Details

analyze503.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample62.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	249×	body	128	valid
17.0ms	287×	pre	128	true
3.0ms	31×	body	128	nan
1.0ms	7×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify401.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune7.0ms (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: 29.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
29.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite69.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_98`
13×	`*-un-lft-identity_binary64_77`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-log-exp_binary64_113`
7×	`add-cube-cbrt_binary64_109`
6×	`sqrt-prod_binary64_92` `times-frac_binary64_83` `associate-/l*_binary64_24` `difference-of-squares_binary64_46`
5×	`pow1_binary64_135`
4×	`flip--_binary64_52` `flip3--_binary64_81`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `sub-neg_binary64_70` `div-exp_binary64_125` `diff-log_binary64_166` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `div-sub_binary64_82` `prod-exp_binary64_123` `pow1/2_binary64_154` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 70

Calls

4 calls:

24.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.0s (9.5%)

Counts

4 → 12

Calls

4 calls:

404.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
252.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
225.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
131.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify177.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune195.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 0.4b

Counts

83 → 8

Compiler

Compiled 2126 to 1280 computations (39.8% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite96.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
22×	`times-frac_binary64_83`
20×	`*-un-lft-identity_binary64_77`
17×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
13×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
11×	`associate-/l*_binary64_24`
10×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
8×	`add-log-exp_binary64_113`
6×	`associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1_binary64_135` `div-inv_binary64_74`
2×	`clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`sub-neg_binary64_70` `flip--_binary64_52` `+-commutative_binary64_9` `flip3--_binary64_81` `diff-log_binary64_166` `associate-/l/_binary64_26` `sum-log_binary64_165`

Counts

4 → 98

Calls

4 calls:

29.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
23.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.6s (15.3%)

Counts

4 → 12

Calls

4 calls:

703.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
567.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
246.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
118.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify135.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune304.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 0.0b

Counts

118 → 9

Compiler

Compiled 3330 to 2059 computations (38.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_77`
15×	`add-sqr-sqrt_binary64_98`
14×	`add-cube-cbrt_binary64_109`
12×	`times-frac_binary64_83`
8×	`add-log-exp_binary64_113`
6×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
5×	`pow1_binary64_135` `distribute-lft-out_binary64_30`
4×	`associate-/r*_binary64_23`
3×	`sqrt-prod_binary64_92` `associate-/l*_binary64_24`
2×	`flip-+_binary64_51` `sqrt-div_binary64_93` `flip3-+_binary64_80` `flip--_binary64_52` `associate-/r/_binary64_25` `flip3--_binary64_81`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `sub-neg_binary64_70` `+-commutative_binary64_9` `div-exp_binary64_125` `pow1/2_binary64_154` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `sum-log_binary64_165` `div-inv_binary64_74`

Counts

4 → 71

Calls

4 calls:

16.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series1.2s (11.4%)

Counts

4 → 12

Calls

4 calls:

626.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
244.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
219.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
128.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify156.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune222.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 0b

Counts

92 → 9

Compiler

Compiled 2440 to 1529 computations (37.3% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)))))
0.2b	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
0.7b	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

rewrite98.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_77`
19×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
12×	`times-frac_binary64_83` `cbrt-prod_binary64_105`
7×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`add-log-exp_binary64_113` `unpow-prod-down_binary64_153` `cube-prod_binary64_102`
5×	`pow1_binary64_135` `distribute-lft-out_binary64_30`
4×	`associate-/r*_binary64_23` `cube-div_binary64_103`
3×	`associate-/l*_binary64_24` `pow-unpow_binary64_151`
2×	`flip-+_binary64_51` `sqr-pow_binary64_49` `flip3-+_binary64_80` `cube-mult_binary64_104` `cbrt-div_binary64_106` `flip--_binary64_52` `associate-/r/_binary64_25` `flip3--_binary64_81` `unpow3_binary64_140`
1×	`pow-to-exp_binary64_143` `rem-cbrt-cube_binary64_100` `rem-cube-cbrt_binary64_99` `cbrt-undiv_binary64_108` `pow-exp_binary64_142` `+-commutative_binary64_9` `div-exp_binary64_125` `clear-num_binary64_76` `pow1/3_binary64_156` `frac-2neg_binary64_88` `pow-pow_binary64_146` `sum-log_binary64_165` `div-inv_binary64_74`

Counts

4 → 93

Calls

4 calls:

31.0ms	(/.f64 c (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)))))
22.0ms	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
12.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
12.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

series1.4s (12.7%)

Counts

4 → 12

Calls

4 calls:

646.0ms	(/.f64 c (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)))))
338.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
247.0ms	(+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))))
129.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

simplify158.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4961	2529
1	4961	2529

prune247.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	105	9	114

Merged error: 0b

Counts

114 → 9

Compiler

Compiled 2869 to 1813 computations (36.8% saved)

regimes166.0ms (1.6%)

Compiler: Compiled 975 to 708 computations (27.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	66	29
1	66	29

end0.0ms (0%)

sample2.3s (21.5%)

Algorithm

1×

intervals

Results

721.0ms	7682×	body	128	valid
507.0ms	8806×	pre	128	true
78.0ms	806×	body	128	nan
61.0ms	318×	body	256	valid

Compiler

Compiled 372 to 273 computations (26.6% saved)

Details

analyze503.0ms (4.7%)

sample62.0ms (0.6%)

simplify401.0ms (3.8%)

prune7.0ms (0.1%)

localize21.0ms (0.2%)

rewrite69.0ms (0.6%)

series1.0s (9.5%)

simplify177.0ms (1.7%)

prune195.0ms (1.8%)

localize29.0ms (0.3%)

rewrite96.0ms (0.9%)

series1.6s (15.3%)

simplify135.0ms (1.3%)

prune304.0ms (2.8%)

localize23.0ms (0.2%)

rewrite59.0ms (0.6%)

series1.2s (11.4%)

simplify156.0ms (1.5%)

prune222.0ms (2.1%)

localize33.0ms (0.3%)

rewrite98.0ms (0.9%)

series1.4s (12.7%)

simplify158.0ms (1.5%)

prune247.0ms (2.3%)

regimes166.0ms (1.6%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.3s (21.5%)

Profiling