Details

sample25.0ms

Algorithm

intervals

Results

15.0ms

297×

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: 14.6b

localize12.0ms

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)))
4.4b	(- (* b b) (* a a))
9.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite100.0ms

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:

21.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
66.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms	(/ 1.0 (- (* b b) (* a a)))
34.0ms	(- (* b b) (* a a))
85.0ms	(* (* (/ 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 (21.0ms)

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

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
9.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
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` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
52.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
88.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (- b a))
63.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
48.0ms	(/ (/ PI 2.0) (+ b a))
92.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune682.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 190

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
56.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
73.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
53.0ms	(/ (/ PI 2.0) (+ b a))
99.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify109.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5001	1596

prune450.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
0.3b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
0.8b	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

247×	`add-exp-log` `add-cbrt-cube`
129×	`times-frac`
108×	`prod-exp` `cbrt-unprod`
105×	`*-un-lft-identity`
88×	`cbrt-undiv` `div-exp`
77×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
19×	`associate-/l*`
16×	`pow1`
14×	`div-inv` `distribute-lft-out`
12×	`associate-*r/`
10×	`associate-/r*`
8×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-*l/`
7×	`associate-/l/`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-times` `sub-neg` `associate-/r/` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`flip3-+` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 269

Calls

4 calls:

50.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
45.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
51.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

series331.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
54.0ms	(/ (/ PI 2.0) (+ b a))
88.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
118.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

simplify58.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1249	3709
1	5001	2766

prune579.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes56.0ms

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

sample558.0ms

Algorithm

intervals

Results

405.0ms

9531×

body

valid