Details

sample47.0ms

Algorithm

intervals

Results

19.0ms	109×	body	1280	valid
9.0ms	86×	body	640	valid
5.0ms	385×	pre	80	true
3.0ms	39×	body	320	valid
2.0ms	137×	body	80	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	2
1	7	2
2	7	2

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: 58.5b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

4.9b	(- (exp x) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

(- (exp x) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	81	72
1	185	67
2	499	66
3	1399	66
4	5002	66

prune36.0ms

Filtered

17 candidates to 12 candidates (70.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	2	18

Merged error: 0.0b

Counts

18 → 2

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
0.0b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`associate-l`
10×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `add-log-exp` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-prod-down` `pow-exp` `sum-log`

Counts

3 → 62

Calls

3 calls:

8.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
8.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
4.0ms	(* x 1/6)

series106.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
66.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
13.0ms	(* x 1/6)

simplify57.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	310	356
1	1545	328
2	5001	327

prune104.0ms

Filtered

71 candidates to 47 candidates (66.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x 1/6)
0.3b	(* x 1/6)
0.3b	(* x 1/6)
27.1b	(/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

4.0ms	(* x 1/6)
4.0ms	(* x 1/6)
3.0ms	(* x 1/6)
23.0ms	(/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))

series123.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* x 1/6)
13.0ms	(* x 1/6)
18.0ms	(* x 1/6)
78.0ms	(/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))

simplify52.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	288	914
1	1506	822
2	5001	812

prune215.0ms

Filtered

98 candidates to 67 candidates (68.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	98	4	102

Merged error: 0.0b

Counts

102 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))
0.7b	(cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))
3.6b	(/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)))
23.2b	(* (/ 1 (* (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)))) (/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
51×	`add-exp-log` `times-frac`
39×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`cbrt-prod`
24×	`associate-r`
20×	`cbrt-div` `prod-exp`
19×	`add-cbrt-cube`
16×	`div-exp`
15×	`associate-l`
12×	`associate-/r/`
11×	`flip3--` `flip--`
9×	`unswap-sqr`
8×	`cbrt-undiv` `cbrt-unprod`
6×	`pow1` `associate-/r*`
5×	`frac-times`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`associate-r/` `associate-l/` `div-inv` `associate-/l*`
2×	`pow1/3` `associate-/l/`
1×	`frac-2neg` `div-sub` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

8.0ms	(cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))
7.0ms	(cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))
25.0ms	(/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)))
52.0ms	(* (/ 1 (* (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)))) (/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))
63.0ms	(cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))
123.0ms	(/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)))
81.0ms	(* (/ 1 (* (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)))) (/ (- (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (pow x 4)) (pow x 2)) (cbrt (- (* (pow x 2) (+ (* x 1/6) 1/2)) x))))

simplify147.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	863	4768
1	4108	4230
2	5002	4006

prune507.0ms

Filtered

162 candidates to 116 candidates (71.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	162	4	166

Merged error: 0.0b

Counts

166 → 4

regimes55.0ms

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	13	5
1	13	5

end0.0ms

sample1.4s

Algorithm

intervals

Results

606.0ms	3547×	body	1280	valid
267.0ms	2471×	body	640	valid
136.0ms	11905×	pre	80	true
85.0ms	1209×	body	320	valid
71.0ms	4087×	body	80	valid
27.0ms	591×	body	160	valid