Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	65×	body	640	valid
3.0ms	134×	body	80	valid
3.0ms	45×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	15	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
2.5b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

662×	`*-un-lft-identity`
589×	`times-frac`
496×	`add-sqr-sqrt`
378×	`prod-diff`
368×	`add-cube-cbrt`
86×	`associate-/r/`
79×	`distribute-lft-out--`
76×	`distribute-lft-out`
62×	`difference-of-squares`
44×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 504

Calls

3 calls:

5.0ms	(/ 1.0 (- x 1.0))
6.0ms	(/ 1.0 (+ x 1.0))
71.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series420.0ms

Counts

3 → 9

Calls

3 calls:

221.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
174.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify165.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	1200	13350
1	3593	9620
2	5001	9568

prune679.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))
13.0b	(- (* (/ (sqrt 1.0) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (sqrt 1.0) (cbrt (+ x 1.0)))) (/ (/ (/ 1.0 (cbrt (- x 1.0))) (cbrt (- x 1.0))) (cbrt (- x 1.0))))

rewrite916.0ms

Algorithm

rewrite-expression-head

Rules

5424×	`times-frac`
3405×	`cbrt-prod`
3310×	`add-sqr-sqrt` `*-un-lft-identity`
1974×	`prod-diff`
1948×	`add-cube-cbrt`
681×	`distribute-lft-out--` `difference-of-squares`
152×	`cbrt-div`
146×	`associate-/r/`
77×	`flip3--` `flip--`
73×	`div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3` `frac-sub`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r/` `associate-l/`

Counts

4 → 2043

Calls

4 calls:

2.0ms	(cbrt (- x 1.0))
2.0ms	(cbrt (- x 1.0))
2.0ms	(cbrt (- x 1.0))
574.0ms	(- (* (/ (sqrt 1.0) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (sqrt 1.0) (cbrt (+ x 1.0)))) (/ (/ (/ 1.0 (cbrt (- x 1.0))) (cbrt (- x 1.0))) (cbrt (- x 1.0))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (- x 1.0))
98.0ms	(cbrt (- x 1.0))
95.0ms	(cbrt (- x 1.0))
153.0ms	(- (* (/ (sqrt 1.0) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (sqrt 1.0) (cbrt (+ x 1.0)))) (/ (/ (/ 1.0 (cbrt (- x 1.0))) (cbrt (- x 1.0))) (cbrt (- x 1.0))))

simplify1.3s

Algorithm

egg-herbie

Counts

2055 → 2055

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	8299	182370

prune9.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
0.0b	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
0.5b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
28.7b	(fma (- x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))) (/ (- (pow (cbrt 1.0) 3)) (- x 1.0)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

412×	`times-frac`
391×	`add-sqr-sqrt` `*-un-lft-identity`
227×	`add-cube-cbrt`
216×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
144×	`cbrt-prod` `unpow-prod-down` `cube-prod`
86×	`difference-of-squares`
83×	`associate-/l*`
82×	`distribute-lft-out--`
24×	`cube-mult` `unpow3` `sqr-pow`
14×	`associate-/r*`
12×	`neg-mul-1`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`neg-sub0` `div-sub` `distribute-frac-neg`
1×	`fma-udef`

Counts

4 → 571

Calls

4 calls:

23.0ms	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
27.0ms	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (- x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))) (/ (- (pow (cbrt 1.0) 3)) (- x 1.0)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
36.0ms	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
47.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
179.0ms	(fma (- x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))) (/ (- (pow (cbrt 1.0) 3)) (- x 1.0)))

simplify178.0ms

Algorithm

egg-herbie

Counts

583 → 583

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	839	5266
1	4784	4840
2	5001	4840

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
0.2b	(/ (- 2.0) (pow x 6))
0.3b	(/ 1 (pow x 4))
0.6b	(/ 1 (pow x 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
83×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
57×	`unpow-prod-down`
27×	`add-exp-log`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
22×	`associate-/r*`
19×	`sqr-pow`
16×	`associate-/l*`
15×	`div-exp`
10×	`add-cbrt-cube`
8×	`neg-mul-1`
7×	`pow-to-exp` `pow-exp`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-flip` `inv-pow`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `fma-udef`

Counts

4 → 229

Calls

4 calls:

0.0ms	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
6.0ms	(/ (- 2.0) (pow x 6))
4.0ms	(/ 1 (pow x 4))
4.0ms	(/ 1 (pow x 2))

series175.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4))))
50.0ms	(/ (- 2.0) (pow x 6))
26.0ms	(/ 1 (pow x 4))
16.0ms	(/ 1 (pow x 2))

simplify62.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	584	1345
1	2344	1132
2	5002	1058

prune455.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 19.7b

bsearch97.0ms

Steps

Iters	Range		Point
9	1.2499789889099044	556939279.5099251	246.3673785262834
9	-15640006985.087824	-4.508778152722845	-281.7751988528153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	33
1	56	33
2	56	33

end0.0ms

sample444.0ms

Algorithm

intervals

Results

161.0ms	1915×	body	640	valid
94.0ms	4241×	body	80	valid
75.0ms	1213×	body	320	valid
26.0ms	631×	body	160	valid