Details

sample27.0ms

Algorithm

intervals

Results

17.0ms

299×

body

valid

simplify41.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.4b

Counts

2 → 1

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)))
3.5b	(- (* b b) (* a a))
8.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite8.2s

Algorithm

rewrite-expression-head

Rules

66210×	`add-sqr-sqrt`
63118×	`frac-times`
59991×	`associate-/r*`
34546×	`associate-/l*`
33531×	`*-un-lft-identity`
32562×	`frac-sub`
23106×	`add-cube-cbrt`
21529×	`difference-of-squares`
11572×	`clear-num`
11487×	`frac-2neg`
10332×	`swap-sqr`
8627×	`unswap-sqr`
8613×	`*-commutative`
4310×	`distribute-lft-out--`
3597×	`associate-l`
3398×	`associate-*r/`
1166×	`associate-*l/`
406×	`flip3--` `flip--`
337×	`times-frac`
222×	`associate-r`
170×	`un-div-inv`
36×	`add-exp-log` `add-cbrt-cube`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`associate-/r/` `add-log-exp`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`diff-log`

Counts

4 → 34666

Calls

4 calls:

69.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
21.0ms	(/ 1.0 (- (* b b) (* a a)))
28.0ms	(- (* b b) (* a a))
1.0s	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
33.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify8.0s

Algorithm

egg-herbie

Counts

34678 → 34678

Iterations

Useful iterations: 0 (222.0ms)

Iter	Nodes	Cost
0	19332	837088

prune52.6s

Filtered

34678 candidates to 11965 candidates (34.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	34670	8	34678
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34670	9	34679

Merged error: 0b

Counts

34679 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (* (/ 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)))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

33636×	`frac-times`
24492×	`associate-/r*`
23028×	`associate-/l*`
19208×	`*-un-lft-identity`
18225×	`frac-sub`
15865×	`add-sqr-sqrt`
15421×	`add-cube-cbrt`
9407×	`associate-/l/`
7769×	`clear-num`
7600×	`frac-2neg`
1856×	`associate-*r/`
1743×	`associate-*l/`
1714×	`distribute-lft-out`
618×	`times-frac`
384×	`associate-l`
338×	`un-div-inv`
228×	`associate-r`
226×	`flip3--` `flip--`
103×	`distribute-lft-out--`
95×	`difference-of-squares` `unswap-sqr`
59×	`add-exp-log` `add-cbrt-cube`
33×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp` `associate-/r/`
15×	`*-commutative`
11×	`pow1`
8×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`diff-log`

Counts

4 → 19561

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
822.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
259.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
19.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
107.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
49.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify3.1s

Algorithm

egg-herbie

Counts

19573 → 19573

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	13184	285914

prune47.4s

Filtered

19573 candidates to 11579 candidates (59.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	19571	2	19573
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	19574	8	19582

Merged error: 0b

Counts

19582 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ b a))
0.2b	(/ (* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.2b	(* (/ (* (/ PI 2.0) 1.0) 1) (/ (* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
0.4b	(* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite8.8s

Algorithm

rewrite-expression-head

Rules

70852×	`frac-times`
61432×	`associate-/l*`
45650×	`associate-/l/`
44154×	`associate-/r*`
43473×	`*-un-lft-identity`
41793×	`add-sqr-sqrt`
36531×	`frac-sub`
35556×	`add-cube-cbrt`
13642×	`associate-l`
13544×	`clear-num`
13543×	`frac-2neg`
11497×	`times-frac`
9178×	`associate-*l/`
4372×	`associate-*r/`
3727×	`associate-r`
3601×	`distribute-lft-out`
2175×	`unswap-sqr`
1131×	`div-inv`
1025×	`*-commutative`
453×	`flip3--` `flip--`
371×	`distribute-lft-out--`
320×	`difference-of-squares`
240×	`add-exp-log`
108×	`div-exp` `associate-/r/`
102×	`prod-exp`
100×	`add-cbrt-cube`
52×	`flip3-+` `flip-+`
38×	`cbrt-undiv`
36×	`cbrt-unprod`
28×	`1-exp`
10×	`rec-exp`
9×	`pow1`
4×	`un-div-inv` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down`
1×	`pow-flip` `inv-pow`

