Details

sample24.0ms

Algorithm

intervals

Results

14.0ms

305×

body

valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (100.0%)

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: 14.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.0b	(/ 1.0 (- (* b b) (* a a)))
3.6b	(- (* b b) (* a a))
9.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite7.6s

Algorithm

rewrite-expression-head

Rules

66791×	`add-sqr-sqrt`
63118×	`frac-times`
59991×	`associate-/r*`
34546×	`associate-/l*`
34050×	`*-un-lft-identity`
32562×	`frac-sub`
23625×	`add-cube-cbrt`
21529×	`difference-of-squares`
11572×	`clear-num`
11487×	`frac-2neg`
10425×	`swap-sqr`
8658×	`unswap-sqr`
8644×	`*-commutative`
4310×	`distribute-lft-out--`
3690×	`associate-l`
3398×	`associate-*r/`
1166×	`associate-*l/`
805×	`times-frac`
563×	`prod-diff`
406×	`flip3--` `flip--`
315×	`associate-r`
171×	`distribute-rgt-in` `distribute-lft-in`
170×	`un-div-inv`
59×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
15×	`fma-neg`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
1×	`diff-log`

Counts

4 → 35252

Calls

4 calls:

74.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
28.0ms	(/ 1.0 (- (* b b) (* a a)))
24.0ms	(- (* b b) (* a a))
988.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
36.0ms	(- (* b b) (* a a))
95.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify9.2s

Algorithm

egg-herbie

Counts

35264 → 35264

Iterations

Useful iterations: 0 (407.0ms)

Iter	Nodes	Cost
0	20152	854233

prune46.5s

Filtered

35264 candidates to 11825 candidates (66.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	35256	8	35264
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35256	9	35265

Merged error: 0b

Counts

35265 → 9

localize18.0ms

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)))
0.4b	(* (/ PI 2.0) (/ 1.0 (+ b a)))

rewrite4.6s

Algorithm

rewrite-expression-head

Rules

33636×	`frac-times`
24492×	`associate-/r*`
23028×	`associate-/l*`
19761×	`*-un-lft-identity`
18225×	`frac-sub`
16418×	`add-sqr-sqrt`
15974×	`add-cube-cbrt`
9407×	`associate-/l/`
7769×	`clear-num`
7600×	`frac-2neg`
1856×	`associate-*r/`
1743×	`associate-*l/`
1714×	`distribute-lft-out`
1329×	`times-frac`
507×	`prod-diff`
384×	`associate-l`
338×	`un-div-inv`
228×	`associate-r`
226×	`flip3--` `flip--`
171×	`distribute-rgt-in` `distribute-lft-in`
112×	`div-inv`
103×	`distribute-lft-out--`
95×	`difference-of-squares` `unswap-sqr`
59×	`add-exp-log` `add-cbrt-cube`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp` `associate-/r/`
15×	`*-commutative`
13×	`fma-neg`
11×	`pow1`
8×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
1×	`diff-log`

Counts

4 → 20089

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
962.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
325.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
21.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
103.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
108.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
63.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify3.5s

Algorithm

egg-herbie

Counts

20101 → 20101

Iterations

Useful iterations: 0 (241.0ms)

Iter	Nodes	Cost
0	13797	302872

prune48.3s

Filtered

20101 candidates to 12107 candidates (39.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	20095	6	20101
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	20102	8	20110

Merged error: 0b

Counts

20110 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

9933×	`times-frac`
9693×	`add-sqr-sqrt`
7715×	`*-un-lft-identity`
4949×	`add-cube-cbrt`
4429×	`associate-l`
3111×	`associate-/l*`
2678×	`associate-r`
2578×	`associate-/l/`
2511×	`frac-sub`
2461×	`associate-/r*`
2295×	`associate-*l/`
2241×	`frac-times`
1257×	`unswap-sqr`
1067×	`distribute-lft-out--`
972×	`difference-of-squares`
813×	`frac-2neg` `clear-num`
507×	`prod-diff`
505×	`*-commutative`
371×	`div-inv`
317×	`distribute-lft-out`
263×	`associate-*r/`
171×	`distribute-rgt-in` `distribute-lft-in`
110×	`add-exp-log`
87×	`add-cbrt-cube`
45×	`prod-exp`
41×	`div-exp`
33×	`cbrt-unprod`
32×	`flip3--` `flip--`
30×	`cbrt-undiv`
16×	`associate-/r/`
13×	`fma-neg`
9×	`pow1`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `pow-prod-down`
1×	`diff-log`

