Details

Time bar (total: 4.8s)

sample20.0ms

Algorithm
intervals
Results
6.0ms59×body1280valid
4.0ms45×body640valid
3.0ms134×body80valid
1.0ms13×body320valid
0.0ms5×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)))

rewrite146.0ms

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:
7.0ms
(/ x (+ x 1.0))
11.0ms
(/ (+ x 1.0) (- x 1.0))
78.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series210.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
42.0ms
(/ (+ x 1.0) (- x 1.0))
135.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify210.0ms

Algorithm
egg-herbie
Counts
605 → 605
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
0120818366
1368713388
2500113292

prune752.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
15.4b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.4b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
28.8b
(fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0))) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
32×times-frac
25×add-sqr-sqrt add-cube-cbrt
11×distribute-lft-out
10×difference-of-squares
8×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×pow1 cbrt-prod expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
3×flip3-+ flip-+
2×cbrt-undiv cbrt-div flip3-- frac-2neg div-exp clear-num flip-- div-inv
1×pow1/3 fma-udef
Counts
4 → 110
Calls
4 calls:
2.0ms
(cbrt (+ x 1.0))
11.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
11.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms
(fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0))) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (+ x 1.0))
43.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
36.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
330.0ms
(fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0))) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04851187
118191079
250021023

prune426.0ms

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)
0.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series690.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(cbrt x)
187.0ms
(cbrt x)
182.0ms
(cbrt x)
139.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify52.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0123312
1340272
21569258
35002253

prune182.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow (pow 1.0 2) 1/3) x (- (fma 2.0 (pow x 2) (fma 2.0 x 1.0)) (* 1.0 (* (pow x 2) (pow (pow 1.0 2) 1/3)))))
0.0b
(fma 2.0 (pow x 2) (fma 2.0 x 1.0))
13.2b
(- (fma 2.0 (pow x 2) (fma 2.0 x 1.0)) (* 1.0 (* (pow x 2) (pow (pow 1.0 2) 1/3))))
15.4b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
16×add-sqr-sqrt add-cube-cbrt times-frac
6×add-exp-log add-cbrt-cube add-log-exp
5×distribute-lft-out difference-of-squares
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
3×fma-neg prod-diff fma-udef
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp associate--l+ clear-num flip-+ div-inv
Counts
4 → 83
Calls
4 calls:
0.0ms
(fma (pow (pow 1.0 2) 1/3) x (- (fma 2.0 (pow x 2) (fma 2.0 x 1.0)) (* 1.0 (* (pow x 2) (pow (pow 1.0 2) 1/3)))))
0.0ms
(fma 2.0 (pow x 2) (fma 2.0 x 1.0))
3.0ms
(- (fma 2.0 (pow x 2) (fma 2.0 x 1.0)) (* 1.0 (* (pow x 2) (pow (pow 1.0 2) 1/3))))
15.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(fma (pow (pow 1.0 2) 1/3) x (- (fma 2.0 (pow x 2) (fma 2.0 x 1.0)) (* 1.0 (* (pow x 2) (pow (pow 1.0 2) 1/3)))))
21.0ms
(fma 2.0 (pow x 2) (fma 2.0 x 1.0))
88.0ms
(- (fma 2.0 (pow x 2) (fma 2.0 x 1.0)) (* 1.0 (* (pow x 2) (pow (pow 1.0 2) 1/3))))
37.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))

simplify61.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0401964
11760864
25001836

prune399.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 29.9b

bsearch92.0ms

Steps
ItersRangePoint
9
15.365363555117188
8982319.97820102
12712.567100005474
9
-152849402421631.16
-48882.64719934817
-121810688.58492981

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05637
15737
25737

end0.0ms

sample517.0ms

Algorithm
intervals
Results
183.0ms1748×body1280valid
103.0ms1185×body640valid
91.0ms4099×body80valid
39.0ms647×body320valid
13.0ms321×body160valid