Details

sample129.0ms

Algorithm

intervals

Results

44.0ms	118×	body	320	valid
32.0ms	243×	body	80	nan
30.0ms	127×	body	160	valid
2.0ms	11×	body	80	valid

simplify124.0ms

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: 36.5b

localize17.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
6.9b	(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)))

rewrite43.0ms

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))))))
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)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
305.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify45.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

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

prune457.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 33.3b

localize18.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
6.9b	(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)))

rewrite32.0ms

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:

3.0ms	(- (* 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)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify47.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune462.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
6.9b	(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)))

rewrite34.0ms

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:

3.0ms	(- (* g g) (* h h))
17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
310.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune498.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 33.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
6.8b	(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)))
5.0ms	(sqrt (- (* g g) (* h h)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
324.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

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

prune416.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 33.0b

regimes811.0ms

Accuracy

65.5% (1.1b remaining)

Error of 31.6b against oracle of 30.6b and baseline of 33.7b

bsearch335.0ms

Steps

Iters	Range		Point
9	-3.57416073242495e-229	-1.1545435191862917e-238	-1.1782238543655228e-238

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	54
1	53	54
2	57	54
3	60	54
4	60	54

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	3742×	body	320	valid
1.1s	7939×	body	80	nan
978.0ms	4092×	body	160	valid
23.0ms	166×	body	80	valid