Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

314×

body

valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	90	10
2	384	10
3	1828	10
4	5001	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
5.7b	(- (* b b) (* a a))
6.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
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×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

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))
147.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
38.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
82.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify154.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune852.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize13.0ms

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))
6.6b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
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*`
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×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

11.0ms	(/ 1.0 (- b a))
78.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
17.0ms	(/ (/ PI 2.0) (+ b a))
171.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (- b a))
59.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
45.0ms	(/ (/ PI 2.0) (+ b a))
87.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify176.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2933	16072
1	5002	14991

prune1.2s

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

rewrite528.0ms

Algorithm

rewrite-expression-head

Rules

1630×	`times-frac`
1285×	`*-un-lft-identity`
1240×	`add-sqr-sqrt`
1209×	`add-cube-cbrt`
1014×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
171×	`div-inv`
79×	`associate-l`
52×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`frac-times` `associate-r/` `associate-/l`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`flip3--` `associate-/r/` `flip--`
6×	`sub-neg` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 1314

Calls

4 calls:

11.0ms	(/ 1.0 (- b a))
226.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
132.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
17.0ms	(/ (/ PI 2.0) (+ b a))

series225.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (- b a))
88.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
52.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
47.0ms	(/ (/ PI 2.0) (+ b a))

simplify353.0ms

Algorithm

egg-herbie

Counts

1326 → 1326

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5002	40379

prune4.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize13.0ms

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

rewrite430.0ms

Algorithm

rewrite-expression-head

Rules

833×	`times-frac`
661×	`*-un-lft-identity`
641×	`add-sqr-sqrt`
613×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
90×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
13×	`fma-neg`
12×	`associate-r` `distribute-lft-out--`
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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 718

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
165.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
148.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))
21.0ms	(/ (/ PI 2.0) (+ b a))

series263.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
88.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
94.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))
47.0ms	(/ (/ PI 2.0) (+ b a))

simplify181.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2586	18289
1	5001	15335

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes70.0ms

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

416.0ms

9563×

body

valid