Details

Time bar (total: 31.3s)

sample97.0ms

Algorithm
intervals
Results
56.0ms83×body10240exit
18.0ms266×body80valid
5.0ms8×body1280valid
4.0ms11×body640valid
1.0ms4×body320valid
1.0ms4×body160valid

simplify40.0ms

Calls
1 calls:
Slowest
40.0ms
(- (log (+ 1 (exp x))) (* x y))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b
(log1p (exp x))
0.0b
(- (log1p (exp x)) (* y x))

rewrite9.0ms

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--
Calls
2 calls:
Slowest
8.0ms
(- (log1p (exp x)) (* y x))
1.0ms
(log1p (exp x))

series128.0ms

Calls
2 calls:
Slowest
66.0ms
(- (log1p (exp x)) (* y x))
62.0ms
(log1p (exp x))

simplify429.0ms

Calls
17 calls:
Slowest
110.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
65.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
39.0ms
(/ (exp (log1p (exp x))) (exp (* y x)))
35.0ms
(fma 1 (log1p (exp x)) (- (* x y)))
30.0ms
(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* x y)))

prune253.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.9b
(expm1 (log1p (- (log1p (exp x)) (* y x))))
0.2b
(log1p (exp x))
0.0b
(log1p (- (log1p (exp x)) (* y x)))
0.0b
(- (log1p (exp x)) (* y x))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×log1p-udef fma-neg prod-diff
2×diff-log log1p-expm1
1×expm1-log1p sub-neg flip3-- flip-- expm1-udef
Calls
4 calls:
Slowest
7.0ms
(- (log1p (exp x)) (* y x))
0.0ms
(log1p (- (log1p (exp x)) (* y x)))
0.0ms
(log1p (exp x))
0.0ms
(expm1 (log1p (- (log1p (exp x)) (* y x))))

series691.0ms

Calls
4 calls:
Slowest
301.0ms
(expm1 (log1p (- (log1p (exp x)) (* y x))))
265.0ms
(log1p (- (log1p (exp x)) (* y x)))
68.0ms
(- (log1p (exp x)) (* y x))
57.0ms
(log1p (exp x))

simplify2.3s

Calls
25 calls:
Slowest
612.0ms
(- (log -1) (+ (log (/ 1 x)) (+ (/ 1 (* x y)) (+ (log (/ 1 y)) (+ (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))) (+ (/ (log (+ (exp x) 1)) (* x y)) (+ (* 1/2 (/ (pow (log (+ (exp x) 1)) 2) (* (pow x 2) (pow y 2)))) (/ (log (+ (exp x) 1)) (* (pow x 2) (pow y 2))))))))))
483.0ms
(- (log -1) (+ (* 1/2 (/ (pow (log (+ (exp x) 1)) 2) (* (pow x 2) (pow y 2)))) (+ (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))) (+ (/ (log (+ (exp x) 1)) (* x y)) (+ (log (/ -1 x)) (+ (log (/ -1 y)) (+ (/ 1 (* x y)) (/ (log (+ (exp x) 1)) (* (pow x 2) (pow y 2))))))))))
293.0ms
(+ (log 2) (+ (* 1/8 (pow x 2)) (+ (* 1/2 (/ (* (log 2) x) (+ (log 2) 1))) (* 1/2 (/ x (+ (log 2) 1))))))
207.0ms
(- (+ (* 1/8 (/ (pow x 2) (+ (log 2) 1))) (+ (log (+ (log 2) 1)) (* 1/2 (/ x (+ (log 2) 1))))) (* 1/8 (/ (pow x 2) (pow (+ (log 2) 1) 2))))
141.0ms
(- (exp (- (log -1) (+ (log (/ 1 x)) (log (/ 1 y))))) (+ (/ (* (log (+ (exp x) 1)) (exp (- (log -1) (+ (log (/ 1 x)) (log (/ 1 y)))))) (* x y)) (+ (/ (exp (- (log -1) (+ (log (/ 1 x)) (log (/ 1 y))))) (* x y)) 1)))

