Details

sample26.0ms

Algorithm

intervals

Results

16.0ms

291×

body

valid

simplify40.0ms

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

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: 14.2b

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)))
3.3b	(- (* b b) (* a a))
10.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite109.0ms

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:

14.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
41.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
88.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify168.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune845.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	506	7	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	507	7	514

Merged error: 10.0b

Counts

514 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
10.1b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

940×	`times-frac`
738×	`*-un-lft-identity`
713×	`add-sqr-sqrt`
662×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
95×	`div-inv`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`fma-neg` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 801

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
33.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
11.0ms	(/ (/ PI 2.0) (+ b a))
44.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
65.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
49.0ms	(/ (/ PI 2.0) (+ b a))
102.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify223.0ms

Algorithm

egg-herbie

Counts

813 → 813

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	2928	20392
1	5001	18352

prune1.3s

Filtered

813 candidates to 378 candidates (46.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	809	4	813
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	812	8	820

Merged error: 0.0b

Counts

820 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

1868×	`times-frac`
1466×	`*-un-lft-identity`
1425×	`add-sqr-sqrt`
1390×	`add-cube-cbrt`
1183×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
199×	`div-inv`
79×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
13×	`fma-neg` `associate-r` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-l/` `associate-/r` `log1p-expm1-u`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 1481

Calls

4 calls:

22.0ms	(- (/ 1.0 a) (/ 1.0 b))
67.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
8.0ms	(/ (/ PI 2.0) (+ b a))
38.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
97.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
51.0ms	(/ (/ PI 2.0) (+ b a))
61.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify550.0ms

Algorithm

egg-herbie

Counts

1493 → 1493

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5002	44700

prune4.7s

Filtered

1493 candidates to 1159 candidates (77.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1489	4	1493
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	1492	9	1501

Merged error: 0b

Counts

1501 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

129×	`times-frac`
120×	`add-exp-log` `add-cbrt-cube`
115×	`*-un-lft-identity`
92×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
49×	`cbrt-undiv` `div-exp`
42×	`prod-exp` `cbrt-unprod`
21×	`associate-l`
17×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-/l/`
11×	`frac-times` `associate-*r/`
10×	`associate-/r*`
9×	`div-inv`
8×	`flip3--` `flip--`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r` `clear-num`
2×	`sub-neg` `prod-diff` `unswap-sqr`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 245

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
13.0ms	(* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))
26.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))) (* a b))
8.0ms	(/ (/ PI 2.0) (+ b a))

series295.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (- b a))
50.0ms	(* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))
141.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (* 1.0 b) (* a 1.0)))) (* a b))
58.0ms	(/ (/ PI 2.0) (+ b a))

simplify54.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1218	2622
1	5002	2012

prune485.0ms

Filtered

257 candidates to 163 candidates (63.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	258	8	266

Merged error: 0b

Counts

266 → 8

regimes112.0ms

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	18	10
1	18	10

end0.0ms

sample815.0ms

Algorithm

intervals

Results

622.0ms

9562×

body

valid