Details

sample36.0ms

Algorithm

intervals

Results

12.0ms	258×	body	80	nan
11.0ms	275×	body	80	valid

simplify102.0ms

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

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

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))
0.3b	(* 3.0 (sqrt x))
0.7b	(/ 1.0 (* x 9.0))

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

series153.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ y (/ 1.0 (* x 9.0)))
61.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
49.0ms	(* 3.0 (sqrt x))
18.0ms	(/ 1.0 (* x 9.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	456	548
1	2172	486
2	5002	484

prune203.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.3b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
0.7b	(/ 1.0 (* x 9.0))

rewrite36.0ms

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:

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

series162.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
57.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
64.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
16.0ms	(/ 1.0 (* x 9.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	427	770
1	1858	694
2	5002	694

prune179.0ms

Filtered

110 candidates to 67 candidates (60.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	110	12	122

Merged error: 0.0b

Counts

122 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
0.5b	(* (cbrt 3.0) (sqrt x))
0.7b	(/ 1.0 (* x 9.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
36×	`pow1`
28×	`add-cbrt-cube`
23×	`prod-exp` `cbrt-unprod`
22×	`pow-prod-down`
21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`associate-r`
11×	`add-cube-cbrt`
8×	`associate-l`
5×	`cbrt-prod` `sqrt-prod`
4×	`add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `sub-neg` `associate-*r/` `div-exp` `associate--l+` `distribute-lft-out--`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `div-inv` `distribute-lft-out` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

18.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
13.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
6.0ms	(* (cbrt 3.0) (sqrt x))
4.0ms	(/ 1.0 (* x 9.0))

series254.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
77.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
66.0ms	(* (cbrt 3.0) (sqrt x))
16.0ms	(/ 1.0 (* x 9.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	573	1128
1	3010	841
2	5001	776

prune222.0ms

Filtered

120 candidates to 69 candidates (57.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	119	13	132

Merged error: 0b

Counts

132 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cbrt 3.0)) (sqrt x))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt (* (cbrt 3.0) (cbrt 3.0))) (* (cbrt (cbrt 3.0)) (sqrt x))))
0.3b	(* (cbrt (* (cbrt 3.0) (cbrt 3.0))) (* (cbrt (cbrt 3.0)) (sqrt x)))
0.7b	(/ 1.0 (* x 9.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
32×	`pow1`
24×	`add-sqr-sqrt`
21×	`add-cbrt-cube`
20×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
16×	`cbrt-prod`
14×	`associate-l`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`sqrt-prod` `unswap-sqr`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 100

Calls

4 calls:

6.0ms	(* (cbrt (cbrt 3.0)) (sqrt x))
13.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt (* (cbrt 3.0) (cbrt 3.0))) (* (cbrt (cbrt 3.0)) (sqrt x))))
8.0ms	(* (cbrt (* (cbrt 3.0) (cbrt 3.0))) (* (cbrt (cbrt 3.0)) (sqrt x)))
4.0ms	(/ 1.0 (* x 9.0))

series302.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (cbrt (cbrt 3.0)) (sqrt x))
81.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt (* (cbrt 3.0) (cbrt 3.0))) (* (cbrt (cbrt 3.0)) (sqrt x))))
69.0ms	(* (cbrt (* (cbrt 3.0) (cbrt 3.0))) (* (cbrt (cbrt 3.0)) (sqrt x)))
16.0ms	(/ 1.0 (* x 9.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	529	1075
1	2283	899
2	5002	873

prune247.0ms

Filtered

112 candidates to 73 candidates (65.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	112	13	125

Merged error: 0b

Counts

125 → 13

regimes143.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample1.0s

Algorithm

intervals

Results

362.0ms	8583×	body	80	valid
360.0ms	8711×	body	80	nan