Details

sample24.0ms

Algorithm

intervals

Results

14.0ms

315×

body

valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	89	10
2	377	10
3	1779	10
4	5001	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.9b	(- (* b b) (* a a))
8.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

22.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
70.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
88.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify111.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5002	1342

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
0.3b	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
8.5b	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
137×	`add-cbrt-cube`
83×	`prod-exp` `cbrt-unprod`
81×	`add-sqr-sqrt`
67×	`times-frac`
65×	`*-un-lft-identity`
58×	`associate-r`
49×	`cbrt-undiv` `div-exp`
47×	`frac-times`
35×	`add-cube-cbrt`
33×	`associate-*l/`
20×	`pow1`
19×	`associate-*r/`
16×	`distribute-lft-out--`
15×	`cbrt-prod` `associate-l`
14×	`difference-of-squares`
10×	`flip3--` `pow-prod-down` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp`
4×	`associate-/r/` `unswap-sqr`
3×	`sub-neg` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`flip3-+` `diff-log` `flip-+` `distribute-lft-out`

Counts

4 → 244

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
64.0ms	(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
24.0ms	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
254.0ms	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
124.0ms	(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
233.0ms	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
161.0ms	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify65.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1413	3876
1	5001	3230

prune658.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
0.3b	(* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.3b	(* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a)))

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-exp-log`
110×	`add-cbrt-cube`
77×	`prod-exp` `cbrt-unprod`
62×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
51×	`times-frac`
48×	`associate-r`
28×	`cbrt-undiv` `div-exp`
27×	`pow1`
26×	`add-cube-cbrt`
17×	`associate-*r/`
16×	`pow-prod-down` `distribute-lft-out--`
15×	`cbrt-prod`
14×	`difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate-l/` `-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 187

Calls

4 calls:

19.0ms	(- (/ 1.0 a) (/ 1.0 b))
166.0ms	(/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
186.0ms	(* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
50.0ms	(* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
153.0ms	(/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
142.0ms	(* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
112.0ms	(* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1093	2909
1	5001	2435

prune583.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.5b	(/ PI (* a b))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
3×	`associate-*r/`
2×	`pow1` `frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `div-inv` `add-log-exp`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

2 → 53

Calls

2 calls:

14.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
3.0ms	(/ PI (* a b))

series93.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
20.0ms	(/ PI (* a b))

simplify52.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	390	416
1	2377	290
2	5003	290

prune83.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6

end0.0ms

sample602.0ms

Algorithm

intervals

Results

437.0ms

9606×

body

valid