Details

sample25.0ms

Algorithm

intervals

Results

14.0ms

306×

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: 12.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
2.9b	(- (* b b) (* a a))
8.8b	(* (* (/ 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)))
8.0ms	(- (* b b) (* a a))
110.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
38.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
85.0ms	(* (* (/ 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 (22.0ms)

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

prune390.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.8b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-exp-log` `add-cbrt-cube`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/`
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` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

10.0ms	(/ 1.0 (+ b a))
27.0ms	(/ (/ 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)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (+ b a))
49.0ms	(/ (/ 1.0 (+ b a)) (- b a))
55.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
89.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify70.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1467	3480
1	5002	3169

prune816.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.2b	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.4b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 190

Calls

4 calls:

10.0ms	(/ 1.0 (+ b a))
82.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
101.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
37.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (+ b a))
87.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
98.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
51.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	963	1767
1	5001	1458

prune455.0ms

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

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

281×	`add-sqr-sqrt`
267×	`times-frac`
239×	`*-un-lft-identity`
87×	`add-cube-cbrt`
84×	`associate-r`
80×	`distribute-lft-out--`
69×	`difference-of-squares`
61×	`add-exp-log` `add-cbrt-cube`
27×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-/l*`
14×	`associate-l`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-/r/`
7×	`distribute-lft-out`
6×	`frac-times` `associate-*l/`
4×	`associate-*r/` `pow-prod-down` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`div-sub` `frac-sub`

Counts

4 → 287

Calls

4 calls:

10.0ms	(/ 1.0 (+ b a))
121.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
67.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
38.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (+ b a))
89.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
47.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
47.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1205	2894
1	5002	2585

prune756.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes63.0ms

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	18	10
1	18	10

end0.0ms

sample621.0ms

Algorithm

intervals

Results

420.0ms

9500×

body

valid