Details

sample27.0ms

Algorithm

intervals

Results

16.0ms

307×

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: 12.5b

localize12.0ms

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)))

rewrite191.0ms

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:

44.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
119.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
47.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

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

prune402.0ms

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)))

rewrite309.0ms

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:

24.0ms	(- (/ 1.0 a) (/ 1.0 b))
29.0ms	(/ (/ 1.0 (+ b a)) (- b a))
83.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
149.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
55.0ms	(/ (/ 1.0 (+ b a)) (- b a))
61.0ms	(* (/ 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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune802.0ms

Pruning

10 alts after pruning (10 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 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* PI (/ 1.0 (+ b a)))
0.4b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log` `add-cbrt-cube`
47×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
34×	`times-frac`
30×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
18×	`add-cube-cbrt`
17×	`associate-*r/`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`distribute-lft-out--`
8×	`difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`frac-sub`
4×	`associate-l` `pow-prod-down` `associate-/r/`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 137

Calls

4 calls:

25.0ms	(- (/ 1.0 a) (/ 1.0 b))
75.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
28.0ms	(* PI (/ 1.0 (+ b a)))
98.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
98.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
50.0ms	(* PI (/ 1.0 (+ b a)))
105.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	762	1319
1	4686	1036
2	5001	1036

prune472.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
94×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
50×	`add-exp-log` `add-cbrt-cube`
31×	`associate-/r*`
29×	`add-cube-cbrt`
25×	`distribute-lft-out--`
21×	`cbrt-undiv` `div-exp`
20×	`difference-of-squares`
18×	`associate-r`
15×	`div-inv`
12×	`prod-exp` `associate-/r/` `cbrt-unprod`
6×	`pow1` `add-log-exp`
5×	`flip3--` `flip--`
4×	`associate-*r/` `frac-sub`
3×	`associate-l` `associate-/l/` `distribute-lft-out`
2×	`frac-2neg` `clear-num` `associate-/l*` `unswap-sqr`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 172

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
61.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
52.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
27.0ms	(* PI (/ 1.0 (+ b a)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
58.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
52.0ms	(* PI (/ 1.0 (+ b a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	872	1738
1	4713	1451
2	5001	1451

prune404.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes57.0ms

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

sample624.0ms

Algorithm

intervals

Results

416.0ms

9598×

body

valid