Details

sample52.0ms

Algorithm

intervals

Results

42.0ms

302×

body

valid

simplify41.0ms

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: 12.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
3.9b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite166.0ms

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:

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))
96.0ms	(* (* (/ 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))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* b b) (* a a))
93.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify153.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

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))
7.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite235.0ms

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:

5.0ms	(/ 1.0 (- b a))
53.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
117.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (- b a))
63.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
49.0ms	(/ (/ PI 2.0) (+ b a))
93.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify173.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	2933	16072
1	5002	14991

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(/ (* (* (/ 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)))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

525×	`times-frac`
437×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
399×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
61×	`add-exp-log` `add-cbrt-cube`
58×	`div-inv`
33×	`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`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`associate-/r*`
8×	`frac-sub`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`sub-neg` `frac-2neg` `clear-num` `*-commutative` `distribute-lft-out`
1×	`flip3-+` `flip-+`

Counts

4 → 541

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
112.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
96.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
22.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (- b a))
93.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
73.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
54.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify153.0ms

Algorithm

egg-herbie

Counts

553 → 553

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2636	13889
1	5001	12841

prune953.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ (* (* 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)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

765×	`times-frac`
607×	`*-un-lft-identity`
599×	`add-sqr-sqrt`
575×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
90×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*r/`
14×	`associate-/r/`
13×	`fma-neg`
12×	`associate-r`
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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`sub-neg` `pow-prod-down` `frac-sub`
2×	`frac-2neg` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 680

Calls

4 calls:

23.0ms	(- (/ 1.0 a) (/ 1.0 b))
34.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a))) (+ b a))
90.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
78.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a))) (+ b a))
72.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
67.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify165.0ms

Algorithm

egg-herbie

Counts

692 → 692

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2426	16270
1	5001	13237

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.3s

9607×

body

valid