Details

analyze267.0ms

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

sample38.0ms

Algorithm

intervals

Results

13.0ms	144×	body	160	valid
8.0ms	287×	pre	80	true
5.0ms	112×	body	80	valid
1.0ms	31×	body	80	nan

simplify223.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (220.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

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

localize13.0ms

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))
0.3b	(/.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)

rewrite32.0ms

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)))
5.0ms	(-.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)

series74.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
17.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify63.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4900	1294
1	4900	1294

prune67.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

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

localize16.0ms

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))
0.3b	(/.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)))))

rewrite42.0ms

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))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
15.0ms	(/.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)))))

series144.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
50.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
68.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4949	2008
1	4949	2008

prune106.0ms

Filtered

75 candidates to 110 candidates (-46.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	108	8	116

Merged error: 0.0b

Counts

116 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac_binary64`
114×	`*-un-lft-identity_binary64`
106×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
61×	`add-exp-log_binary64`
47×	`add-cbrt-cube_binary64`
37×	`div-exp_binary64`
26×	`div-inv_binary64`
25×	`cbrt-undiv_binary64`
19×	`associate-/l*_binary64`
18×	`associate-/r/_binary64`
15×	`associate-*r/_binary64`
13×	`associate-/r*_binary64`
8×	`prod-exp_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64` `1-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 225

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
12.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
18.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
54.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
53.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
10.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify98.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4893	5612
1	4893	5612

prune156.0ms

Filtered

139 candidates to 237 candidates (-70.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	238	7	245

Merged error: 0b

Counts

245 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
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)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `cube-div_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `associate-/l*_binary64` `times-frac_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `prod-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `associate-/r/_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 83

Calls

4 calls:

18.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
6.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
6.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

series99.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
10.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
23.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

simplify46.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5069	1428

prune53.0ms

Filtered

59 candidates to 95 candidates (-61.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Merged error: 0b

Counts

102 → 7

regimes126.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	23
1	67	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

419.0ms	4445×	body	160	valid
256.0ms	8865×	pre	80	true
178.0ms	3555×	body	80	valid
42.0ms	865×	body	80	nan

Details

analyze267.0ms

sample38.0ms

simplify223.0ms

prune6.0ms

localize13.0ms

rewrite32.0ms

series74.0ms

simplify63.0ms

prune67.0ms

localize16.0ms

rewrite42.0ms

series144.0ms

simplify53.0ms

prune106.0ms

localize17.0ms

rewrite56.0ms

series171.0ms

simplify98.0ms

prune156.0ms

localize18.0ms

rewrite37.0ms

series99.0ms

simplify46.0ms

prune53.0ms

regimes126.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling