Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

311×

body

valid

simplify41.0ms

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: 14.6b

Counts

2 → 1

localize16.0ms

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)))
3.4b	(- (* b b) (* a a))
9.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite105.0ms

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))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
36.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
42.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
89.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify165.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune876.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	504	9	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	505	9	514

Merged error: 9.6b

Counts

514 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1.0) (+ b a))
0.1b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.3b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
9.8b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

572×	`times-frac`
473×	`*-un-lft-identity`
470×	`add-sqr-sqrt`
427×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
112×	`add-exp-log` `add-cbrt-cube`
78×	`associate-r`
58×	`div-inv`
51×	`prod-exp` `cbrt-unprod`
47×	`frac-times`
44×	`sqrt-prod`
33×	`associate-*l/`
31×	`cbrt-undiv` `div-exp`
20×	`pow1`
19×	`associate-*r/`
15×	`associate-l`
13×	`distribute-lft-out`
11×	`distribute-lft-out--`
10×	`pow-prod-down` `difference-of-squares`
9×	`flip3--` `flip--`
8×	`frac-sub`
6×	`associate-/r/` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sub-neg` `flip3-+` `flip-+`
1×	`frac-2neg` `clear-num`

Counts

4 → 618

Calls

4 calls:

6.0ms	(/ (sqrt 1.0) (+ b a))
20.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
21.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
47.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (sqrt 1.0) (+ b a))
193.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
138.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
275.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify209.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 1 (64.0ms)

Iter	Nodes	Cost
0	2995	18470
1	5001	17642

prune1.1s

Filtered

630 candidates to 274 candidates (43.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	622	8	630
Fresh	8	0	8
Picked	0	1	1
Done	0	0	0
Total	630	9	639

Merged error: 0.0b

Counts

639 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

274×	`times-frac`
234×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
202×	`add-cube-cbrt`
169×	`prod-diff`
50×	`add-exp-log` `add-cbrt-cube`
34×	`div-inv`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
13×	`fma-neg` `distribute-lft-out--`
12×	`associate-l`
11×	`associate-r` `difference-of-squares`
7×	`flip3--` `flip--` `associate-/l/`
6×	`pow1` `frac-times` `associate-l/` `associate-/r` `associate-/r/` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `associate-/l*`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 323

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
6.0ms	(/ (* PI 1.0) (- b a))
22.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
91.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
56.0ms	(/ (* PI 1.0) (- b a))
77.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

335 → 335

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1265	5736
1	5002	4349

prune616.0ms

Filtered

335 candidates to 173 candidates (51.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	329	6	335
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	335	9	344

Merged error: 0.0b

Counts

344 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

289×	`times-frac`
236×	`add-sqr-sqrt`
228×	`*-un-lft-identity`
204×	`add-cube-cbrt`
169×	`prod-diff`
50×	`add-exp-log` `add-cbrt-cube`
35×	`div-inv`
17×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
14×	`distribute-lft-out--`
13×	`fma-neg`
12×	`associate-l` `associate-/l*` `difference-of-squares`
9×	`pow1`
8×	`associate-/r/`
6×	`flip3--` `associate-l/` `associate-/r` `flip--` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`pow-prod-down` `frac-sub`
2×	`frac-2neg` `associate-*r/` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `associate-r` `*-commutative` `flip-+`

Counts

4 → 326

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
24.0ms	(/ (/ (* (- (/ 1.0 a) (/ 1.0 b)) (* PI 1.0)) (- b a)) (* 2.0 (+ b a)))
22.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* PI 1.0)) (- b a))
17.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (* PI 1.0))

series259.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (/ (* (- (/ 1.0 a) (/ 1.0 b)) (* PI 1.0)) (- b a)) (* 2.0 (+ b a)))
72.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* PI 1.0)) (- b a))
59.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (* PI 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1266	5871
1	5001	4169

prune598.0ms

Filtered

338 candidates to 174 candidates (51.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	336	2	338
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	339	8	347

Merged error: 0.0b

Counts

347 → 8

regimes57.0ms

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	17	9
1	17	9

end0.0ms

sample577.0ms

Algorithm

intervals

Results

417.0ms

9580×

body

valid