Details

sample37.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.777222%

Guaranteed chance to sample good point: 99.987829%

Results

14.0ms	73×	body	1280	valid
7.0ms	54×	body	640	valid
2.0ms	24×	body	320	valid
2.0ms	83×	body	80	valid
1.0ms	22×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

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: 41.3b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
5.6b	(- (exp x) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series10.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- (exp x) 1.0) x)
3.0ms	(- (exp x) 1.0)

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2717	309
3	5001	309

prune75.0ms

Filtered

43 candidates to 58 candidates (-34.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	2	59

Merged error: 0.0b

Counts

59 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
3.3b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log`
11×	`associate-l`
9×	`times-frac` `add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`associate-/r` `associate-/l` `add-log-exp`
2×	`flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `div-inv`

Counts

3 → 78

Calls

3 calls:

8.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
4.0ms	(* x 1/6)
11.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series16.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
2.0ms	(* x 1/6)
5.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	363	567
1	1885	515
2	5002	515

prune112.0ms

Filtered

60 candidates to 87 candidates (-45.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	2	89

Merged error: 0.0b

Counts

89 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
0.0b	(pow (exp x) 3)
5.4b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
38×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
4×	`pow-pow`
3×	`pow-unpow` `exp-prod` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 192

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
26.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
4.0ms	(pow (exp x) 3)
13.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series31.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (exp x))
19.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
4.0ms	(pow (exp x) 3)
6.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify105.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	605	2945
1	2678	2881
2	5001	2803

prune268.0ms

Filtered

108 candidates to 204 candidates (-88.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	203	3	206

Merged error: 0.0b

Counts

206 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
0.0b	(pow (exp x) 3)
0.2b	(exp (log (/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))))
5.4b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

260×	`add-sqr-sqrt`
150×	`times-frac`
148×	`*-un-lft-identity`
128×	`difference-of-squares`
99×	`unpow-prod-down` `cube-prod`
81×	`log-prod` `exp-sum`
68×	`add-cube-cbrt`
65×	`sqr-pow`
40×	`distribute-lft-out--`
25×	`associate-/l*`
8×	`difference-cubes`
7×	`exp-prod` `add-cbrt-cube`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`pow-pow` `associate-/r/`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `log-div` `frac-2neg` `exp-diff` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `log-pow` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 274

Calls

4 calls:

26.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
4.0ms	(pow (exp x) 3)
31.0ms	(exp (log (/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))))
13.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series52.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
4.0ms	(pow (exp x) 3)
24.0ms	(exp (log (/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))))
6.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify129.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	886	5101
1	3287	5018
2	5001	4862

prune448.0ms

Filtered

141 candidates to 286 candidates (-102.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	285	1	286
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	286	3	289

Merged error: 0.0b

Counts

289 → 3

regimes36.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.1b

bsearch22.0ms

Steps

Iters	Range		Point
10	-21869.37453130546	-1.302763117677963e-06	-0.0001768064908054355

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample959.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.777222%

Guaranteed chance to sample good point: 99.987829%

Results

433.0ms	2227×	body	1280	valid
214.0ms	1709×	body	640	valid
67.0ms	2806×	body	80	valid
67.0ms	819×	body	320	valid
23.0ms	439×	body	160	valid
0.0ms	1×	body	80	invalid

Details

sample37.0ms

simplify6.0ms

prune2.0ms

localize4.0ms

rewrite12.0ms

series10.0ms

simplify79.0ms

prune75.0ms

localize8.0ms

rewrite25.0ms

series16.0ms

simplify67.0ms

prune112.0ms

localize14.0ms

rewrite59.0ms

series31.0ms

simplify105.0ms

prune268.0ms

localize15.0ms

rewrite90.0ms

series52.0ms

simplify129.0ms

prune448.0ms

regimes36.0ms

bsearch22.0ms

simplify2.0ms

end0.0ms

sample959.0ms

Profiling