Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	60×	body	640	valid
5.0ms	122×	body	80	valid
4.0ms	40×	body	320	valid
4.0ms	21×	body	1280	valid
1.0ms	13×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

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: 9.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

706×	`*-un-lft-identity`
688×	`times-frac`
505×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
13×	`distribute-lft-out--`
10×	`fma-def` `add-log-exp`
8×	`difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `frac-add` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `clear-num`

Counts

3 → 579

Calls

3 calls:

5.0ms	(/ 1.0 (+ x 1.0))
28.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
57.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series282.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1.0 (+ x 1.0))
45.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
213.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify154.0ms

Algorithm

egg-herbie

Counts

588 → 588

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	1058	10745
1	3283	8083
2	5001	7467

prune1.1s

Filtered

588 candidates to 358 candidates (60.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	585	3	588
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	586	3	589

Merged error: 0.1b

Counts

589 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(* (+ x 1.0) x)
1.2b	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
16.4b	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
9×	`fma-def`
8×	`add-log-exp`
6×	`pow1` `times-frac` `associate-*l/`
4×	`expm1-log1p-u` `flip3-+` `associate-l` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`associate-r` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-sub` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `-commutative` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
6.0ms	(* (+ x 1.0) x)
21.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
9.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series437.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
45.0ms	(* (+ x 1.0) x)
288.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
67.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify62.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	494	782
1	2202	694
2	5001	686

prune189.0ms

Filtered

104 candidates to 86 candidates (82.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 0.1b

Counts

107 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
0.0b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 7))
0.1b	(/ 2.0 (pow x 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
27×	`add-exp-log`
26×	`associate-/r*`
15×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`pow-to-exp` `pow-exp`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-flip` `inv-pow`
1×	`fma-udef`

Counts

4 → 187

Calls

4 calls:

1.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 7))
5.0ms	(/ 2.0 (pow x 3))

series265.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
42.0ms	(/ 1 (pow x 5))
59.0ms	(/ 1 (pow x 7))
36.0ms	(/ 2.0 (pow x 3))

simplify54.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	450	904
1	2278	777
2	5001	777

prune335.0ms

Filtered

199 candidates to 96 candidates (48.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	196	5	201

Merged error: 0.0b

Counts

201 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 7))
0.1b	(/ (/ 2.0 (* x x)) x)
0.2b	(/ 2.0 (* x x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
19×	`div-exp`
18×	`associate-/r*`
16×	`associate-/l*`
9×	`cbrt-undiv`
8×	`div-inv` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`pow-flip` `prod-exp` `cbrt-unprod` `inv-pow`
1×	`associate-/l/`

Counts

4 → 183

Calls

4 calls:

5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 7))
10.0ms	(/ (/ 2.0 (* x x)) x)
5.0ms	(/ 2.0 (* x x))

series169.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1 (pow x 5))
53.0ms	(/ 1 (pow x 7))
43.0ms	(/ (/ 2.0 (* x x)) x)
24.0ms	(/ 2.0 (* x x))

simplify57.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	511	914
1	2528	828
2	5001	768

prune346.0ms

Filtered

195 candidates to 106 candidates (54.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	195	5	200

Merged error: 0.0b

Counts

200 → 5

regimes39.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch144.0ms

Steps

Iters	Range		Point
10	14.716166499582775	2.5158614700293387e+20	111.33784045281939
11	-2193661101726697.2	-1.4639597033977343e-08	-107.94411106005032

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	48	34

end0.0ms

sample753.0ms

Algorithm

intervals

Results

266.0ms	1887×	body	640	valid
152.0ms	4126×	body	80	valid
98.0ms	939×	body	320	valid
97.0ms	551×	body	1280	valid
36.0ms	499×	body	160	valid