Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	68×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	17×	body	1280	valid
2.0ms	19×	body	320	valid
1.0ms	19×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 8.5b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
1.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

1765×	`*-un-lft-identity`
1348×	`add-sqr-sqrt`
1261×	`associate-/r*`
1132×	`add-cube-cbrt`
1080×	`frac-sub`
1012×	`frac-add`
966×	`associate-/l*`
703×	`times-frac`
468×	`prod-diff`
322×	`frac-2neg` `clear-num`
236×	`associate-+l+`
203×	`distribute-lft-out`
109×	`distribute-lft-out--`
104×	`difference-of-squares`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
13×	`flip3--` `flip--`
11×	`add-log-exp`
10×	`fma-def`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `sum-log`
1×	`+-commutative` `associate-+l-`

Counts

4 → 1716

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
29.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
90.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1.0 (- x 1.0))
43.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms	(/ 1.0 (+ x 1.0))
226.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify393.0ms

Algorithm

egg-herbie

Counts

1728 → 1728

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5001	37459

prune3.2s

Filtered

1728 candidates to 918 candidates (53.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1725	3	1728
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1726	3	1729

Merged error: 0.2b

Counts

1729 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
1.9b	(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
27×	`times-frac`
24×	`add-cube-cbrt`
9×	`associate-/r*` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`associate-+r+` `fma-def` `sum-log` `fma-udef`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`flip3--` `flip--`

Counts

4 → 107

Calls

4 calls:

1.0ms	(fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))
6.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
12.0ms	(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0)))
29.0ms	(/ 1.0 (- x 1.0))
30.0ms	(/ 1.0 (+ x 1.0))
289.0ms	(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (* (/ 1 x) 2.0))) (+ (fma (- (/ 1 x)) 2.0 (* (/ 1 x) 2.0)) (/ 1.0 (- x 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	459	919
1	1740	844
2	5002	819

prune279.0ms

Filtered

119 candidates to 94 candidates (79.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Merged error: 0.2b

Counts

122 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
1.7b	(+ (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ (- 2.0) x))
3.5b	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

3662×	`frac-add`
2197×	`associate-/l*`
2084×	`*-un-lft-identity`
1943×	`associate-/r*`
1565×	`add-sqr-sqrt`
1211×	`add-cube-cbrt`
471×	`frac-2neg` `clear-num`
340×	`distribute-rgt-neg-in`
336×	`distribute-lft-neg-in`
256×	`distribute-lft-out`
193×	`distribute-lft-out--`
177×	`difference-of-squares`
114×	`times-frac`
112×	`neg-mul-1`
39×	`fma-def`
21×	`flip-+`
19×	`flip3-+`
11×	`add-log-exp`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv`
4×	`pow1` `expm1-log1p-u` `sum-log` `flip--` `log1p-expm1-u`
3×	`+-commutative`
2×	`cbrt-undiv` `associate-+l+` `flip3--` `distribute-frac-neg` `div-exp`
1×	`neg-sub0` `associate-+r-` `div-sub` `unsub-neg`

Counts

4 → 2072

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
112.0ms	(+ (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ (- 2.0) x))
31.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1.0 (- x 1.0))
26.0ms	(/ 1.0 (+ x 1.0))
227.0ms	(+ (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ (- 2.0) x))
163.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))

simplify550.0ms

Algorithm

egg-herbie

Counts

2084 → 2084

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5001	52102

prune5.0s

Filtered

2084 candidates to 1243 candidates (59.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	2084	0	2084
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	2084	2	2086

Merged error: 0.2b

Counts

2086 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
0.2b	(/ 1 (pow x 5))
0.3b	(/ 2.0 (pow x 3))
0.3b	(/ 1 (pow x 7))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 181

Calls

4 calls:

1.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 2.0 (pow x 3))
6.0ms	(/ 1 (pow x 7))

series211.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
47.0ms	(/ 1 (pow x 5))
36.0ms	(/ 2.0 (pow x 3))
59.0ms	(/ 1 (pow x 7))

simplify53.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	469	924
1	2349	779
2	5001	765

prune322.0ms

Filtered

193 candidates to 100 candidates (51.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	190	5	195

Merged error: 0b

Counts

195 → 5

regimes36.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.7b

bsearch115.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	99.93867250030655
10	-1556119314.230081	-0.05767290693153419	-102.94433550507199

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	30
1	49	30
2	49	30

end0.0ms

sample601.0ms

Algorithm

intervals

Results

199.0ms	1801×	body	640	valid
125.0ms	4258×	body	80	valid
77.0ms	933×	body	320	valid
74.0ms	546×	body	1280	valid
28.0ms	463×	body	160	valid