Details

Time bar (total: 1.6m)

sample122.0ms

Algorithm
intervals
Results
69.0ms67×body10240exit
25.0ms271×body80valid
8.0ms14×body640valid
3.0ms3×body1280valid
2.0ms5×body320valid
0.0ms3×body160valid

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
27.0ms
(- (log (+ 1 (exp x))) (* x y))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize23.0ms

Local error

Found 2 expressions with local error:

1.0b
(log1p (exp x))
0.0b
(- (log1p (exp x)) (* y x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u fma-neg prod-diff
2×pow1 log1p-udef add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- log1p-expm1 flip--
Counts
2 → 34
Calls
2 calls:
Slowest
10.0ms
(- (log1p (exp x)) (* y x))
1.0ms
(log1p (exp x))

series152.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
81.0ms
(- (log1p (exp x)) (* y x))
71.0ms
(log1p (exp x))

simplify545.0ms

Counts
17 → 40
Calls
17 calls:
Slowest
109.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
80.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
66.0ms
(/ (exp (log1p (exp x))) (exp (* y x)))
49.0ms
(/ (+ 1 (exp x)) (exp (* y x)))
46.0ms
(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))

prune332.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0b
(fma (fma 1/8 x 1/2) x (log 2))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
3×fma-neg prod-diff
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
2 → 33
Calls
2 calls:
Slowest
11.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0ms
(fma (fma 1/8 x 1/2) x (log 2))

series115.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
61.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
54.0ms
(fma (fma 1/8 x 1/2) x (log 2))

simplify1.6s

Counts
16 → 39
Calls
16 calls:
Slowest
256.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
215.0ms
(/ (exp (fma (fma 1/8 x 1/2) x (log 2))) (exp (* y x)))
206.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
187.0ms
(fma (* (cbrt (fma (fma 1/8 x 1/2) x (log 2))) (cbrt (fma (fma 1/8 x 1/2) x (log 2)))) (cbrt (fma (fma 1/8 x 1/2) x (log 2))) (- (* x y)))
154.0ms
(fma (sqrt (fma (fma 1/8 x 1/2) x (log 2))) (sqrt (fma (fma 1/8 x 1/2) x (log 2))) (- (* x y)))

prune421.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize74.0ms

Local error

Found 4 expressions with local error:

17.1b
(/ (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
1.0b
(log1p (exp x))
1.0b
(log1p (exp x))
1.0b
(log1p (exp x))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
39×times-frac
32×difference-of-squares
30×*-un-lft-identity
24×sqr-pow
22×add-cube-cbrt
13×associate-/l*
8×unpow-prod-down cube-prod
7×expm1-log1p-u
6×add-cbrt-cube add-exp-log
4×pow1 difference-cubes insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
3×log1p-udef associate-/r* log1p-expm1
2×associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-sub div-exp flip-+ div-inv flip--
Counts
4 → 111
Calls
4 calls:
Slowest
184.0ms
(/ (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
1.0ms
(log1p (exp x))
1.0ms
(log1p (exp x))
1.0ms
(log1p (exp x))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(/ (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
74.0ms
(log1p (exp x))
71.0ms
(log1p (exp x))
58.0ms
(log1p (exp x))

simplify25.6s

Counts
114 → 123
Calls
114 calls:
Slowest
678.0ms
(/ (* (* (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))
494.0ms
(/ 1 (* (cbrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (cbrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))))
438.0ms
(/ (pow (log1p (exp x)) 3) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
425.0ms
(+ (* (* (log1p (exp x)) (log1p (exp x))) (* (log1p (exp x)) (log1p (exp x)))) (- (* (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (* (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))
404.0ms
(/ (+ (pow (sqrt (log1p (exp x))) 3) (pow (* y x) (/ 3 2))) 1)

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize89.0ms

Local error

Found 4 expressions with local error:

17.2b
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
17.2b
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
17.2b
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
11.1b
(/ (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
143×add-sqr-sqrt
117×cbrt-prod
72×difference-of-squares
71×*-un-lft-identity
54×associate-/r* sqr-pow
53×add-cube-cbrt
22×cbrt-div
18×unpow-prod-down cube-prod
16×add-exp-log
11×flip3-- flip--
10×add-cbrt-cube
9×difference-cubes distribute-lft-out--
8×associate-/l/
6×cbrt-undiv div-exp
5×associate-/r/
4×expm1-log1p-u frac-times pow1 insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 div-inv
2×associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×clear-num frac-2neg associate-/l*
Counts
4 → 217
Calls
4 calls:
Slowest
171.0ms
(/ (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))))
11.0ms
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
9.0ms
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
6.0ms
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
311.0ms
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
301.0ms
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
268.0ms
(cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
209.0ms
(/ (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))))

simplify56.6s

Counts
237 → 229
Calls
237 calls:
Slowest
1.2s
(/ (* (* (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))) (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))) (/ (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))
847.0ms
(/ (* (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (/ (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))
806.0ms
(/ (* (* (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))) (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))) (* (* (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))))
720.0ms
(/ (* (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (* (* (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))))
714.0ms
(/ (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (/ 1 (cbrt (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))))))

prune4.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.6b

regimes140.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.9s2429×body10240exit
866.0ms8434×body80valid
147.0ms265×body640valid
116.0ms120×body1280valid
71.0ms191×body320valid
23.0ms104×body160valid