Details

sample65.0ms

Algorithm

intervals

Results

20.0ms	117×	body	320	valid
15.0ms	134×	body	160	valid
12.0ms	232×	body	80	nan
0.0ms	5×	body	80	valid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 33.6b

localize22.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

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:

11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(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)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
294.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
43.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

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

prune391.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.8b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (- g) (sqrt (- (* g g) (* h h))))
4.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-*r/` `flip-+` `distribute-lft-out--`
1×	`associate--l-` `cbrt-prod` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `pow1/3` `neg-log` `associate-*l/`

Counts

4 → 64

Calls

4 calls:

9.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
12.0ms	(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)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
43.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify124.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	333	666
1	1140	629
2	4928	620
3	5002	620

prune425.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.5b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (- g) (sqrt (- (* g g) (* h h))))
4.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-*r/` `flip-+` `distribute-lft-out--`
1×	`associate--l-` `cbrt-prod` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `pow1/3` `neg-log` `associate-*l/`

Counts

4 → 64

Calls

4 calls:

9.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
11.0ms	(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)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
308.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
43.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify124.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	333	668
1	1140	631
2	4928	620
3	5002	620

prune428.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.5b

localize23.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

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` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

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

series186.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))
43.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify53.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	96	424
1	234	412
2	572	412
3	1471	412
4	5002	412

prune428.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.5b

regimes741.0ms

Accuracy

36.3% (2.0b remaining)

Error of 32.8b against oracle of 30.8b and baseline of 33.9b

bsearch161.0ms

Steps

Iters	Range		Point
11	-2.489800818332218e-141	-6.46348463023251e-162	-5.139022009297565e-161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	42
1	42	42
2	42	42

end0.0ms

sample1.9s

Algorithm

intervals

Results

634.0ms	3693×	body	320	valid
467.0ms	4153×	body	160	valid
444.0ms	8089×	body	80	nan
9.0ms	154×	body	80	valid