Counts

4 → 7525

Calls

4 calls:

24.0ms	(- (/ 1.0 a) (/ 1.0 b))
342.0ms	(/ (/ (* (* (/ PI 1) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a))) (- b a))
171.0ms	(/ (* (* (/ PI 1) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
81.0ms	(* (* (/ PI 1) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
103.0ms	(/ (/ (* (* (/ PI 1) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a))) (- b a))
111.0ms	(/ (* (* (/ PI 1) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
76.0ms	(* (* (/ PI 1) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.6s

Algorithm

egg-herbie

Counts

7537 → 7537

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	7567	132312

prune21.9s

Filtered

7537 candidates to 5449 candidates (27.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	7533	4	7537
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	7539	6	7545

Merged error: 0b

Counts

7545 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (/ (* (/ PI 1) (* (cbrt 1.0) (cbrt 1.0))) 2.0) (/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))) (- b a))
0.2b	(/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.3b	(* (/ (* (/ PI 1) (* (cbrt 1.0) (cbrt 1.0))) 2.0) (/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)))

rewrite7.7s

Algorithm

rewrite-expression-head

Rules

44221×	`add-sqr-sqrt`
31888×	`associate-/l*`
26989×	`associate-/l/`
20066×	`*-un-lft-identity`
20010×	`frac-times`
15618×	`times-frac`
14921×	`associate-*r/`
14418×	`frac-sub`
14203×	`add-cube-cbrt`
13607×	`unswap-sqr`
11717×	`associate-/r*`
11599×	`associate-r`
10145×	`cbrt-prod`
7603×	`associate-l`
3848×	`clear-num`
3846×	`frac-2neg`
3204×	`swap-sqr`
2262×	`associate-*l/`
1565×	`*-commutative`
1498×	`distribute-lft-out--`
1288×	`difference-of-squares`
716×	`div-inv`
557×	`add-cbrt-cube`
377×	`distribute-lft-out`
290×	`cbrt-unprod`
287×	`add-exp-log`
252×	`cbrt-undiv`
179×	`flip3--` `flip--`
169×	`prod-diff`
125×	`div-exp`
119×	`prod-exp`
18×	`associate-/r/`
13×	`fma-neg`
12×	`1-exp`
8×	`flip3-+` `flip-+`
6×	`pow1` `un-div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
1×	`sub-neg` `diff-log` `pow-prod-down`

Counts

4 → 24237

Calls

4 calls:

41.0ms	(- (/ 1.0 a) (/ 1.0 b))
2.2s	(/ (* (/ (* (/ PI 1) (* (cbrt 1.0) (cbrt 1.0))) 2.0) (/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))) (- b a))
93.0ms	(/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
853.0ms	(* (/ (* (/ PI 1) (* (cbrt 1.0) (cbrt 1.0))) 2.0) (/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (/ 1.0 a) (/ 1.0 b))
198.0ms	(/ (* (/ (* (/ PI 1) (* (cbrt 1.0) (cbrt 1.0))) 2.0) (/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))) (- b a))
202.0ms	(/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
225.0ms	(* (/ (* (/ PI 1) (* (cbrt 1.0) (cbrt 1.0))) 2.0) (/ (* (cbrt 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)))

simplify5.5s

Algorithm

egg-herbie

Counts

24249 → 24249

Iterations

Useful iterations: 0 (383.0ms)

Iter	Nodes	Cost
0	20101	518333

prune1.3m

Filtered

24249 candidates to 16322 candidates (32.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	24249	0	24249
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	24249	6	24255

Merged error: 0b

Counts

24255 → 6

regimes78.0ms

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	26	16
1	26	16

end0.0ms

sample602.0ms

Algorithm

intervals

Results

444.0ms

9561×

body

valid