Details

sample56.0ms

Algorithm

intervals

Results

39.0ms

431×

body

valid

simplify115.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	70	42
1	252	42
2	1059	42
3	4713	42
4	5001	42

prune4.0ms

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: 0.2b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.0b	(sqrt PI)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-exp-log` `add-cbrt-cube`
70×	`prod-exp` `cbrt-unprod`
51×	`pow1`
48×	`associate-l`
42×	`add-sqr-sqrt`
38×	`times-frac`
35×	`pow-prod-down`
33×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-*l/`
13×	`sqrt-prod`
12×	`frac-add`
11×	`cbrt-undiv` `div-exp`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 173

Calls

4 calls:

12.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
61.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
21.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
2.0ms	(sqrt PI)

series465.0ms

Counts

4 → 10

Calls

4 calls:

45.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
78.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
341.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.0ms	(sqrt PI)

simplify72.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1366	5031
1	5001	3928

prune683.0ms

Filtered

183 candidates to 117 candidates (63.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	178	5	183
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	6	184

Merged error: 0b

Counts

184 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 (sqrt 21.0)) (pow (fabs x) (* 2 3)))
0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
1.0b	(sqrt PI)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
57×	`associate-l`
55×	`associate-*l/`
53×	`times-frac`
43×	`add-exp-log`
41×	`add-cube-cbrt` `*-un-lft-identity`
36×	`frac-add`
35×	`add-cbrt-cube`
25×	`sqrt-prod`
22×	`frac-times` `associate-*r/`
20×	`prod-exp`
16×	`pow1` `cbrt-unprod`
14×	`flip3-+` `flip-+`
12×	`unswap-sqr`
11×	`associate-r`
7×	`div-exp` `pow-prod-down`
6×	`unpow-prod-down`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`*-commutative` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 186

Calls

4 calls:

12.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
11.0ms	(* (/ 1.0 (sqrt 21.0)) (pow (fabs x) (* 2 3)))
24.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
2.0ms	(sqrt PI)

series668.0ms

Counts

4 → 10

Calls

4 calls:

45.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
134.0ms	(* (/ 1.0 (sqrt 21.0)) (pow (fabs x) (* 2 3)))
489.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 (sqrt 21.0)) (* (* (/ 1.0 (sqrt 21.0)) (pow (fabs x) (* 2 3))) (fabs x)))))
0.0ms	(sqrt PI)

simplify84.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1441	5688
1	5001	4964

prune1.2s

Filtered

196 candidates to 148 candidates (75.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	196	6	202

Merged error: 0b

Counts

202 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))))
1.0b	(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
54×	`times-frac`
44×	`associate-l`
40×	`add-cube-cbrt` `*-un-lft-identity`
27×	`sqrt-prod`
21×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
10×	`pow1`
9×	`unswap-sqr`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/`

Counts

4 → 139

Calls

4 calls:

8.0ms	(* (/ 1.0 (sqrt PI)) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))))
13.0ms	(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series231.0ms

Counts

4 → 6

Calls

4 calls:

231.0ms	(* (/ 1.0 (sqrt PI)) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))))
0.0ms	(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify70.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	539	1595
1	2365	1449
2	5001	1441

prune620.0ms

Filtered

145 candidates to 108 candidates (74.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	145	6	151

Merged error: 0b

Counts

151 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1.0 (sqrt PI))) (+ (* (sqrt (/ 1.0 (sqrt PI))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

44×	`sqrt-prod`
35×	`add-sqr-sqrt`
25×	`associate-l`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
9×	`pow1`
8×	`sqrt-div`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-*l/`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
2×	`flip3-+` `frac-add` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

17.0ms	(* (sqrt (/ 1.0 (sqrt PI))) (+ (* (sqrt (/ 1.0 (sqrt PI))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))))
1.0ms	(sqrt PI)
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series1.3s

Counts

4 → 6

Calls

4 calls:

1.3s	(* (sqrt (/ 1.0 (sqrt PI))) (+ (* (sqrt (/ 1.0 (sqrt PI))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify83.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	506	2848
1	2158	2622
2	5002	2548

prune504.0ms

Filtered

106 candidates to 85 candidates (80.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	106	6	112

Merged error: 0b

Counts

112 → 6

regimes254.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	42
1	41	42

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.3s

14120×

body

valid