Details

sample19.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

10.0ms

256×

body

valid

simplify11.0ms

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

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: 0.1b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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:

6.0ms	(+ (+ 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))))

series15.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
3.0ms	(* 6.0 (- x 1.0))
8.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (45.0ms)

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

prune110.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Merged error: 0b

Counts

74 → 5

localize10.0ms

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

rewrite29.0ms

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)))
12.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
8.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series19.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
8.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
7.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify66.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (55.0ms)

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

prune164.0ms

Filtered

79 candidates to 102 candidates (-29.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	103	4	107

Merged error: 0b

Counts

107 → 4

localize13.0ms

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)))
0.0b	(/ (- 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)

rewrite66.0ms

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:

21.0ms	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) 3)))
9.0ms	(/ (- 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)

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* 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))))
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)

simplify131.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 1 (26.0ms)

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

prune342.0ms

Filtered

135 candidates to 245 candidates (-81.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	245	4	249

Merged error: 0b

Counts

249 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.0b	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.1b	(/ (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.3b	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

456×	`times-frac`
318×	`add-sqr-sqrt`
316×	`*-un-lft-identity`
240×	`sqrt-prod`
218×	`add-cube-cbrt`
49×	`distribute-lft-out--` `difference-of-squares`
41×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`flip3--` `flip--`

Counts

4 → 364

Calls

4 calls:

5.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
5.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
21.0ms	(/ (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
10.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
7.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
8.0ms	(/ (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
15.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1283	8471
1	5001	7732

prune656.0ms

Filtered

172 candidates to 376 candidates (-118.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	376	0	376
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	376	4	380

Merged error: 0b

Counts

380 → 4

regimes55.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	18	9

end0.0ms

sample468.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.993897%

Results

337.0ms	8000×	body	80	valid
0.0ms	1×	body	80	nan

Details

sample19.0ms

simplify11.0ms

prune2.0ms

localize13.0ms

rewrite22.0ms

series15.0ms

simplify51.0ms

prune110.0ms

localize10.0ms

rewrite29.0ms

series19.0ms

simplify66.0ms

prune164.0ms

localize13.0ms

rewrite66.0ms

series42.0ms

simplify131.0ms

prune342.0ms

localize13.0ms

rewrite67.0ms

series38.0ms

simplify96.0ms

prune656.0ms

regimes55.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample468.0ms

Profiling