Details

sample69.0ms

Algorithm

intervals

Results

21.0ms	125×	body	320	valid
15.0ms	249×	body	80	nan
14.0ms	126×	body	160	valid
0.0ms	5×	body	80	valid

simplify128.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	21
1	125	21
2	317	21
3	648	21
4	1073	21
5	1417	21
6	1725	21
7	3333	21
8	5002	21

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize18.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
16.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
323.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify53.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	403	824
1	1484	782
2	5001	775

prune489.0ms

Filtered

80 candidates to 73 candidates (91.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 31.6b

localize20.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
318.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
52.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune524.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 30.9b

localize19.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
16.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
321.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune517.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 30.9b

localize26.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify58.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	105	456
1	265	444
2	693	444
3	1746	444
4	5001	440

prune540.0ms

Filtered

84 candidates to 76 candidates (90.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.9b

regimes1.1s

Accuracy

79% (0.6b remaining)

Error of 31.7b against oracle of 31.0b and baseline of 34.1b

bsearch104.0ms

Steps

Iters	Range		Point
7	8.83617563358547e-164	1.2581838855652194e-161	1.2333757687565298e-161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	41
1	48	41
2	52	41
3	55	41
4	55	41

end0.0ms

sample1.9s

Algorithm

intervals

Results

630.0ms	3728×	body	320	valid
469.0ms	4138×	body	160	valid
426.0ms	8022×	body	80	nan
8.0ms	134×	body	80	valid