Details

sample24.0ms

Algorithm

intervals

Results

14.0ms

312×

body

valid

simplify41.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.0b	(- (* b b) (* a a))
11.3b	(* (* (/ 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:

24.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
69.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
46.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify111.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (22.0ms)

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

prune408.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.1b

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)))
0.2b	(/ (/ PI 2.0) (+ b a))
11.3b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite186.0ms

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

series249.0ms

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)))
55.0ms	(/ (/ PI 2.0) (+ b a))
97.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify51.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune670.0ms

Pruning

9 alts after pruning (9 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) (/ 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	(* (/ PI 2.0) (/ 1.0 (- b a)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 180

Calls

4 calls:

18.0ms	(- (/ 1.0 a) (/ 1.0 b))
47.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
67.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
26.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
75.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify42.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	975	1762
1	5001	1452

prune451.0ms

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
34.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a))) (+ b a))
27.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
49.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
95.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a))) (+ b a))
75.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
67.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify136.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	768	1849
1	4635	1516
2	5002	1516

prune328.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes53.0ms

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	17	9
1	17	9

end0.0ms

sample722.0ms

Algorithm

intervals

Results

572.0ms

9585×

body

valid