Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

298×

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: 14.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
4.1b	(- (* b b) (* a a))
9.8b	(* (* (/ 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:

23.0ms	(* (/ 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)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
88.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify107.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune399.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
9.8b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
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` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

6.0ms	(/ 1.0 (- b a))
53.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
10.0ms	(/ (/ PI 2.0) (+ b a))
92.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (- b a))
59.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
53.0ms	(/ (/ PI 2.0) (+ b a))
95.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify52.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune722.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
58.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
79.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
48.0ms	(/ (/ PI 2.0) (+ b a))
108.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify108.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5001	1596

prune468.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* (/ 1 (/ (+ b a) (/ PI 2.0))) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.2b	(/ (+ b a) (/ PI 2.0))
0.3b	(/ 1 (/ (+ b a) (/ PI 2.0)))
0.3b	(* (* (/ 1 (/ (+ b a) (/ PI 2.0))) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

635×	`times-frac`
428×	`*-un-lft-identity`
300×	`add-sqr-sqrt`
284×	`add-cube-cbrt`
131×	`add-exp-log`
75×	`associate-/r*`
66×	`distribute-lft-out`
65×	`add-cbrt-cube`
60×	`div-exp`
42×	`prod-exp`
30×	`div-inv`
27×	`cbrt-undiv`
18×	`cbrt-unprod`
12×	`associate-r`
10×	`pow1` `associate-*l/`
9×	`rec-exp` `1-exp` `associate-/l/`
8×	`associate-/r/` `associate-/l*`
7×	`distribute-lft-out--`
6×	`frac-times` `associate-*r/` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-sub` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-flip` `flip3-+` `associate-l` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 440

Calls

4 calls:

108.0ms	(/ (* (* (/ 1 (/ (+ b a) (/ PI 2.0))) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
11.0ms	(/ (+ b a) (/ PI 2.0))
18.0ms	(/ 1 (/ (+ b a) (/ PI 2.0)))
128.0ms	(* (* (/ 1 (/ (+ b a) (/ PI 2.0))) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (* (* (/ 1 (/ (+ b a) (/ PI 2.0))) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
69.0ms	(/ (+ b a) (/ PI 2.0))
53.0ms	(/ 1 (/ (+ b a) (/ PI 2.0)))
102.0ms	(* (* (/ 1 (/ (+ b a) (/ PI 2.0))) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify78.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1636	4679
1	5001	4164

prune912.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes78.0ms

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	21	11
1	21	11

end0.0ms

sample577.0ms

Algorithm

intervals

Results

427.0ms

9609×

body

valid