Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

306×

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
3.8b	(- (* b b) (* a a))
8.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite109.0ms

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:

24.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
71.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
47.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify109.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (22.0ms)

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

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.1b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-exp-log` `add-cbrt-cube`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
16.0ms	(/ (/ 1.0 (+ b a)) (- b a))
63.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
101.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (+ b a))
53.0ms	(/ (/ 1.0 (+ b a)) (- b a))
67.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
98.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify67.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1467	3480
1	5002	3169

prune820.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
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)))
0.4b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 190

Calls

4 calls:

7.0ms	(/ 1.0 (+ b a))
48.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
69.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
26.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (+ b a))
97.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
110.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
50.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify42.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	963	1767
1	5001	1458

prune459.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

269×	`add-exp-log` `add-cbrt-cube`
129×	`prod-exp` `cbrt-unprod`
85×	`cbrt-undiv` `div-exp`
44×	`times-frac`
43×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
21×	`associate-r`
18×	`pow1`
14×	`associate-*l/`
12×	`associate-*r/`
9×	`pow-prod-down` `div-inv`
6×	`flip3--` `associate-/r` `flip--` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times` `associate-/r/` `add-log-exp`
3×	`distribute-lft-out`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 219

Calls

4 calls:

62.0ms	(/ (/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b))) (- b a))
16.0ms	(* (* 1.0 (- b a)) PI)
57.0ms	(* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a)))
61.0ms	(/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b))) (- b a))
55.0ms	(* (* 1.0 (- b a)) PI)
94.0ms	(* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a)))
122.0ms	(/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b)))

simplify59.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1116	3342
1	5002	2307

prune320.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms

sample711.0ms

Algorithm

intervals

Results

558.0ms

9682×

body

valid