Details

sample28.0ms

Algorithm

intervals

Results

16.0ms

307×

body

valid

simplify40.0ms

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: 12.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
2.9b	(- (* b b) (* a a))
8.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite179.0ms

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:

43.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms	(/ 1.0 (- (* b b) (* a a)))
7.0ms	(- (* b b) (* a a))
111.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
49.0ms	(/ 1.0 (- (* b b) (* a a)))
32.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (22.0ms)

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

prune539.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.9b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
298×	`*-un-lft-identity`
261×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
108×	`associate-r`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
14×	`frac-times` `associate-l`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

23.0ms	(- (/ 1.0 a) (/ 1.0 b))
28.0ms	(/ (/ 1.0 (+ b a)) (- b a))
81.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
142.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
54.0ms	(/ (/ 1.0 (+ b a)) (- b a))
63.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
97.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify67.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune805.0ms

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 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(* (/ PI 2.0) (/ 1.0 (+ b a)))
0.4b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
59×	`add-exp-log` `add-cbrt-cube`
52×	`*-un-lft-identity`
50×	`times-frac`
30×	`associate-r`
27×	`frac-times`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
12×	`distribute-lft-out--`
11×	`pow1`
10×	`flip3--` `flip--` `difference-of-squares`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `unswap-sqr`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

23.0ms	(- (/ 1.0 a) (/ 1.0 b))
83.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
34.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
104.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
56.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
105.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify48.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	987	1768
1	5002	1458

prune425.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b))) (- b a))
0.2b	(* (* 1.0 (- b a)) PI)
0.3b	(* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a)))
0.4b	(/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b)))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

269×	`add-exp-log` `add-cbrt-cube`
129×	`prod-exp` `cbrt-unprod`
85×	`cbrt-undiv` `div-exp`
44×	`times-frac`
43×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
21×	`associate-r`
18×	`pow1`
14×	`associate-*l/`
12×	`associate-*r/`
9×	`pow-prod-down` `div-inv`
6×	`flip3--` `associate-/r` `flip--` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times` `associate-/r/` `add-log-exp`
3×	`distribute-lft-out`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 219

Calls

4 calls:

123.0ms	(/ (/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b))) (- b a))
30.0ms	(* (* 1.0 (- b a)) PI)
114.0ms	(* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a)))
119.0ms	(/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b))) (- b a))
55.0ms	(* (* 1.0 (- b a)) PI)
94.0ms	(* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a)))
126.0ms	(/ (* (* (* 1.0 (- b a)) PI) (/ 1.0 (+ b a))) (* 2.0 (* a b)))

simplify58.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1116	3342
1	5002	2307

prune309.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.3b 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	10
1	17	10

end0.0ms

sample618.0ms

Algorithm

intervals

Results

411.0ms

9598×

body

valid