Details

sample81.0ms

Algorithm

intervals

Results

55.0ms	182×	body	1280	valid
6.0ms	283×	body	80	valid
6.0ms	35×	body	640	valid
2.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5

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: 29.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.5b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
8.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
59.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify96.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune85.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0.0b

Counts

42 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

8.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))

series277.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
52.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
53.0ms	(* 1/360 (pow x 6))
36.0ms	(* 1/12 (pow x 4))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423

prune167.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
0.1b	(* 1/12 (pow x 4))
19.9b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt` `unpow-prod-down`
15×	`add-exp-log`
14×	`cbrt-prod` `associate-r`
9×	`add-cbrt-cube`
8×	`cube-prod`
6×	`associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
5×	`pow1`
4×	`cube-div` `distribute-lft-out` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `*-commutative` `cbrt-unprod` `flip-+`
1×	`pow-pow` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* 1/360 (pow x 6))
8.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
5.0ms	(* 1/12 (pow x 4))
8.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series223.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/360 (pow x 6))
76.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
35.0ms	(* 1/12 (pow x 4))
58.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	419	910
1	1865	843
2	5003	830

prune214.0ms

Filtered

114 candidates to 62 candidates (54.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	114	5	119

Merged error: 0.0b

Counts

119 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
0.0b	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
0.0b	(pow (exp x) 3)
4.0b	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`add-exp-log` `add-log-exp`
7×	`pow1`
4×	`pow-pow` `flip3-+` `associate-*r/` `flip-+`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `times-frac` `cube-prod` `associate-r` `associate-l` `sum-log` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `associate-+r+` `frac-2neg` `distribute-lft-in` `unpow3` `pow-prod-down` `pow-exp` `clear-num` `associate-/r` `-commutative` `div-inv` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

13.0ms	(* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
26.0ms	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
4.0ms	(pow (exp x) 3)
9.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
249.0ms	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
23.0ms	(pow (exp x) 3)
93.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	522	1375
1	3142	1189
2	5001	1182

prune248.0ms

Filtered

98 candidates to 69 candidates (70.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	98	5	103

Merged error: 0b

Counts

103 → 5

regimes64.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5688×	body	1280	valid
189.0ms	1216×	body	640	valid
179.0ms	7996×	body	80	valid
56.0ms	577×	body	320	valid
20.0ms	340×	body	160	valid