Details

Time bar (total: 5.1s)

sample41.0ms

Algorithm
intervals
Results
13.0ms59×body1280valid
11.0ms45×body640valid
8.0ms134×body80valid
2.0ms13×body320valid
1.0ms5×body160valid

simplify22.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 28.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
1.3b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
11.0ms
(/ (+ x 1.0) (- x 1.0))
78.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series203.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ x (+ x 1.0))
36.0ms
(/ (+ x 1.0) (- x 1.0))
131.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify197.0ms

Algorithm
egg-herbie
Counts
605 → 605
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
0120818366
1368713388
2500113292

prune728.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
29.0b
(fma (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0))) (/ (- (pow (cbrt (+ x 1.0)) 3)) (- x 1.0)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0))) (/ (- (pow (cbrt (+ x 1.0)) 3)) (- x 1.0)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(cbrt x)
177.0ms
(cbrt x)
171.0ms
(cbrt x)
112.0ms
(fma (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0))) (/ (- (pow (cbrt (+ x 1.0)) 3)) (- x 1.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0126324
1366281
21554267
35001265

prune233.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
28.9b
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series681.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(cbrt x)
178.0ms
(cbrt x)
178.0ms
(cbrt x)
136.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify53.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0123312
1340272
21569258
35002253

prune172.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(- (/ x (+ x 1.0)) (- (- (* 2.0 (pow x 2))) (fma 2.0 x 1.0)))
0.0b
(- (- (* 2.0 (pow x 2))) (fma 2.0 x 1.0))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
140×add-sqr-sqrt
126×prod-diff
97×add-cube-cbrt
85×times-frac
24×fma-neg
22×distribute-lft-out distribute-lft-out--
21×associate--r+ difference-of-squares
15×add-log-exp
14×associate-/r/
7×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in flip3-+ diff-log flip-+ div-inv
5×add-exp-log add-cbrt-cube
4×associate-/r*
3×pow1 expm1-log1p-u sub-neg flip3-- flip-- log1p-expm1-u associate-/l*
2×neg-log frac-sub
1×cbrt-undiv associate--l- neg-sub0 frac-2neg div-exp clear-num fma-udef associate--r-
Counts
3 → 229
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
56.0ms
(- (/ x (+ x 1.0)) (- (- (* 2.0 (pow x 2))) (fma 2.0 x 1.0)))
6.0ms
(- (- (* 2.0 (pow x 2))) (fma 2.0 x 1.0))

series104.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
43.0ms
(- (/ x (+ x 1.0)) (- (- (* 2.0 (pow x 2))) (fma 2.0 x 1.0)))
27.0ms
(- (- (* 2.0 (pow x 2))) (fma 2.0 x 1.0))

simplify107.0ms

Algorithm
egg-herbie
Counts
238 → 238
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06955135
124663142
250013050

prune400.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.9b

bsearch98.0ms

Steps
ItersRangePoint
9
15.365363555117188
8982319.97820102
12712.567100005474
9
-152849402421631.16
-48882.64719934817
-92822810.0135693

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04626
14926
24926

end0.0ms

sample1.1s

Algorithm
intervals
Results
395.0ms1748×body1280valid
252.0ms4099×body80valid
212.0ms1185×body640valid
94.0ms647×body320valid
32.0ms321×body160valid