Details

sample65.0ms

Algorithm

intervals

Results

20.0ms	128×	body	320	valid
13.0ms	273×	body	80	nan
13.0ms	121×	body	160	valid
0.0ms	7×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize22.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.5b	(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)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
316.0ms	(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)))

simplify45.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (36.0ms)

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

prune455.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.9b

localize20.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
7.0b	(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` `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))
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)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
305.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

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

prune497.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.5b

localize24.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
7.0b	(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` `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))
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)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
306.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

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

prune482.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.5b

localize20.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
7.5b	(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)))

rewrite30.0ms

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))
17.0ms	(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)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
319.0ms	(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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

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

prune407.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 32.5b

regimes844.0ms

Accuracy

80.2% (0.7b remaining)

Error of 31.3b against oracle of 30.6b and baseline of 34.0b

bsearch66.0ms

Steps

Iters	Range		Point
4	3.635204067846e-162	6.212177176123968e-162	5.894619063055018e-162

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	56
1	62	56
2	72	56
3	91	56
4	101	56
5	113	56
6	118	56
7	131	56
8	145	56
9	158	56
10	172	56
11	194	56
12	201	56
13	201	56

end0.0ms

sample1.8s

Algorithm

intervals

Results

585.0ms	3680×	body	320	valid
448.0ms	4170×	body	160	valid
408.0ms	8156×	body	80	nan
8.0ms	150×	body	80	valid

Iter	Nodes	Cost
0	50	56
1	62	56
2	72	56
3	91	56
4	101	56
5	113	56
6	118	56
7	131	56
8	145	56
9	158	56
10	172	56
11	194	56
12	201	56
13	201	56

Iter	Nodes	Cost
0	50	56
1	62	56
2	72	56
3	91	56
4	101	56
5	113	56
6	118	56
7	131	56
8	145	56
9	158	56
10	172	56
11	194	56
12	201	56
13	201	56

Iter	Nodes	Cost
0	50	56
1	62	56
2	72	56
3	91	56
4	101	56
5	113	56
6	118	56
7	131	56
8	145	56
9	158	56
10	172	56
11	194	56
12	201	56
13	201	56