Details

sample27.0ms

Algorithm

intervals

Results

14.0ms

316×

body

valid

simplify42.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
5.4b	(- (* b b) (* a a))
9.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite260.0ms

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))))
14.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
151.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms	(/ 1.0 (- (* b b) (* a a)))
28.0ms	(- (* b b) (* a a))
89.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify158.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune903.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.8b

localize13.0ms

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)))
9.9b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

1061×	`times-frac`
851×	`*-un-lft-identity`
814×	`add-sqr-sqrt`
695×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
108×	`associate-r`
97×	`div-inv`
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×	`associate-/l*`
14×	`frac-times` `associate-l`
13×	`fma-neg`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
2×	`*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 875

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
28.0ms	(/ (/ 1.0 (+ b a)) (- b a))
84.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
180.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (/ 1.0 a) (/ 1.0 b))
66.0ms	(/ (/ 1.0 (+ b a)) (- b a))
89.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
94.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify215.0ms

Algorithm

egg-herbie

Counts

887 → 887

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	3156	21276
1	5003	19725

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite438.0ms

Algorithm

rewrite-expression-head

Rules

761×	`times-frac`
619×	`add-sqr-sqrt`
605×	`*-un-lft-identity`
579×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
86×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
30×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
13×	`fma-neg`
12×	`distribute-lft-out--`
11×	`pow1`
10×	`flip3--` `flip--` `difference-of-squares`
9×	`frac-sub`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `distribute-lft-out`
2×	`*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 707

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
158.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
37.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
144.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
95.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
49.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
103.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify188.0ms

Algorithm

egg-herbie

Counts

719 → 719

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2643	18215
1	5001	16153

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
0.2b	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.4b	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

809×	`times-frac`
641×	`*-un-lft-identity`
633×	`add-sqr-sqrt`
587×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
91×	`div-inv`
47×	`add-exp-log` `add-cbrt-cube`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
16×	`cbrt-undiv` `div-exp` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
13×	`fma-neg`
12×	`associate-r`
11×	`associate-/l*`
10×	`associate-*l/`
9×	`pow1` `associate-/r*`
8×	`associate-/l/` `distribute-lft-out`
7×	`flip3-+` `flip-+`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 714

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
73.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
139.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
118.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
88.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
97.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
70.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify174.0ms

Algorithm

egg-herbie

Counts

726 → 726

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2578	17411
1	5001	15285

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes53.0ms

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	14	8
1	14	8

end0.0ms

sample666.0ms

Algorithm

intervals

Results

438.0ms	9648×	body	80	valid
0.0ms	1×	body	160	valid