Details

analyze278.0ms

Algorithm

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

sample42.0ms

Algorithm

intervals

Results

16.0ms	154×	body	160	valid
9.0ms	289×	pre	80	true
5.0ms	102×	body	80	valid
2.0ms	33×	body	80	nan

simplify320.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (312.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 29.6b

Counts

2 → 1

localize11.0ms

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))
29.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

series271.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
105.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
67.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify87.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4988	1963
1	4988	1963

prune84.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 0.3b

Counts

83 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

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))
15.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
155.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
202.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5150	3003

prune130.0ms

Filtered

76 candidates to 110 candidates (-44.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Merged error: 0b

Counts

117 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`pow1_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64`
3×	`flip3-+_binary64` `associate-l_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
8.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
13.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
37.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
101.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
188.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))

simplify94.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5175	2595

prune108.0ms

Filtered

77 candidates to 105 candidates (-36.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Merged error: 0b

Counts

115 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (.f64 16 (*.f64 a c)))
0.2b	(.f64 a (.f64 c (.f64 16 (.f64 a c))))
0.3b	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 16 (.f64 a c))))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.4b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 16 (.f64 a c))))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow1_binary64`
20×	`*-un-lft-identity_binary64`
19×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`pow-prod-down_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`times-frac_binary64`
7×	`associate-/r*_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `flip--_binary64`

Counts

4 → 104

Calls

4 calls:

8.0ms	(.f64 c (.f64 16 (*.f64 a c)))
11.0ms	(.f64 a (.f64 c (.f64 16 (.f64 a c))))
19.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 16 (.f64 a c))))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
11.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 16 (.f64 a c))))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 c (.f64 16 (*.f64 a c)))
31.0ms	(.f64 a (.f64 c (.f64 16 (.f64 a c))))
253.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 16 (.f64 a c))))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
82.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 16 (.f64 a c))))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

simplify97.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5125	3672

prune132.0ms

Filtered

71 candidates to 116 candidates (-63.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	116	9	125

Merged error: 0b

Counts

125 → 9

regimes72.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

458.0ms	4423×	body	160	valid
266.0ms	8880×	pre	80	true
191.0ms	3577×	body	80	valid
44.0ms	880×	body	80	nan

Details

analyze278.0ms

sample42.0ms

simplify320.0ms

prune6.0ms

localize11.0ms

rewrite31.0ms

series271.0ms

simplify87.0ms

prune84.0ms

localize17.0ms

rewrite41.0ms

series456.0ms

simplify69.0ms

prune130.0ms

localize11.0ms

rewrite35.0ms

series391.0ms

simplify94.0ms

prune108.0ms

localize26.0ms

rewrite52.0ms

series383.0ms

simplify97.0ms

prune132.0ms

regimes72.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling