Details

sample26.0ms

Algorithm

intervals

Results

16.0ms

307×

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: 14.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.3b	(/ 1.0 (- (* b b) (* a a)))
5.1b	(- (* b b) (* a a))
8.4b	(* (* (/ 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:

71.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
21.0ms	(/ 1.0 (- (* b b) (* a a)))
23.0ms	(- (* b b) (* a a))
899.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
47.0ms	(/ 1.0 (- (* b b) (* a a)))
32.0ms	(- (* b b) (* a a))
98.0ms	(* (* (/ 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 (409.0ms)

Iter	Nodes	Cost
0	20152	855490

prune48.9s

Filtered

35264 candidates to 12467 candidates (35.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	35255	9	35264
Fresh	0	0	0
Picked	1	0	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 (+ b a))
0.2b	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (/ 2.0 PI) (- b a)))
0.4b	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* (/ 2.0 PI) (- b a))

rewrite880.0ms

Algorithm

rewrite-expression-head

Rules

3831×	`add-sqr-sqrt`
3641×	`*-un-lft-identity`
3022×	`times-frac`
2535×	`add-cube-cbrt`
2149×	`associate-/l*`
2123×	`associate-/r*`
2106×	`frac-sub`
2028×	`frac-times`
1850×	`associate-*r/`
1593×	`associate-l`
1091×	`associate-/l/`
1080×	`associate-r`
812×	`clear-num`
644×	`frac-2neg`
459×	`unswap-sqr`
356×	`prod-diff`
336×	`un-div-inv`
253×	`distribute-lft-out`
189×	`div-inv` `distribute-lft-out--`
182×	`distribute-rgt-in` `distribute-lft-in`
162×	`difference-of-squares`
108×	`*-commutative`
106×	`add-exp-log`
85×	`associate-/r/`
74×	`add-cbrt-cube`
50×	`prod-exp`
46×	`flip3--` `flip--`
42×	`associate-*l/`
34×	`div-exp`
30×	`cbrt-unprod`
28×	`flip3-+` `flip-+`
22×	`cbrt-undiv`
11×	`pow1`
8×	`1-exp`
4×	`expm1-log1p-u` `sub-neg` `pow-prod-down` `log1p-expm1-u` `add-log-exp`

Counts

4 → 4160

Calls

4 calls:

6.0ms	(/ 1.0 (+ b a))
225.0ms	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (/ 2.0 PI) (- b a)))
92.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
12.0ms	(* (/ 2.0 PI) (- b a))

series322.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (+ b a))
105.0ms	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* (/ 2.0 PI) (- b a)))
86.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
85.0ms	(* (/ 2.0 PI) (- b a))

simplify825.0ms

Algorithm

egg-herbie

Counts

4172 → 4172

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5001	71444

prune11.4s

Filtered

4172 candidates to 3020 candidates (72.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	4169	3	4172
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	4173	8	4181

Merged error: 0b

Counts

4181 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.2b	(* (/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a))) PI)
0.4b	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

4578×	`add-sqr-sqrt`
4576×	`*-un-lft-identity`
3221×	`associate-/l*`
3159×	`frac-sub`
3146×	`associate-/r*`
3038×	`add-cube-cbrt`
2988×	`frac-times`
2773×	`associate-*r/`
2758×	`times-frac`
2182×	`associate-/l/`
2075×	`associate-l`
1463×	`associate-r`
1209×	`clear-num`
1196×	`associate-*l/`
957×	`frac-2neg`
546×	`unswap-sqr`
504×	`un-div-inv`
349×	`distribute-lft-out`
338×	`prod-diff`
261×	`distribute-lft-out--`
230×	`difference-of-squares`
171×	`distribute-rgt-in` `distribute-lft-in`
169×	`*-commutative`
148×	`div-inv`
130×	`add-exp-log`
89×	`add-cbrt-cube`
70×	`prod-exp`
68×	`associate-/r/`
42×	`cbrt-unprod`
41×	`flip3--` `flip--`
35×	`div-exp`
32×	`flip3-+` `flip-+`
22×	`cbrt-undiv`
11×	`pow1`
10×	`1-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`

Counts

4 → 5397

Calls

4 calls:

6.0ms	(/ 1.0 (+ b a))
187.0ms	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
339.0ms	(* (/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a))) PI)
85.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (+ b a))
80.0ms	(/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
103.0ms	(* (/ (* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a))) PI)
89.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify881.0ms

Algorithm

egg-herbie

Counts

5409 → 5409

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5001	77450

prune15.0s

Filtered

5409 candidates to 3749 candidates (69.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	5409	0	5409
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	5409	8	5417

Merged error: 0b

Counts

5417 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

1764×	`frac-times`
1585×	`*-un-lft-identity`
1506×	`associate-/r*`
1424×	`add-sqr-sqrt`
1305×	`add-cube-cbrt`
1272×	`associate-/l*`
1053×	`frac-sub`
987×	`associate-*r/`
558×	`times-frac`
480×	`clear-num`
396×	`frac-2neg`
374×	`prod-diff`
272×	`sqrt-prod`
215×	`distribute-rgt-in` `distribute-lft-in`
182×	`flip3--` `flip--`
180×	`associate-*l/`
168×	`un-div-inv`
87×	`distribute-lft-out`
77×	`associate-l`
70×	`associate-r`
57×	`add-exp-log` `div-inv`
51×	`unswap-sqr`
34×	`add-cbrt-cube`
29×	`prod-exp`
16×	`pow1`
15×	`cbrt-unprod`
12×	`div-exp`
6×	`cbrt-undiv` `sub-neg` `pow-prod-down` `distribute-lft-out--`
5×	`1-exp` `difference-of-squares`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`flip3-+` `flip-+`

Counts

4 → 2187

Calls

4 calls:

55.0ms	(* (/ 1 (sqrt PI)) (* (/ 2.0 (sqrt PI)) (- b a)))
83.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
1.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series164.0ms

Counts

4 → 8

Calls

4 calls:

80.0ms	(* (/ 1 (sqrt PI)) (* (/ 2.0 (sqrt PI)) (- b a)))
84.0ms	(* (* 1 (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify426.0ms

Algorithm

egg-herbie

Counts

2195 → 2195

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5002	37898

prune5.2s

Filtered

2195 candidates to 1117 candidates (50.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	2194	1	2195
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	2195	8	2203

Merged error: 0b

Counts

2203 → 8

regimes73.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	11
1	26	11
2	26	11

end0.0ms

sample597.0ms

Algorithm

intervals

Results

435.0ms

9648×

body

valid