Details

Time bar (total: 6.8s)

sample39.0ms

Algorithm
intervals
Results
7.0ms186×body80valid
5.0ms31×body640valid
3.0ms6×body320nan
3.0ms15×body1280valid
3.0ms110×body80nan
2.0ms15×body1280nan
2.0ms19×body320valid
1.0ms7×body640nan
0.0ms5×body160valid
0.0ms4×body160nan

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0196
1296
2416
3606
4786
5946
61096
71396
82146
92796
102796

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x y) (- 1.0 y))
1.6b
(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
169×*-un-lft-identity
102×times-frac
93×prod-diff
81×add-cube-cbrt
46×difference-of-squares
44×distribute-lft-out--
8×associate-/r/
7×flip3-- flip--
6×add-exp-log log-prod
5×associate-/r* add-cbrt-cube associate-/l* add-log-exp
4×pow1 div-inv
3×expm1-log1p-u fma-neg log1p-expm1-u
2×log-div div-sub associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num log-pow associate--r-
Counts
3 → 187
Calls
3 calls:
12.0ms
(/ (- x y) (- 1.0 y))
31.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
30.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series374.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ (- x y) (- 1.0 y))
248.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
89.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify94.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
08473956
127662899
250012689

prune339.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- 1.0 y))
0.3b
(cbrt (- 1.0 y))
3.1b
(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
11.0b
(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
540×times-frac
485×add-sqr-sqrt
461×*-un-lft-identity
426×prod-diff
303×add-cube-cbrt
298×cbrt-div
269×cbrt-prod
198×associate-/r/
151×flip3-- flip--
96×frac-times
87×difference-of-squares
79×distribute-lft-out--
48×associate-*r/ associate-*l/
27×div-inv
9×log-prod
6×add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg
2×log-div pow1/3 div-sub
1×sub-neg diff-log rem-log-exp log-pow associate--r-
Counts
4 → 506
Calls
4 calls:
2.0ms
(cbrt (- 1.0 y))
4.0ms
(cbrt (- 1.0 y))
93.0ms
(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
85.0ms
(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (- 1.0 y))
86.0ms
(cbrt (- 1.0 y))
83.0ms
(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
50.0ms
(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify293.0ms

Algorithm
egg-herbie
Counts
518 → 518
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
0314832097
1500231058

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- x y))
3.1b
(log (+ (fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))) (fma (- (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))))
10.3b
(fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))))))
61.8b
(fma (- (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-exp-log cbrt-prod
4×expm1-log1p-u log-prod add-cbrt-cube log1p-expm1-u add-log-exp
2×log-div cbrt-div fma-udef
1×flip3-- flip3-+ pow1/3 rem-log-exp log-pow flip-- flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 54
Calls
4 calls:
2.0ms
(cbrt (- x y))
2.0ms
(log (+ (fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))) (fma (- (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))))
0.0ms
(fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))))))
0.0ms
(fma (- (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (- x y))
385.0ms
(log (+ (fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))) (fma (- (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))))
86.0ms
(fma (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0) (- (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))))))
185.0ms
(fma (- (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y))))) (* (/ (/ (cbrt (- x y)) (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))) (/ (/ (* (cbrt (- x y)) (cbrt (- x y))) (cbrt (- 1.0 y))) (* (cbrt (cbrt (- 1.0 y))) (cbrt (cbrt (- 1.0 y)))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04033470
111343174
250013111

prune382.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b
(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b
(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b
(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
152×add-sqr-sqrt
140×*-un-lft-identity
93×prod-diff
79×times-frac
72×add-cube-cbrt
38×difference-of-squares
34×distribute-lft-out--
18×log-prod
7×pow1 add-exp-log flip3-- flip--
6×log-div associate-/r/ add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg rem-log-exp log-pow div-inv
1×sub-neg diff-log div-sub associate--r-
Counts
4 → 171
Calls
4 calls:
28.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
29.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))
31.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))
29.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))
83.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))
84.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify84.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07434004
123232916
250012680

prune417.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes153.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.0b

bsearch132.0ms

Steps
ItersRangePoint
11
0.004380743253548005
1.4777983484669568e+17
31980879.898730252
8
-852931462.9897757
-1008652.5027185878
-96388745.0459895

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03823
13823

end0.0ms

sample1.1s

Algorithm
intervals
Results
248.0ms5672×body80valid
164.0ms819×body1280valid
115.0ms804×body640valid
100.0ms3814×body80nan
58.0ms369×body1280nan
51.0ms494×body320valid
42.0ms355×body640nan
19.0ms212×body320nan
15.0ms211×body160valid
6.0ms115×body160nan