Details

sample101.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 52.5854%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

10.0ms	256×	body	80	valid
0.0ms	2×	body	80	nan

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	182	7
3	338	7
4	488	7
5	757	7
6	1166	7
7	1729	7
8	2793	7
9	5001	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 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(/ 1.0 (* x 9.0))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* 3.0 (sqrt x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

4.0ms	(+ y (/ 1.0 (* x 9.0)))
4.0ms	(/ 1.0 (* x 9.0))
12.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
5.0ms	(* 3.0 (sqrt x))

series26.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ y (/ 1.0 (* x 9.0)))
5.0ms	(/ 1.0 (* x 9.0))
13.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(* 3.0 (sqrt x))

simplify68.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	508	558
1	2557	503
2	5001	501

prune163.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
0.2b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.2b	(/ 1.0 (* x 9.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

4.0ms	(+ y (/ 1.0 (* x 9.0)))
12.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
11.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(/ 1.0 (* x 9.0))

series31.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ y (/ 1.0 (* x 9.0)))
12.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
10.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
2.0ms	(/ 1.0 (* x 9.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	530	786
1	2273	716
2	5001	716

prune148.0ms

Filtered

69 candidates to 110 candidates (-59.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	109	11	120

Merged error: 0.0b

Counts

120 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.2b	(/ 1.0 (* x 9.0))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
0.4b	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

51×	`distribute-rgt-in` `distribute-lft-in`
37×	`add-exp-log`
32×	`pow1`
25×	`add-cbrt-cube`
20×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`sub-neg` `associate--l+`
13×	`associate-l`
12×	`associate-*r/`
11×	`add-cube-cbrt`
8×	`associate-r`
4×	`sqrt-prod` `add-log-exp`
3×	`cbrt-prod` `flip3--` `times-frac` `-commutative` `flip--` `associate-/l`
2×	`cbrt-undiv` `div-exp` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `difference-of-squares`

Counts

4 → 143

Calls

4 calls:

11.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(/ 1.0 (* x 9.0))
19.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
13.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
2.0ms	(/ 1.0 (* x 9.0))
18.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
17.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	807	1792
1	3240	1420
2	5001	1358

prune223.0ms

Filtered

79 candidates to 155 candidates (-96.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	156	10	166

Merged error: 0b

Counts

166 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (sqrt 3.0)) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
0.2b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.2b	(/ 1.0 (* x 9.0))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt (sqrt 3.0)) (* (cbrt (sqrt 3.0)) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

111×	`distribute-rgt-in` `distribute-lft-in`
48×	`add-exp-log`
43×	`pow1`
29×	`prod-exp` `cbrt-unprod`
28×	`pow-prod-down` `add-cbrt-cube`
22×	`sub-neg` `associate--l+`
18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`associate-l`
14×	`associate-*r/`
12×	`add-cube-cbrt`
8×	`associate-r`
7×	`sqrt-prod`
6×	`cbrt-prod`
4×	`add-log-exp`
3×	`flip3--` `times-frac` `-commutative` `flip--` `associate-/l`
2×	`cbrt-undiv` `div-exp` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `difference-of-squares`

Counts

4 → 176

Calls

4 calls:

14.0ms	(* (cbrt (sqrt 3.0)) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
14.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(/ 1.0 (* x 9.0))
25.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt (sqrt 3.0)) (* (cbrt (sqrt 3.0)) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (cbrt (sqrt 3.0)) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
13.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
2.0ms	(/ 1.0 (* x 9.0))
52.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt (sqrt 3.0)) (* (cbrt (sqrt 3.0)) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))))

simplify141.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	1135	2953
1	4810	2346
2	5002	2325

prune293.0ms

Filtered

87 candidates to 188 candidates (-116.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	189	9	198

Merged error: 0b

Counts

198 → 9

regimes132.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

end0.0ms

sample555.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 52.5854%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

341.0ms	8000×	body	80	valid
3.0ms	63×	body	80	nan
1.0ms	30×	body	80	invalid

Details

sample101.0ms

simplify104.0ms

prune3.0ms

localize9.0ms

rewrite28.0ms

series26.0ms

simplify68.0ms

prune163.0ms

localize9.0ms

rewrite35.0ms

series31.0ms

simplify60.0ms

prune148.0ms

localize15.0ms

rewrite52.0ms

series47.0ms

simplify87.0ms

prune223.0ms

localize15.0ms

rewrite64.0ms

series94.0ms

simplify141.0ms

prune293.0ms

regimes132.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample555.0ms

Profiling