Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	56×	body	640	valid
4.0ms	127×	body	80	valid
3.0ms	37×	body	320	valid
2.0ms	13×	body	1280	valid
1.0ms	23×	body	160	valid

simplify20.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize12.0ms

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))
4.1b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite148.0ms

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))
29.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
54.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (+ x 1.0))
27.0ms	(/ 1.0 (- x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
220.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify160.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (78.0ms)

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

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (- x 1.0) (cbrt 1.0)))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
4.1b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (- x 1.0) (cbrt 1.0))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

770×	`times-frac`
737×	`*-un-lft-identity`
564×	`add-sqr-sqrt`
516×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
89×	`distribute-lft-out`
67×	`div-inv`
57×	`associate-/r/`
38×	`associate-/r*`
30×	`cbrt-prod`
29×	`flip3-+` `flip-+`
20×	`difference-of-squares`
19×	`distribute-lft-out--`
18×	`add-exp-log` `fma-neg`
12×	`add-cbrt-cube`
11×	`add-log-exp`
10×	`fma-def`
7×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`frac-add`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `sum-log` `frac-sub` `flip--` `cbrt-unprod`
1×	`+-commutative` `associate-+l-`

Counts

4 → 665

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
14.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (- x 1.0) (cbrt 1.0)))
28.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
67.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (- x 1.0) (cbrt 1.0))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (+ x 1.0))
68.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (- x 1.0) (cbrt 1.0)))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
258.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (- x 1.0) (cbrt 1.0))))

simplify130.0ms

Algorithm

egg-herbie

Counts

677 → 677

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1492	12988
1	5001	10499

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (/ (- x 1.0) (cbrt 1.0)) (* (* (+ x 1.0) x) (* (cbrt 1.0) (cbrt 1.0)))) (* (* (+ x 1.0) x) (/ (- x 1.0) (cbrt 1.0))))
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.1b	(* (* (+ x 1.0) x) (/ (- x 1.0) (cbrt 1.0)))
32.7b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (/ (- x 1.0) (cbrt 1.0)) (* (* (+ x 1.0) x) (* (cbrt 1.0) (cbrt 1.0))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
34×	`add-exp-log` `associate-r`
33×	`times-frac`
30×	`add-cbrt-cube`
23×	`add-cube-cbrt`
15×	`cbrt-prod`
12×	`associate-*l/` `prod-exp` `cbrt-unprod`
9×	`pow1` `cbrt-undiv` `div-exp`
6×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-prod-down` `associate-/l*`
2×	`associate-*r/` `div-inv`
1×	`sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `associate-/r` `-commutative` `flip--` `fma-udef`

Counts

4 → 120

Calls

4 calls:

14.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (/ (- x 1.0) (cbrt 1.0)) (* (* (+ x 1.0) x) (* (cbrt 1.0) (cbrt 1.0)))) (* (* (+ x 1.0) x) (/ (- x 1.0) (cbrt 1.0))))
4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
15.0ms	(* (* (+ x 1.0) x) (/ (- x 1.0) (cbrt 1.0)))
1.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (/ (- x 1.0) (cbrt 1.0)) (* (* (+ x 1.0) x) (* (cbrt 1.0) (cbrt 1.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

664.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (/ (- x 1.0) (cbrt 1.0)) (* (* (+ x 1.0) x) (* (cbrt 1.0) (cbrt 1.0)))) (* (* (+ x 1.0) x) (/ (- x 1.0) (cbrt 1.0))))
37.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
176.0ms	(* (* (+ x 1.0) x) (/ (- x 1.0) (cbrt 1.0)))
204.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (/ (- x 1.0) (cbrt 1.0)) (* (* (+ x 1.0) x) (* (cbrt 1.0) (cbrt 1.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	760	1947
1	3824	1589
2	5001	1581

prune564.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
104×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
51×	`add-exp-log`
47×	`unpow-prod-down`
40×	`associate-r`
26×	`associate-/r*`
24×	`div-exp`
23×	`cube-prod`
17×	`sqr-pow`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
10×	`prod-exp`
9×	`associate-/l*` `unswap-sqr`
7×	`cube-mult` `unpow3`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `frac-2neg` `associate-l` `clear-num` `inv-pow`
2×	`cbrt-unprod`
1×	`associate-r/` `pow-prod-down` `un-div-inv` `-commutative`

Counts

4 → 262

Calls

4 calls:

15.0ms	(* 2.0 (/ 1 (pow x 3)))
5.0ms	(/ 1 (pow x 7))
6.0ms	(/ 1 (pow x 5))
6.0ms	(/ 1 (pow x 3))

series168.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 2.0 (/ 1 (pow x 3)))
52.0ms	(/ 1 (pow x 7))
44.0ms	(/ 1 (pow x 5))
31.0ms	(/ 1 (pow x 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	591	1188
1	3164	890
2	5001	890

prune475.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 9.5b

bsearch111.0ms

Steps

Iters	Range		Point
9	6.164824567421913	3268324.1998729478	119.57592943098413
9	-3875183.9477288676	-0.008763241487176904	-136.1881966537822

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	30
1	47	30

end0.0ms

sample602.0ms

Algorithm

intervals

Results

207.0ms	1845×	body	640	valid
122.0ms	4144×	body	80	valid
78.0ms	591×	body	1280	valid
74.0ms	937×	body	320	valid
26.0ms	487×	body	160	valid