Details

analyze269.0ms (3.8%)

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)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	293×	pre	128	true
9.0ms	167×	body	128	valid
9.0ms	89×	body	256	valid
2.0ms	37×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify225.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

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: 42.2b

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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
37.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite41.0ms (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:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series545.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
135.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune97.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 0.3b

Counts

83 → 3

Compiler

Compiled 1950 to 1156 computations (40.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.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)))))

rewrite55.0ms (0.8%)

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:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series892.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

396.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
313.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
116.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune164.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 0b

Counts

113 → 8

Compiler

Compiled 3324 to 2048 computations (38.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.5%)

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:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
7.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series635.0ms (9%)

Counts

4 → 12

Calls

4 calls:

335.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
120.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
67.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune115.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Merged error: 0b

Counts

91 → 8

Compiler

Compiled 2379 to 1483 computations (37.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
0.2b	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
0.4b	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)
0.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_77`
23×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
18×	`cbrt-prod_binary64_105`
12×	`sqrt-prod_binary64_92` `times-frac_binary64_83` `unpow-prod-down_binary64_153` `cube-prod_binary64_102`
7×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`add-log-exp_binary64_113` `pow1_binary64_135`
5×	`distribute-lft-out_binary64_30`
4×	`associate-/r*_binary64_23` `cube-div_binary64_103` `sqrt-div_binary64_93`
3×	`associate-/l*_binary64_24` `pow-unpow_binary64_151` `pow-pow_binary64_146`
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` `sqrt-pow2_binary64_95` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `pow-exp_binary64_142` `+-commutative_binary64_9` `div-exp_binary64_125` `pow1/2_binary64_154` `clear-num_binary64_76` `pow1/3_binary64_156` `frac-2neg_binary64_88` `sum-log_binary64_165` `div-inv_binary64_74`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
12.0ms	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
8.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)
7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))

series687.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

348.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
129.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))
124.0ms	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
86.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4917	2889
1	4917	2889

prune151.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	120	8	128

Merged error: 0b

Counts

128 → 8

Compiler

Compiled 3217 to 2038 computations (36.6% saved)

regimes446.0ms (6.3%)

Compiler: Compiled 5976 to 4502 computations (24.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	45
1	96	45

end0.0ms (0%)

sample2.3s (31.8%)

Algorithm

1×

intervals

Results

293.0ms	2901×	body	256	valid
273.0ms	8922×	pre	128	true
268.0ms	5099×	body	128	valid
44.0ms	922×	body	128	nan

Compiler

Compiled 1544 to 1163 computations (24.7% saved)

Details

analyze269.0ms (3.8%)

sample38.0ms (0.5%)

simplify225.0ms (3.2%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite41.0ms (0.6%)

series545.0ms (7.7%)

simplify95.0ms (1.3%)

prune97.0ms (1.4%)

localize14.0ms (0.2%)

rewrite55.0ms (0.8%)

series892.0ms (12.6%)

simplify73.0ms (1%)

prune164.0ms (2.3%)

localize12.0ms (0.2%)

rewrite34.0ms (0.5%)

series635.0ms (9%)

simplify83.0ms (1.2%)

prune115.0ms (1.6%)

localize15.0ms (0.2%)

rewrite56.0ms (0.8%)

series687.0ms (9.7%)

simplify80.0ms (1.1%)

prune151.0ms (2.1%)

regimes446.0ms (6.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (31.8%)

Profiling