Details

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.306641%

Guaranteed chance to sample good point: 44.017094%

Results

14.0ms	256×	body	80	valid
3.0ms	55×	body	80	nan
1.0ms	25×	body	80	invalid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

prune5.0ms

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: 27.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
4.1b	(* (* x y) z)
10.3b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
4.0ms	(* (* x y) z)
12.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
28.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune130.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Merged error: 2.6b

Counts

89 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
2.6b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`sqrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(sqrt (- (* z z) (* t a)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
30.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	428	1014
1	2153	912
2	5002	894

prune123.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	124	10	134

Merged error: 2.6b

Counts

134 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.0b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.7b	(* y (/ z (sqrt (- (* z z) (* t a)))))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(sqrt (- (* z z) (* t a)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
28.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
17.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	400	774
1	1768	676
2	5001	668

prune115.0ms

Filtered

67 candidates to 104 candidates (-55.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	103	11	114

Merged error: 2.6b

Counts

114 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
2.0b	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
26.2b	(sqrt (- (* z z) (* t a)))
26.2b	(sqrt (- (* z z) (* t a)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
62×	`add-cbrt-cube`
61×	`associate-r`
60×	`sqrt-prod`
54×	`times-frac`
46×	`add-sqr-sqrt`
44×	`add-cube-cbrt` `*-un-lft-identity`
41×	`prod-exp` `cbrt-unprod`
27×	`cbrt-prod`
20×	`pow1`
16×	`cbrt-undiv` `div-exp`
9×	`associate-*r/` `pow-prod-down`
8×	`sqrt-div`
4×	`associate-l` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/r/` `-commutative`
1×	`div-inv`

Counts

4 → 156

Calls

4 calls:

24.0ms	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
27.0ms	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
22.0ms	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
15.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify142.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	830	3162
1	4754	2602
2	5001	2550

prune142.0ms

Filtered

112 candidates to 168 candidates (-50.0%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	168	11	179

Merged error: 2.6b

Counts

179 → 11

regimes989.0ms

Accuracy

86% (2.8b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 23.1b

bsearch46.0ms

Steps

Iters	Range		Point
5	2.135684305269813e+48	5.711225389897116e+48	5.6430557015530644e+48
6	-2.057529759461471e+117	-3.071603185224283e+116	-6.096387103025836e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	33	10
2	33	10

end0.0ms

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.306641%

Guaranteed chance to sample good point: 44.017094%

Results

443.0ms	8000×	body	80	valid
82.0ms	1649×	body	80	nan
43.0ms	835×	body	80	invalid

Details

sample2.6s

simplify11.0ms

prune5.0ms

localize10.0ms

rewrite25.0ms

series52.0ms

simplify60.0ms

prune130.0ms

localize10.0ms

rewrite27.0ms

series58.0ms

simplify68.0ms

prune123.0ms

localize10.0ms

rewrite30.0ms

series67.0ms

simplify56.0ms

prune115.0ms

localize18.0ms

rewrite65.0ms

series82.0ms

simplify142.0ms

prune142.0ms

regimes989.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

sample3.6s

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