Details

sample70.0ms

Algorithm

intervals

Results

21.0ms	128×	body	320	valid
16.0ms	273×	body	80	nan
13.0ms	121×	body	160	valid
0.0ms	7×	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: 37.5b

localize17.0ms

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)))

rewrite46.0ms

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:

19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* 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)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
324.0ms	(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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	385	768
1	1378	726
2	5001	720

prune432.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.9b

localize21.0ms

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` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

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)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
320.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	297	569
1	1188	537
2	5001	533

prune452.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.5b

localize19.0ms

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)))

rewrite33.0ms

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` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

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)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	297	571
1	1186	537
2	5001	533

prune440.0ms

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)))

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` `sqrt-div` `add-cbrt-cube`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

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)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
331.0ms	(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)))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune355.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 32.5b

regimes1.0s

Accuracy

80.2% (0.7b remaining)

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

bsearch65.0ms

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

sample1.9s

Algorithm

intervals

Results

610.0ms	3680×	body	320	valid
469.0ms	4170×	body	160	valid
419.0ms	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