Details

sample26.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.987794%

Results

14.0ms

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: 0.4b

Counts

2 → 1

localize8.0ms

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))))

rewrite24.0ms

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))))

simplify54.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (47.0ms)

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

prune102.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Merged error: 0b

Counts

74 → 4

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))))

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))))

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))))

simplify65.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (54.0ms)

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

prune158.0ms

Filtered

79 candidates to 102 candidates (-29.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	102	4	106

Merged error: 0b

Counts

106 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (* (- x 1.0) (/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x))))))
0.0b	(/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.1b	(* (- x 1.0) (/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac` `add-cbrt-cube`
16×	`associate-r`
13×	`prod-exp`
12×	`pow1`
9×	`add-log-exp`
8×	`associate-r/` `associate-l*`
7×	`cbrt-unprod`
6×	`div-exp`
4×	`frac-times` `flip3--` `pow-prod-down` `associate-*l/` `associate-/r/` `flip--`
3×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-/r` `sum-log` `flip-+` `associate-/l` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`+-commutative` `associate-+l+` `pow-flip` `frac-2neg` `clear-num` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

6.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
14.0ms	(* 6.0 (* (- x 1.0) (/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x))))))
9.0ms	(/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x))))
14.0ms	(* (- x 1.0) (/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x)))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
8.0ms	(* 6.0 (* (- x 1.0) (/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x))))))
6.0ms	(/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x))))
7.0ms	(* (- x 1.0) (/ 1 (+ (+ x 1.0) (* 4.0 (sqrt x)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	785	1307
1	3583	1137
2	5001	1108

prune174.0ms

Filtered

88 candidates to 130 candidates (-47.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	130	4	134

Merged error: 0b

Counts

134 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
0.2b	(* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
0.2b	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
12.8b	(/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

15.0ms	(* (* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
11.0ms	(* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
5.0ms	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
8.0ms	(/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
4.0ms	(* (/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
3.0ms	(+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
4.0ms	(/ (- x 1.0) (+ (* (neg (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

simplify99.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	753	2109
1	3428	1853
2	5001	1834

prune255.0ms

Filtered

101 candidates to 136 candidates (-34.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	136	4	140

Merged error: 0b

Counts

140 → 4

regimes63.0ms

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

sample463.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 99.987794%

Results

322.0ms	8000×	body	80	valid
0.0ms	1×	body	80	nan

Details

sample26.0ms

simplify11.0ms

prune2.0ms

localize8.0ms

rewrite24.0ms

series15.0ms

simplify54.0ms

prune102.0ms

localize10.0ms

rewrite31.0ms

series19.0ms

simplify65.0ms

prune158.0ms

localize9.0ms

rewrite46.0ms

series26.0ms

simplify87.0ms

prune174.0ms

localize17.0ms

rewrite43.0ms

series22.0ms

simplify99.0ms

prune255.0ms

regimes63.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample463.0ms

Profiling