Details

sample47.0ms

Algorithm

intervals

Results

17.0ms

313×

body

valid

simplify38.0ms

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

prune3.0ms

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: 14.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.2b	(/ 1.0 (- (* b b) (* a a)))
4.6b	(- (* b b) (* a a))
8.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
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×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

12.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
7.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
22.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify104.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5001	1342

prune228.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	159	6	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	6	166

Merged error: 8.2b

Counts

166 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
8.4b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
29.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
28.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
9.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
7.0ms	(/ (/ PI 2.0) (+ b a))
17.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune392.0ms

Filtered

204 candidates to 300 candidates (-47.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	296	4	300
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	299	7	306

Merged error: 0.0b

Counts

306 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

11.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
7.0ms	(/ (/ PI 2.0) (+ b a))
25.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
12.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
7.0ms	(/ (/ PI 2.0) (+ b a))
16.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5002	1596

prune246.0ms

Filtered

137 candidates to 202 candidates (-47.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	200	9	209

Merged error: 0b

Counts

209 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
0.3b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
0.6b	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

247×	`add-exp-log` `add-cbrt-cube`
129×	`times-frac`
108×	`prod-exp` `cbrt-unprod`
105×	`*-un-lft-identity`
88×	`cbrt-undiv` `div-exp`
77×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
19×	`associate-/l*`
16×	`pow1`
14×	`div-inv` `distribute-lft-out`
12×	`associate-*r/`
10×	`associate-/r*`
8×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-*l/`
7×	`associate-/l/`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-times` `sub-neg` `associate-/r/` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`flip3-+` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 269

Calls

4 calls:

24.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
7.0ms	(/ (/ PI 2.0) (+ b a))
16.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
20.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

series48.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
11.0ms	(/ (/ PI 2.0) (+ b a))
11.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
16.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

simplify58.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1249	3709
1	5001	2766

prune205.0ms

Filtered

139 candidates to 281 candidates (-102.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	281	9	290

Merged error: 0b

Counts

290 → 9

regimes104.0ms

Accuracy

0% (0.2b 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	20	11
1	20	11

end0.0ms

sample795.0ms

Algorithm

intervals

Results

543.0ms

9619×

body

valid

Details

sample47.0ms

simplify38.0ms

prune3.0ms

localize12.0ms

rewrite50.0ms

series32.0ms

simplify104.0ms

prune228.0ms

localize12.0ms

rewrite85.0ms

series37.0ms

simplify53.0ms

prune392.0ms

localize12.0ms

rewrite78.0ms

series39.0ms

simplify105.0ms

prune246.0ms

localize12.0ms

rewrite84.0ms

series48.0ms

simplify58.0ms

prune205.0ms

regimes104.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample795.0ms

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