Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	78×	body	1280	valid
7.0ms	54×	body	640	valid
4.0ms	192×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

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: 40.7b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.2b	(- (exp x) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309

prune101.0ms

Filtered

58 candidates to 43 candidates (74.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Merged error: 0.0b

Counts

59 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.4b	(* 1/6 (pow x 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

7.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
5.0ms	(* 1/6 (pow x 2))

series45.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
25.0ms	(* 1/6 (pow x 2))

simplify35.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	201	222
1	825	201
2	5001	198

prune67.0ms

Filtered

46 candidates to 29 candidates (63.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Merged error: 0.0b

Counts

50 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(/ (/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
0.0b	(* (exp x) (exp x))
4.2b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

146×	`times-frac`
125×	`*-un-lft-identity`
85×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
26×	`associate-/l*`
22×	`difference-of-squares`
21×	`distribute-lft-out`
18×	`exp-prod`
13×	`add-cbrt-cube`
11×	`pow1` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
3×	`div-sub` `swap-sqr` `associate-r` `associate-l` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 195

Calls

4 calls:

12.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
14.0ms	(/ (/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
6.0ms	(* (exp x) (exp x))
10.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series170.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
81.0ms	(/ (/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
13.0ms	(* (exp x) (exp x))
26.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	723	2502
1	3607	2358
2	5001	2353

prune533.0ms

Filtered

207 candidates to 149 candidates (72.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	207	4	211

Merged error: 0.0b

Counts

211 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(pow (exp 2) x)
0.0b	(/ (/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
4.4b	(- (pow (exp 2) x) (* 1.0 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac`
198×	`*-un-lft-identity`
147×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
88×	`difference-of-squares`
48×	`unpow-prod-down`
41×	`associate-/l*`
36×	`distribute-lft-out`
23×	`exp-lft-sqr` `sqr-pow`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `pow-pow` `div-exp`
3×	`pow-unpow` `exp-prod` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp`

Counts

4 → 248

Calls

4 calls:

10.0ms	(/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0))
3.0ms	(pow (exp 2) x)
18.0ms	(/ (/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
5.0ms	(- (pow (exp 2) x) (* 1.0 1.0))

series198.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0))
23.0ms	(pow (exp 2) x)
84.0ms	(/ (/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
35.0ms	(- (pow (exp 2) x) (* 1.0 1.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	924	3330
1	4097	3174
2	5002	3125

prune468.0ms

Filtered

260 candidates to 168 candidates (64.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	259	5	264

Merged error: 0.0b

Counts

264 → 5

regimes25.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch39.0ms

Steps

Iters	Range		Point
10	-0.05202343663643454	-5.738045557766166e-18	-0.00012167591385668957

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample964.0ms

Algorithm

intervals

Results

408.0ms	2213×	body	1280	valid
208.0ms	1672×	body	640	valid
116.0ms	5409×	body	80	valid
66.0ms	839×	body	320	valid
25.0ms	437×	body	160	valid