Details

sample23.0ms

Algorithm

intervals

Results

14.0ms

308×

body

valid

simplify55.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
5.4b	(- (* b b) (* a a))
8.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite101.0ms

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:

13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
37.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
51.0ms	(/ 1.0 (- (* b b) (* a a)))
36.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify147.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune860.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

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))
8.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite142.0ms

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))
36.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
43.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1.0 (- b a))
59.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
53.0ms	(/ (/ PI 2.0) (+ b a))
95.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify170.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2933	16072
1	5002	14991

prune1.1s

Filtered

646 candidates to 303 candidates (46.9%)

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

rewrite181.0ms

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:

18.0ms	(- (/ 1.0 a) (/ 1.0 b))
54.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
40.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(/ (/ PI 2.0) (+ b a))

series296.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
101.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))
59.0ms	(/ (/ PI 2.0) (+ b a))

simplify185.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2586	18289
1	5001	15335

prune1.6s

Filtered

730 candidates to 321 candidates (44.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

129×	`times-frac`
125×	`add-exp-log` `add-cbrt-cube`
106×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
49×	`cbrt-undiv` `div-exp`
45×	`prod-exp` `cbrt-unprod`
19×	`associate-/l*`
14×	`div-inv` `distribute-lft-out`
10×	`associate-/r*`
9×	`pow1`
8×	`associate-*l/`
7×	`associate-/l/`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r` `pow-prod-down` `clear-num`
2×	`sub-neg` `prod-diff`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

4 → 235

Calls

4 calls:

22.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b)) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
16.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
20.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b))

series450.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b)) (- b a))
50.0ms	(/ (/ PI 2.0) (+ b a))
115.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0)))
147.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (* 1.0 b) (* a 1.0))) (* a b))

simplify55.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1136	3191
1	5001	2539

prune537.0ms

Filtered

247 candidates to 152 candidates (61.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes45.0ms

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	28	13
1	28	13

end0.0ms

sample591.0ms

Algorithm

intervals

Results

439.0ms

9593×

body

valid