Details

sample29.0ms

Algorithm

intervals

Results

16.0ms

314×

body

valid

simplify37.0ms

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: 13.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
5.7b	(- (* b b) (* a a))
6.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite184.0ms

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:

44.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
114.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
28.0ms	(- (* b b) (* a a))
82.0ms	(* (* (/ 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 (20.0ms)

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

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize12.0ms

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))
6.6b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite265.0ms

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:

11.0ms	(/ 1.0 (- b a))
78.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
17.0ms	(/ (/ PI 2.0) (+ b a))
143.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (- b a))
61.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
46.0ms	(/ (/ PI 2.0) (+ b a))
90.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify58.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune691.0ms

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

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

226×	`times-frac`
193×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
79×	`associate-l`
52×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`frac-times` `associate-r/` `associate-/l`
15×	`div-inv`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-/r*`
8×	`flip3--` `associate-/r/` `flip--`
6×	`sub-neg` `frac-sub`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 292

Calls

4 calls:

11.0ms	(/ 1.0 (- b a))
133.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
103.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
20.0ms	(/ (/ PI 2.0) (+ b a))

series231.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (- b a))
88.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
47.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
53.0ms	(/ (/ PI 2.0) (+ b a))

simplify53.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1243	2856
1	5001	2568

prune721.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(/ (* (/ 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	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
61×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
54×	`times-frac`
35×	`add-cube-cbrt`
34×	`associate-l`
29×	`frac-times` `associate-*r/`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-/l/`
13×	`associate-r`
12×	`flip3--` `flip--` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in` `frac-sub`
9×	`associate-/r*`
7×	`associate-*l/`
6×	`sub-neg` `associate-/r/` `div-inv`
4×	`pow-prod-down` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `distribute-lft-out` `unswap-sqr`
1×	`flip3-+` `flip-+`

Counts

4 → 205

Calls

4 calls:

11.0ms	(/ 1.0 (- b a))
113.0ms	(/ (* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (+ b a))
100.0ms	(* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
104.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (- b a))
232.0ms	(/ (* (/ 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))))
47.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify49.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	959	2052
1	5001	1708

prune457.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes71.0ms

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	14	6
1	14	6

end0.0ms

sample614.0ms

Algorithm

intervals

Results

402.0ms

9563×

body

valid