Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	56×	body	640	valid
4.0ms	138×	body	80	valid
3.0ms	32×	body	320	valid
2.0ms	17×	body	1280	valid
1.0ms	13×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
1.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite143.0ms

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:

24.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
56.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms	(/ 1.0 (+ x 1.0))
26.0ms	(/ 1.0 (- x 1.0))
218.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify155.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (73.0ms)

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

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
29.7b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt` `prod-diff`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*l/`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`frac-times` `associate-/r/`
7×	`flip3--` `flip--`
6×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`cbrt-undiv` `sub-neg` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
1×	`frac-2neg` `fma-neg` `diff-log` `associate-l` `clear-num` `associate-/r` `-commutative` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

11.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
11.0ms	(* (* (+ x 1.0) x) (- x 1.0))
4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series605.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
93.0ms	(* (* (+ x 1.0) x) (- x 1.0))
36.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
181.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	637	1498
1	3084	1198
2	5001	1198

prune270.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
17.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
37×	`prod-diff`
33×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`frac-add`
31×	`add-cube-cbrt` `flip3--` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
18×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
12×	`associate-*r/`
9×	`pow1`
8×	`associate-/r/` `add-log-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`sub-neg` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
1×	`+-commutative` `fma-def` `frac-2neg` `fma-neg` `diff-log` `associate-l` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 171

Calls

4 calls:

22.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
14.0ms	(* (* (+ x 1.0) x) (- x 1.0))
4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
13.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series228.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
99.0ms	(* (* (+ x 1.0) x) (- x 1.0))
37.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1200	2824
1	5002	2473

prune552.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (/ 1 (pow x 3)))
0.1b	(/ 1 (pow x 5))
0.2b	(/ 1 (pow x 7))
0.5b	(/ 1 (pow x 3))

rewrite42.0ms

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:

18.0ms	(* 2.0 (/ 1 (pow x 3)))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 7))
6.0ms	(/ 1 (pow x 3))

series170.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 2.0 (/ 1 (pow x 3)))
48.0ms	(/ 1 (pow x 5))
57.0ms	(/ 1 (pow x 7))
30.0ms	(/ 1 (pow x 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 1 (17.0ms)

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

prune459.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes56.0ms

Accuracy

96.2% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 9.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	45
1	50	45

end0.0ms

sample645.0ms

Algorithm

intervals

Results

211.0ms	1834×	body	640	valid
132.0ms	4196×	body	80	valid
87.0ms	916×	body	320	valid
83.0ms	574×	body	1280	valid
28.0ms	480×	body	160	valid