Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

304×

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: 14.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.8b	(- (* b b) (* a a))
9.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite105.0ms

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:

21.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
68.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
89.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify108.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune407.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.6b

localize12.0ms

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 (- 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)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
14×	`frac-times`
13×	`associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

18.0ms	(- (/ 1.0 a) (/ 1.0 b))
51.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
10.0ms	(/ (/ PI 2.0) (+ b a))
89.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
65.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
54.0ms	(/ (/ PI 2.0) (+ b a))
96.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify49.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune657.0ms

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 a) (/ 1.0 b))
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))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
185×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
79×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `div-inv`
13×	`associate-r` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub`
6×	`associate-/r/` `add-log-exp`
4×	`pow-prod-down` `associate-l/` `associate-/r`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
88.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
73.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(/ (/ PI 2.0) (+ b a))

series237.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
57.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
51.0ms	(/ (/ PI 2.0) (+ b a))

simplify57.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1236	2823
1	5001	2529

prune687.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 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	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
0.3b	(/ (/ PI 2.0) (+ b a))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

315×	`times-frac`
264×	`*-un-lft-identity`
238×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
58×	`associate-l`
48×	`distribute-lft-out--`
47×	`add-exp-log` `add-cbrt-cube`
41×	`difference-of-squares`
27×	`distribute-lft-out`
26×	`div-inv`
25×	`associate-/l*`
16×	`cbrt-undiv` `div-exp`
15×	`prod-exp` `cbrt-unprod`
9×	`pow1` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
4×	`associate-/l/`
3×	`flip3--` `associate-*r/` `pow-prod-down` `flip--`
2×	`frac-2neg` `flip3-+` `clear-num` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `associate-r` `associate-l/` `-commutative`

Counts

4 → 293

Calls

4 calls:

18.0ms	(- (/ 1.0 a) (/ 1.0 b))
89.0ms	(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))))
51.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))

series240.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
97.0ms	(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))))
47.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
59.0ms	(/ (/ PI 2.0) (+ b a))

simplify111.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1217	3075
1	4983	2800
2	5001	2800

prune713.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes74.0ms

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	18	10
1	18	10

end0.0ms

sample572.0ms

Algorithm

intervals

Results

417.0ms

9589×

body

valid