Details

sample25.0ms

Algorithm

intervals

Results

14.0ms

315×

body

valid

simplify39.0ms

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: 17.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
4.5b	(- (* b b) (* a a))
11.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite179.0ms

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:

42.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
111.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
37.0ms	(/ 1.0 (- (* b b) (* a a)))
32.0ms	(- (* b b) (* a a))
79.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune388.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
11.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
14×	`frac-times`
13×	`associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

23.0ms	(- (/ 1.0 a) (/ 1.0 b))
74.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
17.0ms	(/ (/ PI 2.0) (+ b a))
137.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
55.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
50.0ms	(/ (/ PI 2.0) (+ b a))
87.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify52.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune645.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
59×	`add-exp-log` `add-cbrt-cube`
53×	`*-un-lft-identity`
52×	`times-frac`
33×	`associate-r`
27×	`frac-times` `add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
13×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `unswap-sqr`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `distribute-lft-out`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 180

Calls

4 calls:

23.0ms	(- (/ 1.0 a) (/ 1.0 b))
84.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
101.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
39.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (/ 1.0 a) (/ 1.0 b))
85.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
67.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
48.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify40.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	975	1762
1	5001	1452

prune421.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (/ PI (* a b)))
0.2b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.9b	(/ PI (* a b))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `add-cube-cbrt` `times-frac` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`associate-l` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*r/` `clear-num` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`

Counts

3 → 78

Calls

3 calls:

20.0ms	(* 0.5 (/ PI (* a b)))
24.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
11.0ms	(/ PI (* a b))

series116.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 0.5 (/ PI (* a b)))
59.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
21.0ms	(/ PI (* a b))

simplify44.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	333	455
1	1752	363
2	5001	363

prune125.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.3b 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	17	6
1	17	6

end0.0ms

sample618.0ms

Algorithm

intervals

Results

415.0ms

9556×

body

valid