prune685.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

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--
Calls
2 calls:
Slowest
4.0ms
(- (fma x (fma 1/8 x 1/2) (log 2)) (* y x))
0.0ms
(fma x (fma 1/8 x 1/2) (log 2))

series111.0ms

Calls
2 calls:
Slowest
60.0ms
(- (fma x (fma 1/8 x 1/2) (log 2)) (* y x))
50.0ms
(fma x (fma 1/8 x 1/2) (log 2))

simplify1.4s

Calls
16 calls:
Slowest
217.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
178.0ms
(fma (* (cbrt (fma x (fma 1/8 x 1/2) (log 2))) (cbrt (fma x (fma 1/8 x 1/2) (log 2)))) (cbrt (fma x (fma 1/8 x 1/2) (log 2))) (- (* x y)))
176.0ms
(/ (exp (fma x (fma 1/8 x 1/2) (log 2))) (exp (* y x)))
175.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
149.0ms
(fma 1 (fma x (fma 1/8 x 1/2) (log 2)) (- (* x y)))

prune374.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

11.5b
(/ (/ -1 x) (* (/ -1 x) (/ -1 y)))
11.5b
(/ (/ -1 x) (* (/ -1 x) (/ -1 y)))
2.9b
(+ (- (/ -1 (* (/ -1 x) (/ -1 y))) (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y))) -1)
0.9b
(/ -1 (* (/ -1 x) (/ -1 y)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
23×associate-+l+
22×add-sqr-sqrt
21×*-un-lft-identity prod-diff
19×add-cube-cbrt
18×associate-/r/
14×add-cbrt-cube add-exp-log
10×div-inv
8×times-frac associate-/l*
6×frac-times associate-*l/ associate-*r/
5×fma-def
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num associate-/r* frac-2neg
2×prod-exp cbrt-unprod associate-/l/
1×+-commutative difference-of-sqr--1 sub-neg flip3-+ associate-+l- flip-+ distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
40.0ms
(+ (- (/ -1 (* (/ -1 x) (/ -1 y))) (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y))) -1)
5.0ms
(/ (/ -1 x) (* (/ -1 x) (/ -1 y)))
5.0ms
(/ (/ -1 x) (* (/ -1 x) (/ -1 y)))
1.0ms
(/ -1 (* (/ -1 x) (/ -1 y)))

series118.0ms

Calls
4 calls:
Slowest
70.0ms
(+ (- (/ -1 (* (/ -1 x) (/ -1 y))) (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y))) -1)
23.0ms
(/ -1 (* (/ -1 x) (/ -1 y)))
14.0ms
(/ (/ -1 x) (* (/ -1 x) (/ -1 y)))
10.0ms
(/ (/ -1 x) (* (/ -1 x) (/ -1 y)))

simplify18.8s

Calls
74 calls:
Slowest
924.0ms
(fma (/ -1 (* -1 (/ -1 y))) x (- (* (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y)) 1)))
897.0ms
(sqrt (- (/ -1 (* (/ -1 x) (/ -1 y))) (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y))))
734.0ms
(fma (/ -1 (* (/ -1 x) -1)) y (- (* (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y)) 1)))
732.0ms
(fma (* (cbrt (/ -1 (* (/ -1 x) (/ -1 y)))) (cbrt (/ -1 (* (/ -1 x) (/ -1 y))))) (cbrt (/ -1 (* (/ -1 x) (/ -1 y)))) (- (* (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y)) 1)))
687.0ms
(fma 1 (/ -1 (* (/ -1 x) (/ -1 y))) (- (* (fma (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y) (log1p (exp x)) (/ (/ (/ -1 x) (* (/ -1 x) (/ -1 y))) y)) 1)))

prune1.4s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes72.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.6s2417×body10240exit
1.0s8443×body80valid
150.0ms277×body640valid
145.0ms128×body1280valid
63.0ms184×body320valid
22.0ms105×body160valid