Details

Time bar (total: 41.1s)

sample130.0ms

Algorithm
intervals
Results
82.0ms78×body10240exit
25.0ms274×body80valid
5.0ms8×body640valid
4.0ms4×body1280valid
2.0ms5×body320valid
0.0ms1×body160valid

simplify38.0ms

Calls
1 calls:
Slowest
38.0ms
(- (log (+ 1 (exp x))) (* x y))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize22.0ms

Local error

Found 2 expressions with local error:

0.7b
(log1p (exp x))
0.0b
(- (log1p (exp x)) (* y x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
35×add-sqr-sqrt
28×*-un-lft-identity
24×add-cube-cbrt
10×associate-*l*
9×associate-*r*
5×add-log-exp
4×unswap-sqr
3×expm1-log1p-u fma-neg *-commutative
2×pow1 log1p-udef add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- log1p-expm1 flip--
Calls
2 calls:
Slowest
27.0ms
(- (log1p (exp x)) (* y x))
1.0ms
(log1p (exp x))

series136.0ms

Calls
2 calls:
Slowest
70.0ms
(log1p (exp x))
66.0ms
(- (log1p (exp x)) (* y x))

simplify6.9s

Calls
89 calls:
Slowest
244.0ms
(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* (cbrt (* y x)) (* (cbrt (* y x)) (cbrt (* y x))))))
195.0ms
(fma (- (cbrt (* y x))) (* (cbrt (* y x)) (cbrt (* y x))) (* (cbrt (* y x)) (* (cbrt (* y x)) (cbrt (* y x)))))
188.0ms
(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* (* (sqrt y) (sqrt x)) (* (sqrt y) (sqrt x)))))
178.0ms
(fma 1 (log1p (exp x)) (- (* (cbrt (* y x)) (* (cbrt (* y x)) (cbrt (* y x))))))
176.0ms
(fma (- (* (sqrt y) (sqrt x))) (* (sqrt y) (sqrt x)) (* (* (sqrt y) (sqrt x)) (* (sqrt y) (sqrt x))))

prune695.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(log1p (exp x))
0.7b
(log1p (exp x))
0.7b
(* (sqrt (log1p (exp x))) (sqrt (log1p (exp x))))
0.7b
(sqrt (log1p (exp x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
20×pow1
13×*-un-lft-identity add-cube-cbrt
9×sqrt-pow1 pow1/2
8×swap-sqr
6×expm1-log1p-u add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×log1p-udef log1p-expm1
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
25.0ms
(* (sqrt (log1p (exp x))) (sqrt (log1p (exp x))))
2.0ms
(sqrt (log1p (exp x)))
1.0ms
(log1p (exp x))
1.0ms
(log1p (exp x))

series306.0ms

Calls
4 calls:
Slowest
95.0ms
(sqrt (log1p (exp x)))
81.0ms
(* (sqrt (log1p (exp x))) (sqrt (log1p (exp x))))
65.0ms
(log1p (exp x))
64.0ms
(log1p (exp x))

simplify1.5s

Calls
79 calls:
Slowest
438.0ms
(- (+ (* 1/16 (* (sqrt (/ 1 (log 2))) (pow x 2))) (+ (* 1/4 (* (sqrt (/ 1 (log 2))) x)) (sqrt (log 2)))) (* 1/32 (* (sqrt (/ 1 (pow (log 2) 3))) (pow x 2))))
159.0ms
(* (* (* (sqrt (log1p (exp x))) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x)))) (* (* (sqrt (log1p (exp x))) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x)))))
102.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
93.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
85.0ms
(* (* (cbrt (sqrt (log1p (exp x)))) (cbrt (sqrt (log1p (exp x))))) (* (cbrt (sqrt (log1p (exp x)))) (cbrt (sqrt (log1p (exp x))))))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(expm1 (log1p (- (log1p (exp x)) (* y x))))
0.7b
(log1p (exp x))
0.0b
(- (log1p (exp x)) (* y x))
0.0b
(log1p (- (log1p (exp x)) (* y x)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×prod-diff
30×*-un-lft-identity
26×add-cube-cbrt
10×associate-*l*
9×associate-*r*
7×add-log-exp
6×expm1-log1p-u
5×log1p-expm1-u
4×pow1 add-cbrt-cube add-exp-log insert-posit16 unswap-sqr
3×log1p-udef fma-neg *-commutative
2×expm1-log1p diff-log log1p-expm1 distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip-- expm1-udef
Calls
4 calls:
Slowest
10.0ms
(- (log1p (exp x)) (* y x))
1.0ms
(log1p (- (log1p (exp x)) (* y x)))
0.0ms
(expm1 (log1p (- (log1p (exp x)) (* y x))))
0.0ms
(log1p (exp x))

series733.0ms

Calls
4 calls:
Slowest
350.0ms
(expm1 (log1p (- (log1p (exp x)) (* y x))))
226.0ms
(log1p (- (log1p (exp x)) (* y x)))
84.0ms
(- (log1p (exp x)) (* y x))
73.0ms
(log1p (exp x))

simplify9.1s

Calls
98 calls:
Slowest
617.0ms
(fma (- (cbrt (* y x))) (* (cbrt (* y x)) (cbrt (* y x))) (* (cbrt (* y x)) (* (cbrt (* y x)) (cbrt (* y x)))))
490.0ms
(- (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))))))))))
439.0ms
(- (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))))))))))
355.0ms
(+ (log 2) (+ (* 1/8 (pow x 2)) (+ (* 1/2 (/ (* (log 2) x) (+ (log 2) 1))) (* 1/2 (/ x (+ (log 2) 1))))))
291.0ms
(- (+ (* 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))))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
35×add-sqr-sqrt
28×*-un-lft-identity
24×add-cube-cbrt
10×associate-*l*
9×associate-*r*
4×add-log-exp unswap-sqr
3×fma-neg *-commutative
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- diff-log associate--l+ flip--
Calls
2 calls:
Slowest
20.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
1.0ms
(fma (fma 1/8 x 1/2) x (log 2))

series110.0ms

Calls
2 calls:
Slowest
80.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
30.0ms
(fma (fma 1/8 x 1/2) x (log 2))

simplify13.7s

Calls
88 calls:
Slowest
441.0ms
(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* (* y x) 1)))
397.0ms
(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* (* y x) 1)))
383.0ms
(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* (* (sqrt y) x) (sqrt y))))
379.0ms
(fma (sqrt (fma (fma 1/8 x 1/2) x (log 2))) (sqrt (fma (fma 1/8 x 1/2) x (log 2))) (- (* (* (cbrt y) x) (* (cbrt y) (cbrt y)))))
378.0ms
(fma (sqrt (fma (fma 1/8 x 1/2) x (log 2))) (sqrt (fma (fma 1/8 x 1/2) x (log 2))) (- (* (cbrt x) (* y (* (cbrt x) (cbrt x))))))

prune714.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes86.0ms

Accuracy

0% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 0.9b

bsearch2.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.3s2425×body10240exit
1.5s8451×body80valid
240.0ms277×body640valid
126.0ms134×body1280valid
109.0ms204×body320valid
22.0ms98×body160valid