Details

sample281.0ms

Algorithm

intervals

Results

10.0ms	421×	body	80	valid
6.0ms	421×	pre	80	true

simplify129.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	5
1	34	5
2	72	5
3	188	5
4	406	5
5	636	5
6	938	5
7	1312	5
8	1969	5
9	2932	5
10	3912	5
11	5001	5

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: 0.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* m (- 1.0 m)) v) 1.0)
0.0b	(* m (- 1.0 m))
0.1b	(/ (* m (- 1.0 m)) v)
0.1b	(* (- (/ (* m (- 1.0 m)) v) 1.0) m)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

277×	`add-sqr-sqrt`
227×	`*-un-lft-identity`
214×	`times-frac`
189×	`add-cube-cbrt`
156×	`prod-diff`
88×	`associate-r`
58×	`associate-l`
46×	`fma-neg`
23×	`difference-of-squares`
20×	`unswap-sqr`
19×	`distribute-lft-out--`
18×	`*-commutative`
14×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u`
3×	`sub-neg` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-*l/` `associate-/l/`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 351

Calls

4 calls:

30.0ms	(- (/ (* m (- 1.0 m)) v) 1.0)
8.0ms	(* m (- 1.0 m))
26.0ms	(/ (* m (- 1.0 m)) v)
30.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) m)

series157.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (/ (* m (- 1.0 m)) v) 1.0)
47.0ms	(* m (- 1.0 m))
36.0ms	(/ (* m (- 1.0 m)) v)
50.0ms	(* (- (/ (* m (- 1.0 m)) v) 1.0) m)

simplify128.0ms

Algorithm

egg-herbie

Counts

363 → 363

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	893	3765
1	3681	2658
2	5001	2656

prune524.0ms

Filtered

363 candidates to 185 candidates (51.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	354	9	363
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	355	9	364

Merged error: 0b

Counts

364 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* v (+ 1.0 m))
0.1b	(* m (- (* 1.0 1.0) (* m m)))
0.1b	(/ (* m (- (* 1.0 1.0) (* m m))) (* v (+ 1.0 m)))
0.1b	(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (* v (+ 1.0 m))) 1.0) m)

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

1489×	`add-sqr-sqrt`
854×	`associate-r`
751×	`*-un-lft-identity`
550×	`times-frac`
481×	`add-cube-cbrt`
450×	`prod-diff`
426×	`associate-l`
380×	`difference-of-squares`
360×	`swap-sqr`
274×	`unswap-sqr`
270×	`*-commutative`
229×	`distribute-rgt-in` `distribute-lft-in`
76×	`distribute-lft-out--`
44×	`distribute-lft-out`
42×	`associate-/l*`
22×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
10×	`pow1`
8×	`associate-*r/`
7×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`+-commutative` `sub-neg` `flip3-+` `associate-*l/` `associate-/r/` `flip-+` `associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 1186

Calls

4 calls:

10.0ms	(* v (+ 1.0 m))
41.0ms	(* m (- (* 1.0 1.0) (* m m)))
76.0ms	(/ (* m (- (* 1.0 1.0) (* m m))) (* v (+ 1.0 m)))
213.0ms	(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (* v (+ 1.0 m))) 1.0) m)

series240.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* v (+ 1.0 m))
70.0ms	(* m (- (* 1.0 1.0) (* m m)))
71.0ms	(/ (* m (- (* 1.0 1.0) (* m m))) (* v (+ 1.0 m)))
68.0ms	(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (* v (+ 1.0 m))) 1.0) m)

simplify194.0ms

Algorithm

egg-herbie

Counts

1198 → 1198

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2856	14692
1	5002	13643

prune909.0ms

Filtered

1198 candidates to 277 candidates (23.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1194	4	1198
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	1198	9	1207