Counts

4 → 40392

Calls

4 calls:

5.0ms	(/ 1 (+ b a))
117.0ms	(/ (* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
1.1s	(* (/ (* (/ PI 2.0) 1.0) 1) (/ (* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
57.0ms	(* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (+ b a))
66.0ms	(/ (* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
91.0ms	(* (/ (* (/ PI 2.0) 1.0) 1) (/ (* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a)))
75.0ms	(* (/ 1 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify10.5s

Algorithm

egg-herbie

Counts

40404 → 40404

Iterations

Useful iterations: 0 (552.0ms)

Iter	Nodes	Cost
0	36485	979052

prune1.7m

Filtered

40404 candidates to 24846 candidates (61.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	40403	1	40404
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	40404	8	40412

Merged error: 0b

Counts

40412 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b a) (* (/ a (sqrt 1.0)) b))
0.3b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (* (sqrt 1.0) b) (* (/ a (sqrt 1.0)) (/ 1.0 1))))
0.3b	(* (/ PI 2.0) (/ 1.0 (+ b a)))
0.4b	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (* (sqrt 1.0) b) (* (/ a (sqrt 1.0)) (/ 1.0 1)))) (* (- b a) (* (/ a (sqrt 1.0)) b)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

12819×	`add-sqr-sqrt`
9257×	`times-frac`
5917×	`associate-r`
5209×	`associate-l`
4182×	`*-un-lft-identity`
3834×	`unswap-sqr`
2724×	`add-cube-cbrt`
1928×	`sqrt-prod`
1559×	`difference-of-squares`
1122×	`frac-times`
594×	`associate-/r*`
553×	`associate-/l*`
361×	`associate-*l/`
335×	`associate-/l/`
285×	`distribute-lft-out--`
277×	`*-commutative`
250×	`flip3--` `flip--`
220×	`distribute-lft-out`
190×	`div-inv`
179×	`add-exp-log` `add-cbrt-cube`
161×	`clear-num`
154×	`frac-2neg`
138×	`associate-/r/`
98×	`associate-*r/`
84×	`prod-exp` `cbrt-unprod`
55×	`cbrt-undiv` `div-exp`
50×	`flip3-+` `flip-+`
16×	`pow1`
14×	`un-div-inv`
7×	`pow-prod-down`
4×	`add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`

Counts

4 → 5354

Calls

4 calls:

24.0ms	(* (- b a) (* (/ a (sqrt 1.0)) b))
96.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (* (sqrt 1.0) b) (* (/ a (sqrt 1.0)) (/ 1.0 1))))
24.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
235.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (* (sqrt 1.0) b) (* (/ a (sqrt 1.0)) (/ 1.0 1)))) (* (- b a) (* (/ a (sqrt 1.0)) b)))

series889.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- b a) (* (/ a (sqrt 1.0)) b))
372.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (* (sqrt 1.0) b) (* (/ a (sqrt 1.0)) (/ 1.0 1))))
50.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
336.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (* (sqrt 1.0) b) (* (/ a (sqrt 1.0)) (/ 1.0 1)))) (* (- b a) (* (/ a (sqrt 1.0)) b)))

simplify1.4s

Algorithm

egg-herbie

Counts

5366 → 5366

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5662	163015

prune15.7s

Filtered

5366 candidates to 3246 candidates (60.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	5365	1	5366
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	5366	8	5374

Merged error: 0b

Counts

5374 → 8

regimes109.0ms

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	24	11
1	24	11

end0.0ms

sample558.0ms

Algorithm

intervals

Results

416.0ms

9660×

body

valid