Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	292×	body	80	nan
11.0ms	271×	body	80	valid

simplify108.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	190	7
3	412	7
4	644	7
5	1083	7
6	1628	7
7	2273	7
8	3723	7
9	5001	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
36×	`prod-diff`
32×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r` `distribute-lft-out`
11×	`pow1`
9×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `fma-neg` `associate-l` `pow-prod-down` `sqrt-prod` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `times-frac` `associate--l+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `diff-log` `associate-r/` `div-exp` `-commutative` `flip--` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv`

Counts

4 → 137

Calls

4 calls:

8.0ms	(- (+ y (/ 1.0 (* x 9.0))) 1.0)
12.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(/ 1.0 (* x 9.0))
5.0ms	(* 3.0 (sqrt x))

series136.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (+ y (/ 1.0 (* x 9.0))) 1.0)
58.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
19.0ms	(/ 1.0 (* x 9.0))
36.0ms	(* 3.0 (sqrt x))

simplify74.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	577	1398
1	2857	1037
2	5001	1031

prune223.0ms

Filtered

149 candidates to 79 candidates (53.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	138	11	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Merged error: 0.0b

Counts

150 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
84×	`prod-diff`
75×	`distribute-rgt-in` `distribute-lft-in`
68×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
24×	`distribute-lft-out`
16×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`associate-l` `add-log-exp`
7×	`sub-neg` `associate-r` `associate--l+`
6×	`associate-*r/`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `fma-neg` `pow-prod-down` `sqrt-prod` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `times-frac` `flip--` `associate-/l*`
2×	`cbrt-undiv` `diff-log` `div-exp` `*-commutative` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv`

Counts

4 → 199

Calls

4 calls:

11.0ms	(- (+ y (/ 1.0 (* x 9.0))) 1.0)
4.0ms	(/ 1.0 (* x 9.0))
14.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
13.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

series165.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (+ y (/ 1.0 (* x 9.0))) 1.0)
16.0ms	(/ 1.0 (* x 9.0))
65.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
57.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	616	2672
1	2634	1913
2	5001	1907

prune230.0ms

Filtered

211 candidates to 88 candidates (41.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	211	11	222

Merged error: 0.0b

Counts

222 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
15×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`associate-r` `prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `div-inv`

Counts

4 → 89

Calls

4 calls:

11.0ms	(* 3.0 (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x)))
4.0ms	(/ 1.0 (* x 9.0))
5.0ms	(* 3.0 (* y (sqrt x)))
5.0ms	(* y (sqrt x))

series227.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* 3.0 (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x)))
23.0ms	(/ 1.0 (* x 9.0))
56.0ms	(* 3.0 (* y (sqrt x)))
42.0ms	(* y (sqrt x))

simplify57.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	460	533
1	1962	454
2	5002	443

prune205.0ms

Filtered

101 candidates to 69 candidates (68.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	101	11	112

Merged error: 0.0b

Counts

112 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
80×	`add-sqr-sqrt`
75×	`times-frac`
72×	`add-cube-cbrt`
36×	`prod-diff`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-/l*`
12×	`associate-r` `distribute-lft-out`
11×	`pow1`
9×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `fma-neg` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`cbrt-undiv` `sub-neg` `div-exp` `associate--l+` `associate-/r*`
2×	`flip3--` `diff-log` `associate-r/` `-commutative` `flip--` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `clear-num` `sum-log` `associate-/l/`

Counts

4 → 186

Calls

4 calls:

17.0ms	(- (+ y (/ (/ 1.0 x) 9.0)) 1.0)
19.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
6.0ms	(/ (/ 1.0 x) 9.0)
5.0ms	(* 3.0 (sqrt x))

series134.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- (+ y (/ (/ 1.0 x) 9.0)) 1.0)
63.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
15.0ms	(/ (/ 1.0 x) 9.0)
36.0ms	(* 3.0 (sqrt x))

simplify102.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	800	1764
1	3732	1397
2	5001	1393

prune278.0ms

Filtered

198 candidates to 122 candidates (61.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	198	11	209

Merged error: 0.0b

Counts

209 → 11

regimes117.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample975.0ms

Algorithm

intervals

Results

349.0ms	8534×	body	80	valid
345.0ms	8450×	body	80	nan