Details

analyze264.0ms (3.4%)

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)

sample33.0ms (0.4%)

Algorithm

1×

intervals

Results

13.0ms	244×	body	128	valid
8.0ms	282×	pre	128	true
1.0ms	26×	body	128	nan
1.0ms	12×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify223.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0%)

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: 28.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite40.0ms (0.5%)

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))

series526.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
132.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify97.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune101.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 0.4b

Counts

83 → 6

Compiler

Compiled 2037 to 1217 computations (40.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite55.0ms (0.7%)

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:

20.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series912.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

398.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
309.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
135.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune171.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	11	110
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Merged error: 0.0b

Counts

116 → 11

Compiler

Compiled 3338 to 2073 computations (37.9% saved)

localize15.0ms (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 b (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))))))
0.3b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite31.0ms (0.4%)

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:

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

series671.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
69.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune112.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 0.0b

Counts

94 → 8

Compiler

Compiled 2388 to 1494 computations (37.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/2 (+.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)))))
0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.3b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_77`
24×	`times-frac_binary64_83`
21×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
18×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `associate-r_binary64_19`
9×	`pow1_binary64_135`
8×	`add-log-exp_binary64_113` `distribute-lft-out_binary64_30`
6×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
4×	`associate-/r*_binary64_23` `associate-/r/_binary64_25`
3×	`pow-prod-down_binary64_145` `flip-+_binary64_51` `cbrt-undiv_binary64_108` `flip3-+_binary64_80` `associate-/l*_binary64_24` `div-exp_binary64_125`
2×	`div-inv_binary64_74`
1×	`associate-l_binary64_20` `sub-neg_binary64_70` `flip--_binary64_52` `+-commutative_binary64_9` `associate-r/_binary64_21` `-commutative_binary64_10` `clear-num_binary64_76` `flip3--_binary64_81` `diff-log_binary64_166` `frac-2neg_binary64_88` `sum-log_binary64_165`

Counts

4 → 94

Calls

4 calls:

17.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
8.0ms	(/.f64 1/2 (+.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)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series800.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

371.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
225.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
139.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4940	2605
1	4940	2605

prune129.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0b

Counts

114 → 8

Compiler

Compiled 2726 to 1721 computations (36.9% saved)

regimes623.0ms (8.1%)

Compiler: Compiled 8240 to 6206 computations (24.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.5s (33.1%)

Algorithm

1×

intervals

Results

416.0ms	7689×	body	128	valid
271.0ms	8823×	pre	128	true
43.0ms	823×	body	128	nan
32.0ms	311×	body	256	valid

Compiler

Compiled 2096 to 1580 computations (24.6% saved)

Details

analyze264.0ms (3.4%)

sample33.0ms (0.4%)

simplify223.0ms (2.9%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite40.0ms (0.5%)

series526.0ms (6.9%)

simplify97.0ms (1.3%)

prune101.0ms (1.3%)

localize15.0ms (0.2%)

rewrite55.0ms (0.7%)

series912.0ms (11.9%)

simplify74.0ms (1%)

prune171.0ms (2.2%)

localize15.0ms (0.2%)

rewrite31.0ms (0.4%)

series671.0ms (8.7%)

simplify82.0ms (1.1%)

prune112.0ms (1.5%)

localize12.0ms (0.2%)

rewrite47.0ms (0.6%)

series800.0ms (10.4%)

simplify80.0ms (1%)

prune129.0ms (1.7%)

regimes623.0ms (8.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.5s (33.1%)

Profiling