Details

sample28.0ms

Algorithm

intervals

Results

17.0ms

311×

body

valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 13.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.4b	(/ 1.0 (- (* b b) (* a a)))
3.8b	(- (* b b) (* a a))
7.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite107.0ms

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:

22.0ms	(* (/ 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)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify154.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (33.0ms)

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

prune414.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
7.9b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite191.0ms

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:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
55.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
92.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
68.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
52.0ms	(/ (/ PI 2.0) (+ b a))
97.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify52.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune679.0ms

Pruning

8 alts after pruning (8 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 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
0.2b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite205.0ms

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:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
90.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
9.0ms	(/ (/ PI 2.0) (+ b a))
75.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
104.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
50.0ms	(/ (/ PI 2.0) (+ b a))
58.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify55.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1236	2823
1	5001	2529

prune705.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (/ (/ PI 2.0) (+ b a)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
0.2b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

200×	`times-frac`
165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
59×	`add-exp-log` `add-cbrt-cube`
58×	`associate-l`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
18×	`associate-*r/` `prod-exp` `cbrt-unprod`
14×	`div-inv` `associate-/l*`
9×	`pow1` `associate-/r*`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`
7×	`distribute-lft-out--`
6×	`frac-times` `flip3--` `associate-/r/` `flip--` `add-log-exp` `difference-of-squares`
5×	`sub-neg` `frac-sub`
3×	`pow-prod-down`
2×	`frac-2neg` `flip3-+` `associate-*l/` `clear-num` `flip-+`
1×	`diff-log` `associate-r` `*-commutative`

Counts

4 → 248

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
65.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
78.0ms	(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
98.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
51.0ms	(/ (/ PI 2.0) (+ b a))
110.0ms	(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1134	2501
1	5002	2172

prune735.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes62.0ms

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	20	11
1	20	11

end0.0ms

sample585.0ms

Algorithm

intervals

Results

429.0ms

9650×

body

valid