Details

analyze262.0ms

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

sample33.0ms

Algorithm

intervals

Results

8.0ms	174×	body	128	valid
8.0ms	281×	pre	128	true
7.0ms	82×	body	256	valid
1.0ms	25×	body	128	nan

simplify264.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (258.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	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: 42.1b

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

rewrite37.0ms

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:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
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)

series538.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
214.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
137.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify68.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5008	1963

prune82.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	6	83

Merged error: 0.2b

Counts

83 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.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)))))

rewrite56.0ms

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:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
19.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series921.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
326.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
400.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5155	3003

prune129.0ms

Filtered

76 candidates to 110 candidates (-44.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	4	0	4
Picked	1	0	1
Done	1	0	1
Total	108	8	116

Merged error: 0.0b

Counts

116 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (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 -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)))))))

rewrite44.0ms

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:

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)))
9.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
14.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))

series779.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
207.0ms	(/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
390.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))

simplify96.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4903	2595
1	4903	2595

prune110.0ms

Filtered

78 candidates to 105 candidates (-34.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Merged error: 0b

Counts

113 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `times-frac_binary64`
3×	`distribute-lft-out_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(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)))))
10.0ms	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
140.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
378.0ms	(/.f64 (.f64 c -2) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
66.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify76.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4959	1662
1	4959	1662

prune65.0ms

Filtered

57 candidates to 75 candidates (-31.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	75	7	82

Merged error: 0b

Counts

82 → 7

regimes56.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

267.0ms	2882×	body	256	valid
254.0ms	8930×	pre	128	true
242.0ms	5118×	body	128	valid
40.0ms	930×	body	128	nan

Details

analyze262.0ms

sample33.0ms

simplify264.0ms

prune6.0ms

localize11.0ms

rewrite37.0ms

series538.0ms

simplify68.0ms

prune82.0ms

localize15.0ms

rewrite56.0ms

series921.0ms

simplify59.0ms

prune129.0ms

localize12.0ms

rewrite44.0ms

series779.0ms

simplify96.0ms

prune110.0ms

localize11.0ms

rewrite32.0ms

series715.0ms

simplify76.0ms

prune65.0ms

regimes56.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling