Details

sample32.0ms

Algorithm

intervals

Results

21.0ms

314×

body

valid

simplify42.0ms

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

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: 12.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.3b	(- (* b b) (* a a))
7.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite56.0ms

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:

14.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify107.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune403.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	9	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	9	166

Merged error: 7.2b

Counts

166 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
7.4b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
298×	`*-un-lft-identity`
261×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
108×	`associate-r`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
14×	`frac-times` `associate-l`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
11.0ms	(/ (/ 1.0 (+ b a)) (- b a))
44.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
32.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
52.0ms	(/ (/ 1.0 (+ b a)) (- b a))
66.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
97.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify69.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune716.0ms

Filtered

359 candidates to 230 candidates (64.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	353	6	359
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	357	11	368

Merged error: 0.0b

Counts

368 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* PI (/ 1.0 (+ b a)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log` `add-cbrt-cube`
47×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
34×	`times-frac`
30×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
18×	`add-cube-cbrt`
17×	`associate-*r/`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`distribute-lft-out--`
8×	`difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`frac-sub`
4×	`associate-l` `pow-prod-down` `associate-/r/`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 137

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
21.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(* PI (/ 1.0 (+ b a)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
101.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
104.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
51.0ms	(* PI (/ 1.0 (+ b a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	762	1319
1	4686	1036
2	5001	1036

prune283.0ms

Filtered

149 candidates to 95 candidates (63.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	142	7	149
Fresh	5	4	9
Picked	1	0	1
Done	1	0	1
Total	149	11	160

Merged error: 0b

Counts

160 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
0.4b	(* PI (/ 1.0 (+ b a)))
0.5b	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
94×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
50×	`add-exp-log` `add-cbrt-cube`
31×	`associate-/r*`
29×	`add-cube-cbrt`
25×	`distribute-lft-out--`
21×	`cbrt-undiv` `div-exp`
20×	`difference-of-squares`
18×	`associate-r`
15×	`div-inv`
12×	`prod-exp` `associate-/r/` `cbrt-unprod`
6×	`pow1` `add-log-exp`
5×	`flip3--` `flip--`
4×	`associate-*r/` `frac-sub`
3×	`associate-l` `associate-/l/` `distribute-lft-out`
2×	`frac-2neg` `clear-num` `associate-/l*` `unswap-sqr`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 172

Calls

4 calls:

16.0ms	(- (/ 1.0 a) (/ 1.0 b))
25.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
9.0ms	(* PI (/ 1.0 (+ b a)))
19.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(- (/ 1.0 a) (/ 1.0 b))
115.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
56.0ms	(* PI (/ 1.0 (+ b a)))
53.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	872	1738
1	4713	1451
2	5001	1451

prune339.0ms

Filtered

184 candidates to 129 candidates (70.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	184	11	195

Merged error: 0b

Counts

195 → 11

regimes73.0ms

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

sample691.0ms

Algorithm

intervals

Results

529.0ms

9549×

body

valid

Details

sample32.0ms

simplify42.0ms

prune3.0ms

localize13.0ms

rewrite56.0ms

series221.0ms

simplify107.0ms

prune403.0ms

localize16.0ms

rewrite121.0ms

series247.0ms

simplify69.0ms

prune716.0ms

localize17.0ms

rewrite78.0ms

series287.0ms

simplify106.0ms

prune283.0ms

localize12.0ms

rewrite78.0ms

series391.0ms

simplify105.0ms

prune339.0ms

regimes73.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample691.0ms

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