Details

analyze453.0ms (7.2%)

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)

sample44.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	49×	body	2048	valid
7.0ms	149×	body	128	valid
5.0ms	29×	body	1024	valid
4.0ms	13×	body	4096	valid
1.0ms	10×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	17×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify226.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (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: 39.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% 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)
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
28.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_751`
15×	`add-sqr-sqrt_binary64_772`
14×	`add-cube-cbrt_binary64_783`
12×	`times-frac_binary64_757`
8×	`add-log-exp_binary64_787`
6×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
5×	`distribute-lft-out_binary64_704` `pow1_binary64_809`
4×	`associate-/l*_binary64_698`
3×	`associate-/r*_binary64_697` `sqrt-prod_binary64_766`
2×	`flip3-+_binary64_754` `associate-/l/_binary64_700` `flip--_binary64_726` `sqrt-div_binary64_767` `flip3--_binary64_755` `flip-+_binary64_725`
1×	`+-commutative_binary64_683` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `sqrt-pow1_binary64_768` `div-exp_binary64_799`

Counts

4 → 71

Calls

4 calls:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
8.0ms	(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	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series458.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(/.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))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5412	2012

prune126.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	10	84

Merged error: 5.9b

Counts

84 → 10

Compiler

Compiled 2139 to 1170 computations (45.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.2b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.9b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
28.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite59.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_757`
53×	`add-sqr-sqrt_binary64_772`
40×	`*-un-lft-identity_binary64_751`
28×	`add-cube-cbrt_binary64_783`
27×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
13×	`associate-/l*_binary64_698`
12×	`difference-of-squares_binary64_720`
10×	`associate-/r/_binary64_699` `cbrt-undiv_binary64_782` `div-exp_binary64_799`
9×	`associate-/r*_binary64_697` `sqrt-prod_binary64_766`
7×	`flip--_binary64_726` `flip3--_binary64_755`
6×	`distribute-lft-out--_binary64_705` `prod-exp_binary64_797` `add-log-exp_binary64_787` `div-inv_binary64_748` `cbrt-unprod_binary64_781`
5×	`pow1_binary64_809`
2×	`sqrt-div_binary64_767` `frac-2neg_binary64_762` `clear-num_binary64_750`
1×	`associate-/l/_binary64_700` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `diff-log_binary64_840` `sub-neg_binary64_744` `sqrt-pow1_binary64_768`

Counts

4 → 127

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.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)))

series948.0ms (15%)

Counts

4 → 12

Calls

4 calls:

431.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
327.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5440	4678

prune207.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	3	5	8
Picked	0	1	1
Done	1	0	1
Total	140	9	149

Merged error: 5.8b

Counts

149 → 9

Compiler

Compiled 4509 to 2397 computations (46.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
28.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_772`
26×	`*-un-lft-identity_binary64_751`
18×	`times-frac_binary64_757`
16×	`add-cube-cbrt_binary64_783`
10×	`difference-of-squares_binary64_720`
8×	`add-log-exp_binary64_787` `sqrt-prod_binary64_766`
6×	`associate-/r*_binary64_697` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
5×	`distribute-lft-out--_binary64_705` `pow1_binary64_809`
4×	`flip--_binary64_726` `flip3--_binary64_755`
3×	`associate-/l*_binary64_698`
2×	`sqrt-div_binary64_767` `associate-/r/_binary64_699` `diff-log_binary64_840` `sub-neg_binary64_744`
1×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sqrt-pow1_binary64_768` `div-exp_binary64_799`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/.f64 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)))

series684.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

357.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
132.0ms	(-.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))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5183	2447

prune127.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 5.8b

Counts

102 → 9

Compiler

Compiled 2786 to 1659 computations (40.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
28.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_757`
121×	`add-sqr-sqrt_binary64_772`
94×	`*-un-lft-identity_binary64_751`
68×	`add-cube-cbrt_binary64_783`
26×	`difference-of-squares_binary64_720`
22×	`associate-/r*_binary64_697`
16×	`sqrt-prod_binary64_766`
13×	`distribute-lft-out--_binary64_705`
9×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
8×	`add-log-exp_binary64_787`
5×	`pow1_binary64_809` `div-inv_binary64_748`
3×	`flip--_binary64_726` `cbrt-undiv_binary64_782` `associate-/l*_binary64_698` `flip3--_binary64_755` `div-exp_binary64_799`
2×	`sqrt-div_binary64_767` `diff-log_binary64_840` `sub-neg_binary64_744`
1×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `associate-/r/_binary64_699` `frac-2neg_binary64_762` `clear-num_binary64_750` `sqrt-pow1_binary64_768`

Counts

4 → 146

Calls

4 calls:

13.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) 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)))

series583.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

259.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
134.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify102.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5045	5651

prune238.0ms (3.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	157	10	167

Merged error: 5.8b

Counts

167 → 10

Compiler

Compiled 5181 to 3004 computations (42% saved)

regimes135.0ms (2.1%)

Compiler: Compiled 492 to 438 computations (11% saved)

bsearch109.0ms (1.7%)

Steps

Iters	Range	Point
7	3.365442186936048e+43	6.938607486303588e+44	6.876785701482238e+44
9	-3.2799378618376264e-285	-4.986137685057912e-290	-5.026239265453532e-290
9	-3.0558196015139103e+154	-1.140147330439728e+149	-8.207773183877872e+151

Iters

Range

Point

3.365442186936048e+43

6.938607486303588e+44

6.876785701482238e+44

-3.2799378618376264e-285

-4.986137685057912e-290

-5.026239265453532e-290

-3.0558196015139103e+154

-1.140147330439728e+149

-8.207773183877872e+151

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	109	98
1	109	98

end0.0ms (0%)

sample1.4s (22.6%)

Algorithm

1×

intervals

Results

288.0ms	1175×	body	2048	valid
264.0ms	5096×	body	128	valid
146.0ms	739×	body	1024	valid
130.0ms	413×	body	4096	valid
58.0ms	398×	body	512	valid
32.0ms	665×	body	128	nan
18.0ms	356×	body	128	invalid
17.0ms	179×	body	256	valid

Compiler

Compiled 288 to 230 computations (20.1% saved)

Details

analyze453.0ms (7.2%)

sample44.0ms (0.7%)

simplify226.0ms (3.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite36.0ms (0.6%)

series458.0ms (7.2%)

simplify67.0ms (1.1%)

prune126.0ms (2%)

localize13.0ms (0.2%)

rewrite59.0ms (0.9%)

series948.0ms (15%)

simplify68.0ms (1.1%)

prune207.0ms (3.3%)

localize13.0ms (0.2%)

rewrite35.0ms (0.6%)

series684.0ms (10.8%)

simplify73.0ms (1.2%)

prune127.0ms (2%)

localize14.0ms (0.2%)

rewrite53.0ms (0.8%)

series583.0ms (9.2%)

simplify102.0ms (1.6%)

prune238.0ms (3.8%)

regimes135.0ms (2.1%)

bsearch109.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (22.6%)

Profiling