Details

Time bar (total: 5.9s)

sample20.0ms

Algorithm
intervals
Results
6.0ms57×body1280valid
3.0ms40×body640valid
3.0ms131×body80valid
1.0ms15×body320valid
1.0ms13×body160valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
963×*-un-lft-identity
724×times-frac
575×add-sqr-sqrt
468×prod-diff
409×add-cube-cbrt
185×distribute-lft-out
92×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
46×div-inv
28×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
5×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
2×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num frac-sub
Counts
2 → 561
Calls
2 calls:
11.0ms
(/ (+ x 1.0) (- x 1.0))
77.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series187.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (+ x 1.0) (- x 1.0))
147.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify207.0ms

Algorithm
egg-herbie
Counts
567 → 567
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
0116118191
1335013265
2500213161

prune714.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

16.0b
(/ x (- (* x x) (* 1.0 1.0)))
16.0b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
16.0b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
29.6b
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
44×times-frac
33×add-sqr-sqrt add-cube-cbrt
14×difference-of-squares
12×associate-/r*
11×associate-/l*
10×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/r/
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
2×flip3-+ flip-+
1×fma-udef
Counts
4 → 129
Calls
4 calls:
5.0ms
(/ x (- (* x x) (* 1.0 1.0)))
14.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
11.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ x (- (* x x) (* 1.0 1.0)))
45.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
40.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
201.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03931262
116001156
250011097

prune421.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
2.5b
(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (- (/ (+ x 1.0) (- x 1.0))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
46×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
9×distribute-lft-out
6×associate-/r/
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
1×fma-udef
Counts
4 → 97
Calls
4 calls:
3.0ms
(cbrt (/ x (+ x 1.0)))
3.0ms
(cbrt (/ x (+ x 1.0)))
3.0ms
(cbrt (/ x (+ x 1.0)))
0.0ms
(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (- (/ (+ x 1.0) (- x 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt (/ x (+ x 1.0)))
169.0ms
(cbrt (/ x (+ x 1.0)))
170.0ms
(cbrt (/ x (+ x 1.0)))
545.0ms
(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (- (/ (+ x 1.0) (- x 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03891078
11290987
25001948

prune361.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.5b
(/ 1 (pow x 3))
0.6b
(/ (- 1.0) (pow x 2))
7.6b
(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
440×times-frac
354×add-sqr-sqrt
344×*-un-lft-identity
342×add-cube-cbrt
252×prod-diff
166×unpow-prod-down
123×distribute-lft-neg-in distribute-rgt-neg-in
84×fma-neg
56×sqr-pow
52×unpow2
41×neg-mul-1
20×associate-/r*
18×add-exp-log
13×associate-/l*
12×cube-prod
9×div-exp
8×add-cbrt-cube
6×div-inv add-log-exp
5×difference-of-squares
4×pow1 expm1-log1p-u cube-mult pow-to-exp unpow3 pow-exp log1p-expm1-u
3×rec-exp 1-exp
2×cbrt-undiv neg-sub0 frac-2neg div-sub clear-num fma-udef
1×associate--l- sub-neg flip3-- pow-flip diff-log distribute-frac-neg flip-- associate--r+ distribute-lft-out-- inv-pow
Counts
4 → 559
Calls
4 calls:
0.0ms
(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
5.0ms
(/ 1 (pow x 3))
6.0ms
(/ (- 1.0) (pow x 2))
79.0ms
(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series388.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
34.0ms
(/ 1 (pow x 3))
35.0ms
(/ (- 1.0) (pow x 2))
39.0ms
(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify185.0ms

Algorithm
egg-herbie
Counts
571 → 571
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
0116212951
143537106
250017094

prune811.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.9b

bsearch73.0ms

Steps
ItersRangePoint
6
7065.8830381017015
33294.97377914132
7872.3195656579555
9
-14674.600957416102
-0.00012459925560949148
-7685.4142355256245

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03823
14123
24123

end0.0ms

sample538.0ms

Algorithm
intervals
Results
179.0ms1709×body1280valid
115.0ms1325×body640valid
96.0ms3994×body80valid
39.0ms636×body320valid
14.0ms336×body160valid