Details

sample42.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results

18.0ms	256×	body	80	valid
8.0ms	113×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	39	7
2	61	7
3	80	7
4	105	7
5	114	7
6	114	7

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: 0.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.4b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
6.0ms	(* 6.0 (- x 1.0))
10.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series19.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
6.0ms	(* 6.0 (- x 1.0))
9.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	492	549
1	2177	479
2	5002	478

prune111.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Merged error: 0b

Counts

74 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.1b	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*`
4×	`associate-/r/`
3×	`flip3-+` `associate-l` `associate-/r*` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 93

Calls

3 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
13.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
9.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series23.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
11.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
8.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify71.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	634	1087
1	2675	1000
2	5001	998

prune162.0ms

Filtered

79 candidates to 102 candidates (-29.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	103	4	107

Merged error: 0b

Counts

107 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3)))
0.1b	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.1b	(cbrt (pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3))
0.1b	(pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
117×	`*-un-lft-identity`
107×	`times-frac`
102×	`cbrt-prod`
73×	`add-cube-cbrt`
65×	`unpow-prod-down` `cube-prod`
51×	`associate-r`
22×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
11×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`pow1` `flip3-+` `flip-+` `div-inv` `unswap-sqr`
5×	`associate-/l*`
4×	`add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 233

Calls

4 calls:

36.0ms	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3)))
15.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
11.0ms	(cbrt (pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3))
11.0ms	(pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3)

series47.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3)))
7.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
10.0ms	(cbrt (pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3))
11.0ms	(pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3)

simplify155.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1084	3093
1	4965	2931
2	5001	2931

prune407.0ms

Filtered

134 candidates to 245 candidates (-82.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	245	4	249

Merged error: 0b

Counts

249 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* 6.0 (- x 1.0)) (/ (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)) (+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0)))))
0.5b	(pow (* 4.0 (sqrt x)) 3)
8.0b	(+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0)))
20.1b	(/ (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)) (+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

82×	`times-frac` `associate-*r/`
64×	`frac-add`
55×	`associate-/r/`
53×	`*-un-lft-identity` `flip3-+` `flip-+`
40×	`associate-/r*`
33×	`add-sqr-sqrt` `add-cube-cbrt` `flip3--` `flip--`
32×	`frac-times`
21×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*l/`
10×	`sum-cubes` `distribute-lft-out`
7×	`pow1` `cbrt-undiv` `div-exp`
6×	`associate-/l*` `add-log-exp`
4×	`associate-+l+` `div-inv` `associate-/l/`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-+r+` `pow-pow` `frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `pow-prod-down` `sum-log` `sqr-pow`

Counts

4 → 206

Calls

4 calls:

32.0ms	(/ (* 6.0 (- x 1.0)) (/ (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)) (+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0)))))
4.0ms	(pow (* 4.0 (sqrt x)) 3)
13.0ms	(+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0)))
26.0ms	(/ (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)) (+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (* 6.0 (- x 1.0)) (/ (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)) (+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0)))))
7.0ms	(pow (* 4.0 (sqrt x)) 3)
8.0ms	(+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0)))
14.0ms	(/ (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)) (+ (* (* 4.0 (sqrt x)) (- (* 4.0 (sqrt x)) (+ x 1.0))) (* (+ x 1.0) (+ x 1.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1535	6732
1	5001	6470

prune799.0ms

Filtered

161 candidates to 218 candidates (-35.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	218	4	222

Merged error: 0b

Counts

222 → 4

regimes32.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample670.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results

318.0ms	8000×	body	80	valid
153.0ms	4147×	body	80	nan

Details

sample42.0ms

simplify12.0ms

prune3.0ms

localize9.0ms

rewrite23.0ms

series19.0ms

simplify56.0ms

prune111.0ms

localize9.0ms

rewrite31.0ms

series23.0ms

simplify71.0ms

prune162.0ms

localize11.0ms

rewrite83.0ms

series47.0ms

simplify155.0ms

prune407.0ms

localize18.0ms

rewrite87.0ms

series49.0ms

simplify83.0ms

prune799.0ms

regimes32.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample670.0ms

Profiling