Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

298×

body

valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	4
1	31	4
2	71	4
3	136	4
4	211	4
5	285	4
6	350	4
7	396	4
8	408	4
9	408	4

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: 0.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ 16.0 116.0))
0.0b	(* (- x (/ 16.0 116.0)) 3.0)
0.2b	(* (* (- x (/ 16.0 116.0)) 3.0) y)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
7×	`associate-l`
6×	`add-cube-cbrt` `associate-r` `associate-*l/`
5×	`add-log-exp`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`times-frac` `*-commutative` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

6.0ms	(- x (/ 16.0 116.0))
9.0ms	(* (- x (/ 16.0 116.0)) 3.0)
11.0ms	(* (* (- x (/ 16.0 116.0)) 3.0) y)

series106.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(- x (/ 16.0 116.0))
40.0ms	(* (- x (/ 16.0 116.0)) 3.0)
41.0ms	(* (* (- x (/ 16.0 116.0)) 3.0) y)

simplify103.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	223	336
1	883	287
2	4460	287
3	5001	287

prune111.0ms

Filtered

67 candidates to 45 candidates (67.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	8	68

Merged error: 0.0b

Counts

68 → 8

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (/ 16.0 116.0))
0.3b	(* (- x (/ 16.0 116.0)) (* 3.0 y))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-l`
4×	`add-log-exp` `difference-of-squares`
3×	`add-cube-cbrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `times-frac` `associate-*l/` `flip--` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `associate-r` `*-commutative`

Counts

2 → 38

Calls

2 calls:

6.0ms	(- x (/ 16.0 116.0))
10.0ms	(* (- x (/ 16.0 116.0)) (* 3.0 y))

series61.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- x (/ 16.0 116.0))
36.0ms	(* (- x (/ 16.0 116.0)) (* 3.0 y))

simplify69.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	187	232
1	601	197
2	2588	197
3	5002	197

prune66.0ms

Filtered

44 candidates to 28 candidates (63.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	44	8	52

Merged error: 0.0b

Counts

52 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0)))
0.2b	(* (/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (+ x (/ 16.0 116.0))) y)
0.6b	(* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0)
11.6b	(/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (+ x (/ 16.0 116.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

4.0ms	(- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0)))
13.0ms	(* (/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (+ x (/ 16.0 116.0))) y)
6.0ms	(* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0)
12.0ms	(/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (+ x (/ 16.0 116.0)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0)))
59.0ms	(* (/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (+ x (/ 16.0 116.0))) y)
66.0ms	(* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0)
105.0ms	(/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (+ x (/ 16.0 116.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	413	1035
1	2181	848
2	5002	835

prune169.0ms

Filtered

103 candidates to 70 candidates (68.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	102	9	111

Merged error: 0b

Counts

111 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ x (/ 16.0 116.0)))
0.8b	(* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0))))
5.0b	(/ (/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0))))) (cbrt (+ x (/ 16.0 116.0))))
6.6b	(/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0)))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

124×	`cbrt-div`
100×	`times-frac`
93×	`*-un-lft-identity`
84×	`cbrt-prod`
74×	`associate-/r/`
62×	`flip3-+` `flip-+`
57×	`add-sqr-sqrt`
49×	`add-cube-cbrt`
40×	`frac-times`
36×	`add-exp-log`
22×	`associate-*l/`
21×	`add-cbrt-cube` `distribute-lft-out`
20×	`associate-*r/`
14×	`associate-/l*`
13×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`div-inv`
9×	`swap-sqr` `prod-exp` `cbrt-unprod`
8×	`associate-/r*`
7×	`pow1/3` `associate-r` `associate-l`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `pow-sqr` `pow-prod-up`
1×	`pow2` `flip3--` `pow-plus` `*-commutative` `flip--`

Counts

4 → 232

Calls

4 calls:

6.0ms	(cbrt (+ x (/ 16.0 116.0)))
19.0ms	(* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0))))
29.0ms	(/ (/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0))))) (cbrt (+ x (/ 16.0 116.0))))
21.0ms	(/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0)))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ x (/ 16.0 116.0)))
104.0ms	(* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0))))
106.0ms	(/ (/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0))))) (cbrt (+ x (/ 16.0 116.0))))
169.0ms	(/ (* (- (* x x) (* (/ 16.0 116.0) (/ 16.0 116.0))) 3.0) (* (cbrt (+ x (/ 16.0 116.0))) (cbrt (+ x (/ 16.0 116.0)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1029	5325
1	5001	4931

prune659.0ms

Filtered

244 candidates to 161 candidates (66.0%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	244	9	253

Merged error: 0b

Counts

253 → 9

regimes148.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	4
1	11	4

end0.0ms

sample336.0ms

Algorithm

intervals

Results

194.0ms

9142×

body

valid