Details

sample75.0ms

Algorithm

intervals

Results

22.0ms	134×	body	320	valid
16.0ms	297×	body	80	nan
14.0ms	122×	body	160	valid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	21
1	122	21
2	299	21
3	591	21
4	931	21
5	1162	21
6	1388	21
7	2798	21
8	5002	21

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize23.0ms

Local error

Found 4 expressions with local error:

5.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
6.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite87.0ms

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` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
36.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series696.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
300.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
43.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	385	766
1	1380	724
2	5001	718

prune394.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.7b

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
5.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite61.0ms

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` `sqrt-div` `add-cbrt-cube`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
34.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (* g g) (* h h))
494.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
47.0ms	(sqrt (- (* g g) (* h h)))
43.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune398.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
6.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite61.0ms

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` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* g g) (* h h))
297.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	297	571
1	1186	537
2	5001	533

prune398.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.3b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
5.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite60.0ms

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` `sqrt-div` `add-cbrt-cube`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* g g) (* h h))
296.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
42.0ms	(sqrt (- (* g g) (* h h)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	319	571
1	1259	537
2	5001	533

prune328.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 28.3b

regimes603.0ms

Accuracy

78.7% (0.6b remaining)

Error of 31.6b against oracle of 31.0b and baseline of 33.9b

bsearch135.0ms

Steps

Iters	Range		Point
9	-2.352808649179745e-159	-2.0911397639316354e-167	-2.046386169330917e-159

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	40
1	37	40

end0.0ms

sample2.0s

Algorithm

intervals

Results

643.0ms	3731×	body	320	valid
477.0ms	4129×	body	160	valid
427.0ms	8035×	body	80	nan
8.0ms	140×	body	80	valid