Merged error: 0b

Counts

1207 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ m (/ v (+ 1.0 (sqrt (* m m)))))
0.1b	(* (- (* (/ m (/ v (+ 1.0 (sqrt (* m m))))) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m))) 1.0) m)
22.3b	(sqrt (* m m))
22.3b	(sqrt (* m m))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-sqr-sqrt`
111×	`times-frac`
99×	`*-un-lft-identity`
69×	`add-cube-cbrt`
30×	`sqrt-prod`
22×	`pow1` `associate-/r*`
19×	`associate-l`
18×	`associate-/r/`
13×	`distribute-lft-out`
12×	`sqrt-pow1`
11×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
10×	`rem-sqrt-square`
9×	`associate-r`
8×	`swap-sqr`
7×	`difference-of-squares`
6×	`associate-/l*`
5×	`*-commutative` `div-inv`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`pow2` `frac-2neg` `pow-plus` `pow1/2` `associate-*l/` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out--`
1×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`

Counts

4 → 204

Calls

4 calls:

14.0ms	(/ m (/ v (+ 1.0 (sqrt (* m m)))))
149.0ms	(* (- (* (/ m (/ v (+ 1.0 (sqrt (* m m))))) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m))) 1.0) m)
5.0ms	(sqrt (* m m))
5.0ms	(sqrt (* m m))

series85.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ m (/ v (+ 1.0 (sqrt (* m m)))))
35.0ms	(* (- (* (/ m (/ v (+ 1.0 (sqrt (* m m))))) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m))) 1.0) m)
8.0ms	(sqrt (* m m))
8.0ms	(sqrt (* m m))

simplify93.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	667	1778
1	3276	1619
2	5001	1608

prune569.0ms

Filtered

216 candidates to 152 candidates (70.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	217	8	225

Merged error: 0b

Counts

225 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (/ 1 v) (* (+ (fabs m) 1.0) m)) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m)))
0.1b	(* (- (* (* (/ 1 v) (* (+ (fabs m) 1.0) m)) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m))) 1.0) m)
0.3b	(* (/ 1 v) (* (+ (fabs m) 1.0) m))
22.3b	(sqrt (* m m))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

929×	`frac-times`
818×	`add-sqr-sqrt`
640×	`associate-*l/`
491×	`associate-/l*`
407×	`*-un-lft-identity`
309×	`associate-/r*`
233×	`add-cube-cbrt`
219×	`difference-of-squares`
211×	`flip3-+` `flip-+`
185×	`sqrt-prod`
121×	`unswap-sqr`
101×	`add-exp-log` `associate-l`
96×	`times-frac`
94×	`clear-num`
93×	`frac-2neg`
84×	`associate-r`
61×	`associate-*r/`
60×	`associate-/l/`
59×	`add-cbrt-cube`
55×	`prod-exp`
42×	`*-commutative` `distribute-lft-out`
39×	`distribute-lft-out--`
38×	`swap-sqr`
31×	`flip3--` `flip--`
29×	`cbrt-unprod`
28×	`pow1`
21×	`div-exp`
11×	`cbrt-undiv` `pow-prod-down`
6×	`rec-exp` `sqrt-pow1` `1-exp`
5×	`rem-sqrt-square`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`un-div-inv`
2×	`associate-/r/`
1×	`pow2` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 902

Calls

4 calls:

74.0ms	(* (* (/ 1 v) (* (+ (fabs m) 1.0) m)) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m)))
143.0ms	(* (- (* (* (/ 1 v) (* (+ (fabs m) 1.0) m)) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m))) 1.0) m)
16.0ms	(* (/ 1 v) (* (+ (fabs m) 1.0) m))
5.0ms	(sqrt (* m m))

series245.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* (/ 1 v) (* (+ (fabs m) 1.0) m)) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m)))
149.0ms	(* (- (* (* (/ 1 v) (* (+ (fabs m) 1.0) m)) (/ (- 1.0 (sqrt (* m m))) (+ 1.0 m))) 1.0) m)
27.0ms	(* (/ 1 v) (* (+ (fabs m) 1.0) m))
8.0ms	(sqrt (* m m))

simplify198.0ms

Algorithm

egg-herbie

Counts

914 → 914

Iterations

Useful iterations: 1 (65.0ms)

Iter	Nodes	Cost
0	4250	15267
1	5001	14987

prune2.0s

Filtered

914 candidates to 424 candidates (46.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	914	0	914
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	914	8	922

Merged error: 0b

Counts

922 → 8

regimes91.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	9
1	16	9

end0.0ms

sample713.0ms

Algorithm

intervals

Results

315.0ms	13470×	body	80	valid
174.0ms	13470×	pre	80	true