Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	49×	body	1280	valid
5.0ms	37×	body	640	valid
4.0ms	141×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	13×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	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: 26.9b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out--`

Counts

3 → 60

Calls

3 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series137.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
20.0ms	(+ 1.0 (exp (* -2.0 x)))
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2785	460
3	5002	460

prune137.0ms

Filtered

69 candidates to 50 candidates (72.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 0.0b

Counts

70 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
0.0b	(+ (exp (* -2.0 x)) 1.0)
0.0b	(exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
3.8b	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
24×	`add-sqr-sqrt` `times-frac`
22×	`add-cube-cbrt`
18×	`exp-prod`
8×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`associate-/r*` `associate-/r/`
3×	`log-prod` `flip3-+` `associate--l+` `flip-+` `associate-/l*`
2×	`div-inv` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `log-pow` `flip--` `rem-exp-log` `difference-of-squares`

Counts

4 → 89

Calls

4 calls:

5.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
4.0ms	(+ (exp (* -2.0 x)) 1.0)
6.0ms	(exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
17.0ms	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

series192.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
21.0ms	(+ (exp (* -2.0 x)) 1.0)
52.0ms	(exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
84.0ms	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	300	726
1	811	663
2	2913	655
3	5001	653

prune197.0ms

Filtered

101 candidates to 73 candidates (72.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	101	2	103

Merged error: 0.0b

Counts

103 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
0.1b	(* 0.33333333333333337 (pow x 3))
0.4b	(* 5.551115123125783e-17 (pow x 4))
10.2b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `sub-neg` `flip3--` `flip3-+` `unpow3` `flip--` `flip-+` `associate--r+`

Counts

4 → 81

Calls

4 calls:

9.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
6.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(* 5.551115123125783e-17 (pow x 4))
4.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
42.0ms	(* 0.33333333333333337 (pow x 3))
37.0ms	(* 5.551115123125783e-17 (pow x 4))
110.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	344	493
1	1475	459
2	5001	459

prune167.0ms

Filtered

93 candidates to 58 candidates (62.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Merged error: 0.0b

Counts

95 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 5.551115123125783e-17 (pow x 4))
0.4b	(* 5.551115123125783e-17 (pow x 4))
10.2b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))
10.2b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(* 5.551115123125783e-17 (pow x 4))
5.0ms	(* 5.551115123125783e-17 (pow x 4))
4.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))
5.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 5.551115123125783e-17 (pow x 4))
41.0ms	(* 5.551115123125783e-17 (pow x 4))
107.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))
112.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify214.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	183	426
1	756	392
2	4415	382
3	5002	382

prune210.0ms

Filtered

84 candidates to 54 candidates (64.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	84	3	87

Merged error: 0.0b

Counts

87 → 3

regimes123.0ms

Accuracy

94.7% (1.6b remaining)

Error of 1.6b against oracle of 0.0b and baseline of 29.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample876.0ms

Algorithm

intervals

Results

366.0ms	1702×	body	1280	valid
175.0ms	1238×	body	640	valid
107.0ms	4101×	body	80	valid
64.0ms	661×	body	320	valid
18.0ms	298×	body	160	valid