Details

sample45.0ms

Algorithm

intervals

Results

35.0ms

296×

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: 13.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.8b	(- (* b b) (* a a))
9.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite111.0ms

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))
73.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
36.0ms	(- (* b b) (* a a))
87.0ms	(* (* (/ 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

prune411.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
9.1b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite219.0ms

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))
17.0ms	(/ (/ 1.0 (+ b a)) (- b a))
66.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
105.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (+ b a))
48.0ms	(/ (/ 1.0 (+ b a)) (- b a))
65.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
96.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify61.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1467	3480
1	5002	3169

prune852.0ms

Pruning

11 alts after pruning (11 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 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.3b	(* PI (/ 1.0 (+ b a)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
47×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
36×	`times-frac`
30×	`associate-r`
25×	`add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`cbrt-undiv` `div-exp`
11×	`pow1`
7×	`associate-/l/` `distribute-lft-out`
6×	`frac-times` `associate-/r/`
5×	`flip3--` `associate-/r*` `flip--` `div-inv` `distribute-lft-out--`
4×	`associate-l` `pow-prod-down` `frac-sub` `associate-/l*` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `clear-num` `-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

6.0ms	(/ 1.0 (+ b a))
44.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
66.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
16.0ms	(* PI (/ 1.0 (+ b a)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1.0 (+ b a))
95.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
102.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
54.0ms	(* PI (/ 1.0 (+ b a)))

simplify108.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	738	1318
1	4740	1036
2	5001	1036

prune485.0ms

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

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

18.0ms	(- (/ 1.0 a) (/ 1.0 b))
37.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
29.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
54.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
100.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
63.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify102.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	723	1440
1	3957	1141
2	5001	1141

prune304.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes68.0ms

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	17	9
1	17	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.2s

9559×

body

valid