

prune148.0ms (2.6%)

localize12.0ms (0.2%)

rewrite31.0ms (0.5%)

series329.0ms (5.7%)

simplify56.0ms (1%)

prune159.0ms (2.7%)

localize12.0ms (0.2%)

rewrite35.0ms (0.6%)

series738.0ms (12.7%)

simplify62.0ms (1.1%)

prune152.0ms (2.6%)

regimes168.0ms (2.9%)

bsearch84.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (24.2%)

Profiling