Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	58×	body	640	valid
5.0ms	141×	body	80	valid
5.0ms	28×	body	320	valid
2.0ms	11×	body	1280	valid
1.0ms	18×	body	160	valid

simplify20.0ms

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: 11.2b

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))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
35.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
59.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(/ 1.0 (- x 1.0))
40.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
212.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify165.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670

prune1.2s

Filtered

630 candidates to 390 candidates (61.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	627	3	630
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	628	3	631

Merged error: 0.0b

Counts

631 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.2b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
8.7b	(+ (fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))
11.3b	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 2.0 x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
9.0ms	(+ (fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))
1.0ms	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 2.0 x)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
54.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
269.0ms	(+ (fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))
60.0ms	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 2.0 x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	480	891
1	1821	838
2	5003	824

prune247.0ms

Filtered

114 candidates to 95 candidates (83.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	114	3	117

Merged error: 0.0b

Counts

117 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
0.1b	(/ 1 (pow x 7))
0.1b	(/ 2.0 (pow x 3))
0.2b	(/ 1 (pow x 5))

rewrite21.0ms

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

series268.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
59.0ms	(/ 1 (pow x 7))
35.0ms	(/ 2.0 (pow x 3))
46.0ms	(/ 1 (pow x 5))

simplify57.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (15.0ms)

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

prune344.0ms

Filtered

199 candidates to 96 candidates (48.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	197	5	202

Merged error: 0b

Counts

202 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
50×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log`
24×	`unpow-prod-down`
20×	`add-cbrt-cube`
19×	`associate-/l*`
18×	`div-exp`
15×	`associate-/r*`
8×	`cbrt-undiv` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `prod-exp` `cbrt-unprod` `inv-pow`
1×	`fma-udef` `associate-/l/`

Counts

4 → 168

Calls

4 calls:

1.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ (/ 2.0 x) (* x x)))
5.0ms	(/ 1 (pow x 7))
8.0ms	(/ (/ 2.0 x) (* x x))
5.0ms	(/ 1 (pow x 5))

series260.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ (/ 2.0 x) (* x x)))
57.0ms	(/ 1 (pow x 7))
34.0ms	(/ (/ 2.0 x) (* x x))
45.0ms	(/ 1 (pow x 5))

simplify53.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	520	883
1	2161	783
2	5002	721

prune314.0ms

Filtered

180 candidates to 94 candidates (52.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	180	5	185

Merged error: 0b

Counts

185 → 5

regimes36.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 26.4b

bsearch119.0ms

Steps

Iters	Range		Point
9	0.006602375602419948	2408.9151023461654	109.90066438549296
10	-7888799.454350161	-0.0014566459989916651	-108.93030297428587

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms

sample720.0ms

Algorithm

intervals

Results

258.0ms	1941×	body	640	valid
150.0ms	4169×	body	80	valid
93.0ms	544×	body	1280	valid
93.0ms	917×	body	320	valid
29.0ms	434×	body	160	valid