Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	240×	body	80	valid
5.0ms	1×	body	2560	valid
3.0ms	22×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	9×	body	320	valid
1.0ms	13×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	5001	6

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 24.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
3.4b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.1b	(/ (* (- y z) (- t x)) (- a z))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series100.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
52.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
39.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify56.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune148.0ms

Filtered

90 candidates to 67 candidates (25.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 4.8b

Counts

91 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
38.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
28.0ms	(cbrt (- a z))
56.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
54.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	752	1839
1	3320	1671
2	5001	1580

prune208.0ms

Filtered

146 candidates to 103 candidates (29.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	138	8	146
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	140	16	156

Merged error: 4.8b

Counts

156 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
9.5b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series136.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- t x))
26.0ms	(cbrt (- t x))
26.0ms	(cbrt (- t x))
55.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	270	854
1	864	747
2	5001	713

prune142.0ms

Filtered

68 candidates to 56 candidates (17.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	70	14	84

Merged error: 3.7b

Counts

84 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
0.9b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
0.9b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
9.5b	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`cbrt-div`
24×	`associate-/r/`
18×	`flip3--` `flip--`
16×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`frac-times`
10×	`add-cube-cbrt`
6×	`associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 89

Calls

4 calls:

12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
14.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
93.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
94.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
55.0ms	(+ x (* (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

simplify130.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	424	1880
1	1055	1713
2	4157	1665
3	5001	1632

prune135.0ms

Filtered

101 candidates to 81 candidates (19.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	100	15	115

Merged error: 3.7b

Counts

115 → 15

regimes675.0ms

Accuracy

21.6% (7.6b remaining)

Error of 10.9b against oracle of 3.3b and baseline of 13.0b

bsearch62.0ms

Steps

Iters	Range		Point
9	1.7684261938126428e-161	8.787333476872282e-156	1.2904642367758061e-159
9	-9.600907649315145e-157	-1.1279046134271384e-162	-5.081395861686031e-162

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	19
1	34	19

end0.0ms

sample1.0s

Algorithm

intervals

Results

294.0ms	7743×	body	80	valid
71.0ms	499×	body	640	valid
49.0ms	271×	body	1280	valid
47.0ms	433×	body	320	valid
21.0ms	285×	body	160	valid
2.0ms	11×	body	2560	valid

Details

sample42.0ms

simplify67.0ms

prune4.0ms

localize9.0ms

rewrite31.0ms

series100.0ms

simplify56.0ms

prune148.0ms

localize13.0ms

rewrite53.0ms

series164.0ms

simplify85.0ms

prune208.0ms

localize22.0ms

rewrite14.0ms

series136.0ms

simplify38.0ms

prune142.0ms

localize19.0ms

rewrite45.0ms

series336.0ms

simplify130.0ms

prune135.0ms

regimes675.0ms

bsearch62.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling