Details

sample71.0ms

Algorithm

intervals

Results

21.0ms	111×	body	320	valid
15.0ms	142×	body	160	valid
13.0ms	254×	body	80	nan
0.0ms	3×	body	80	valid

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 35.9b

localize18.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.7b	(sqrt (- (* g g) (* h h)))
29.7b	(sqrt (- (* g g) (* h h)))

rewrite88.0ms

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:

32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
320.0ms	(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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

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

prune459.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.8b

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.7b	(sqrt (- (* g g) (* h h)))
29.7b	(sqrt (- (* g g) (* h h)))

rewrite64.0ms

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:

8.0ms	(- (* g g) (* h h))
33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
10.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
324.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
52.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

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

prune475.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.0b

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.7b	(sqrt (- (* g g) (* h h)))
29.7b	(sqrt (- (* g g) (* h h)))

rewrite65.0ms

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:

8.0ms	(- (* g g) (* h h))
30.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
329.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	337	621
1	1359	588
2	5001	580

prune475.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.0b

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.7b	(sqrt (- (* g g) (* h h)))
29.7b	(sqrt (- (* g g) (* h h)))

rewrite66.0ms

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:

8.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
311.0ms	(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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	315	621
1	1278	588
2	5001	581

prune371.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.0b

regimes675.0ms

Accuracy

0% (1.3b remaining)

Error of 32.5b against oracle of 31.2b and baseline of 32.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

594.0ms	3704×	body	320	valid
447.0ms	4149×	body	160	valid
394.0ms	7905×	body	80	nan
8.0ms	147×	body	80	valid