Details

analyze84.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 52.5854%

Guaranteed chance to sample good point: 98.135288%

sample18.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
0.0ms	3×	body	80	invalid
0.0ms	2×	body	80	nan

simplify105.0ms

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: 0.5b

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))

rewrite27.0ms

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))

series25.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ y (/ 1.0 (* x 9.0)))
2.0ms	(/ 1.0 (* x 9.0))
12.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(* 3.0 (sqrt x))

simplify63.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (55.0ms)

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

prune156.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	83	13	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	13	97

Merged error: 0.0b

Counts

97 → 13

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

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

series31.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ y (/ 1.0 (* x 9.0)))
4.0ms	(/ 1.0 (* x 9.0))
10.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
12.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (13.0ms)

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

prune158.0ms

Filtered

69 candidates to 110 candidates (-59.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* (/ 1 x) (/ 1.0 9.0)))
0.3b	(* (sqrt x) (- (+ y (* (/ 1 x) (/ 1.0 9.0))) 1.0))
0.4b	(* 3.0 (* (sqrt x) (- (+ y (* (/ 1 x) (/ 1.0 9.0))) 1.0)))
0.4b	(* (/ 1 x) (/ 1.0 9.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
33×	`add-exp-log`
26×	`*-un-lft-identity`
25×	`times-frac`
23×	`add-cbrt-cube`
22×	`add-cube-cbrt` `associate-l`
19×	`associate-r`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
12×	`prod-exp`
8×	`div-exp` `cbrt-unprod` `unswap-sqr`
7×	`associate-*r/`
6×	`sub-neg` `associate--l+` `add-log-exp`
5×	`pow-prod-down`
4×	`cbrt-undiv` `sqrt-prod`
3×	`*-commutative`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `div-inv`
1×	`+-commutative` `frac-times` `flip3-+` `associate-*l/` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 131

Calls

4 calls:

3.0ms	(+ y (* (/ 1 x) (/ 1.0 9.0)))
9.0ms	(* (sqrt x) (- (+ y (* (/ 1 x) (/ 1.0 9.0))) 1.0))
10.0ms	(* 3.0 (* (sqrt x) (- (+ y (* (/ 1 x) (/ 1.0 9.0))) 1.0)))
11.0ms	(* (/ 1 x) (/ 1.0 9.0))

series32.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ y (* (/ 1 x) (/ 1.0 9.0)))
13.0ms	(* (sqrt x) (- (+ y (* (/ 1 x) (/ 1.0 9.0))) 1.0))
12.0ms	(* 3.0 (* (sqrt x) (- (+ y (* (/ 1 x) (/ 1.0 9.0))) 1.0)))
2.0ms	(* (/ 1 x) (/ 1.0 9.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	754	1082
1	3562	933
2	5002	921

prune194.0ms

Filtered

96 candidates to 143 candidates (-49.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	144	13	157

Merged error: 0.0b

Counts

157 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ 1.0 9.0) x) y)
0.1b	(* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0))
0.3b	(* (* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0)) (sqrt x))
0.4b	(/ (/ 1.0 9.0) x)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

18.0ms	(+ (/ (/ 1.0 9.0) x) y)
21.0ms	(* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0))
22.0ms	(* (* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0)) (sqrt x))
6.0ms	(/ (/ 1.0 9.0) x)

series23.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (/ (/ 1.0 9.0) x) y)
5.0ms	(* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0))
12.0ms	(* (* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0)) (sqrt x))
2.0ms	(/ (/ 1.0 9.0) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	694	981
1	3098	906
2	5002	906

prune214.0ms

Filtered

107 candidates to 146 candidates (-36.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	4	7	11
Picked	1	0	1
Done	1	0	1
Total	149	10	159

Merged error: 0.0b

Counts

159 → 10

regimes192.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

analyze84.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 52.5854%

Guaranteed chance to sample good point: 98.135288%

sample454.0ms

Algorithm

intervals

Results

327.0ms	8000×	body	80	valid
3.0ms	73×	body	80	nan
2.0ms	41×	body	80	invalid

Details

analyze84.0ms

sample18.0ms

simplify105.0ms

prune3.0ms

localize9.0ms

rewrite27.0ms

series25.0ms

simplify63.0ms

prune156.0ms

localize9.0ms

rewrite35.0ms

series31.0ms

simplify61.0ms

prune158.0ms

localize10.0ms

rewrite37.0ms

series32.0ms

simplify91.0ms

prune194.0ms

localize13.0ms

rewrite73.0ms

series23.0ms

simplify74.0ms

prune214.0ms

regimes192.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze84.0ms

sample454.0ms

Profiling