Details

sample35.0ms

Algorithm

intervals

Results

16.0ms	287×	body	80	valid
4.0ms	95×	body	80	nan

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 23.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
5.9b	(* (* x y) z)
9.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

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)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
80.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5002	510

prune212.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 2.0b

Counts

89 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
1.7b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite46.0ms

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:

8.0ms	(/ z (sqrt (- (* z z) (* t a))))
9.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
6.0ms	(sqrt (- (* z z) (* t a)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ z (sqrt (- (* z z) (* t a))))
35.0ms	(- (* z z) (* t a))
81.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
57.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	431	1015
1	2166	912
2	5002	893

prune266.0ms

Filtered

124 candidates to 82 candidates (66.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Merged error: 2.0b

Counts

135 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.3b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.7b	(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))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
9.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
52.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
80.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	403	775
1	1781	676
2	5001	667

prune204.0ms

Filtered

104 candidates to 67 candidates (64.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Merged error: 2.0b

Counts

116 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
5.9b	(* (* x y) z)
9.4b	(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

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` `cbrt-unprod` `associate-/l*` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

4 → 76

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
4.0ms	(* (* x y) z)
9.0ms	(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
3.0ms	(sqrt (- (* z z) (* t a)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
112.0ms	(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
57.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	383	598
1	2032	530
2	5002	528

prune177.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	88	11	99

Merged error: 2.0b

Counts

99 → 11

regimes526.0ms

Accuracy

79.5% (4.4b remaining)

Error of 7.7b against oracle of 3.3b and baseline of 24.8b

bsearch94.0ms

Steps

Iters	Range		Point
5	9.825461176600007e+97	3.541309604326139e+98	1.1611135688740357e+98
11	-1199119032805.3176	-6.671394545181793e-10	-1063963419286.4185

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	35	11
2	35	11

end0.0ms

sample931.0ms

Algorithm

intervals

Results

438.0ms	8847×	body	80	valid
146.0ms	3072×	body	80	nan