Details

sample70.0ms

Algorithm

intervals

Results

23.0ms	117×	body	320	valid
15.0ms	134×	body	160	valid
13.0ms	232×	body	80	nan
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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize18.0ms

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)))

rewrite37.0ms

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:

12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
15.0ms	(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)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
306.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (39.0ms)

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

prune436.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 29.8b

localize24.0ms

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)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

70×	`prod-diff`
56×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`add-cube-cbrt`
49×	`sqrt-prod`
25×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
14×	`difference-of-squares`
10×	`fma-neg`
8×	`neg-mul-1` `add-log-exp`
6×	`pow1`
5×	`cbrt-div`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
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` `pow1/3` `neg-log` `associate-*l/`

Counts

4 → 152

Calls

4 calls:

11.0ms	(- (- 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)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
319.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify74.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	528	2961
1	1761	2051
2	5002	1864

prune604.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 29.0b

localize21.0ms

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)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

70×	`prod-diff`
56×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`add-cube-cbrt`
49×	`sqrt-prod`
25×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
14×	`difference-of-squares`
10×	`fma-neg`
8×	`neg-mul-1` `add-log-exp`
6×	`pow1`
5×	`cbrt-div`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
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` `pow1/3` `neg-log` `associate-*l/`

Counts

4 → 152

Calls

4 calls:

11.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (- g) (sqrt (- (* g g) (* h h))))
323.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify67.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	528	2959
1	1761	2049
2	5002	1862

prune613.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 29.0b

localize24.0ms

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)))

rewrite19.0ms

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)))
5.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (- (* g g) (* h h)))
43.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify58.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	105	452
1	265	440
2	693	440
3	1746	440
4	5001	440

prune480.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 29.0b

regimes837.0ms

Accuracy

80.9% (0.5b remaining)

Error of 31.5b against oracle of 31.0b and baseline of 33.8b

bsearch293.0ms

Steps

Iters	Range		Point
8	1.548099995353248e-142	4.0847624128472e-139	4.3494482620317246e-142
11	-2.489800818332218e-141	-6.46348463023251e-162	-1.2198156791199691e-160

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	75
1	52	75

end0.0ms

sample2.0s

Algorithm

intervals

Results

650.0ms	3693×	body	320	valid
490.0ms	4153×	body	160	valid
453.0ms	8089×	body	80	nan
9.0ms	154×	body	80	valid