Details

sample121.0ms

Algorithm

intervals

Results

34.0ms	101×	body	320	valid
33.0ms	152×	body	160	valid
33.0ms	282×	body	80	nan
0.0ms	3×	body	80	valid

simplify127.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize17.0ms

Local error

Found 4 expressions with local error:

8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite45.0ms

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:

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

series709.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
301.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

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

prune464.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 33.5b

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite29.0ms

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`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
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)))
4.0ms	(sqrt (- (* g g) (* h h)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* g g) (* h h))
309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	337	619
1	1359	588
2	5001	580

prune518.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 33.0b

localize22.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
4.8b	(- (* g g) (* h h))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
43.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify51.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	135	420
1	482	394
2	1632	388
3	5001	378

prune528.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 33.0b

localize31.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
6.0b	(fma g g (- (* h h)))
31.5b	(sqrt (- (* g g) (* h h)))
31.5b	(sqrt (fma g g (- (* h h))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
0.0ms	(fma g g (- (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))
1.0ms	(sqrt (fma g g (- (* h h))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
37.0ms	(fma g g (- (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (fma g g (- (* h h))))

simplify54.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	159	350
1	506	327
2	1656	324
3	5001	318

prune368.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 33.0b

regimes904.0ms

Accuracy

80.7% (0.6b remaining)

Error of 31.1b against oracle of 30.5b and baseline of 33.6b

bsearch233.0ms

Steps

Iters	Range		Point
11	-1.5627956907882408e-164	-7.044561979089967e-184	-1.4401173585185467e-164

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	54
1	52	54

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	3665×	body	320	valid
938.0ms	8043×	body	80	nan
919.0ms	4225×	body	160	valid
14.0ms	110×	body	80	valid