Details

sample51.0ms

Algorithm

intervals

Results

41.0ms

302×

body

valid

simplify41.0ms

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: 12.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
3.9b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite113.0ms

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))
75.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* 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 (21.0ms)

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

prune408.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1.0) (- b a))
0.2b	(* (/ PI 2.0) (* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a))))
0.2b	(* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a)))
7.5b	(* (* (/ PI 2.0) (* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
115×	`times-frac`
112×	`add-exp-log` `add-cbrt-cube`
111×	`*-un-lft-identity`
65×	`add-cube-cbrt`
51×	`prod-exp` `sqrt-prod` `cbrt-unprod`
49×	`associate-r`
47×	`frac-times`
44×	`associate-l`
31×	`cbrt-undiv` `div-exp`
29×	`associate-*r/`
23×	`associate-*l/`
20×	`pow1`
18×	`distribute-lft-out--`
17×	`difference-of-squares`
10×	`flip3--` `pow-prod-down` `flip--`
9×	`unswap-sqr`
8×	`frac-sub`
6×	`associate-/r/` `div-inv` `distribute-lft-out` `associate-/l*`
5×	`associate-/r*`
4×	`add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+`

Counts

4 → 282

Calls

4 calls:

7.0ms	(/ (sqrt 1.0) (- b a))
45.0ms	(* (/ PI 2.0) (* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a))))
52.0ms	(* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a)))
200.0ms	(* (* (/ PI 2.0) (* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

series703.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (sqrt 1.0) (- b a))
213.0ms	(* (/ PI 2.0) (* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a))))
122.0ms	(* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a)))
287.0ms	(* (* (/ PI 2.0) (* (/ (sqrt 1.0) (+ b a)) (/ (sqrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify56.0ms

Algorithm

egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1323	3294
1	5002	2543

prune671.0ms

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

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 191

Calls

4 calls:

7.0ms	(/ 1.0 (- b a))
54.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ 1.0 (- b a)) (/ PI 2.0))) (+ b a))
87.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ 1.0 (- b a)) (/ PI 2.0)))
28.0ms	(* (/ 1.0 (- b a)) (/ PI 2.0))

series280.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (- b a))
108.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ 1.0 (- b a)) (/ PI 2.0))) (+ b a))
72.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ 1.0 (- b a)) (/ PI 2.0)))
52.0ms	(* (/ 1.0 (- b a)) (/ PI 2.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	924	1762
1	4730	1453
2	5003	1453

prune586.0ms

Pruning

9 alts after pruning (9 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))
0.1b	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* 1.0 (/ PI 2.0)) (- b a))) (+ b a))
0.3b	(/ (* 1.0 (/ PI 2.0)) (- b a))
0.3b	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* 1.0 (/ PI 2.0)) (- b a)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

18.0ms	(- (/ 1.0 a) (/ 1.0 b))
46.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* 1.0 (/ PI 2.0)) (- b a))) (+ b a))
8.0ms	(/ (* 1.0 (/ PI 2.0)) (- b a))
88.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* 1.0 (/ PI 2.0)) (- b a)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* 1.0 (/ PI 2.0)) (- b a))) (+ b a))
57.0ms	(/ (* 1.0 (/ PI 2.0)) (- b a))
71.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* 1.0 (/ PI 2.0)) (- b a)))

simplify87.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	679	1404
1	3626	1144
2	5002	1143

prune324.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.2s

9607×

body

valid