Details

Time bar (total: 30.4s)

sample127.0ms

Algorithm
intervals
Results
56.0ms71×body10240exit
43.0ms266×body80valid
6.0ms5×body1280valid
4.0ms11×body320valid
2.0ms5×body640valid
2.0ms6×body160valid

simplify31.0ms

Calls
1 calls:
Slowest
31.0ms
(- (log (+ 1 (exp x))) (* x y))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize13.0ms

Local error

Found 2 expressions with local error:

1.0b
(log (+ 1 (exp x)))
0.0b
(- (log (+ 1 (exp x))) (* x y))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt log-prod *-un-lft-identity add-cube-cbrt
5×pow1
4×log-div fma-neg prod-diff
3×associate--l+ add-exp-log log-pow add-log-exp
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u
1×sub-neg log1p-def flip3-- diff-log rem-log-exp flip--
Calls
2 calls:
Slowest
6.0ms
(- (log (+ 1 (exp x))) (* x y))
1.0ms
(log (+ 1 (exp x)))

series103.0ms

Calls
2 calls:
Slowest
66.0ms
(log (+ 1 (exp x)))
37.0ms
(- (log (+ 1 (exp x))) (* x y))

simplify767.0ms

Calls
29 calls:
Slowest
88.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
82.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
53.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
52.0ms
(fma (* (cbrt (log (+ 1 (exp x)))) (cbrt (log (+ 1 (exp x))))) (cbrt (log (+ 1 (exp x)))) (- (* y x)))
38.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))

prune462.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

1.7b
(log (sqrt (+ 1 (exp x))))
1.7b
(log (sqrt (+ 1 (exp x))))
0.0b
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
32×log-pow
29×*-un-lft-identity
25×pow1
21×fma-neg prod-diff
17×add-sqr-sqrt add-cube-cbrt
14×distribute-rgt-out distribute-lft-out
12×log-prod
10×pow1/2
8×log-div sqrt-div
6×sqrt-prod add-log-exp
5×add-exp-log
4×associate--l- distribute-lft1-in flip3-+ distribute-rgt1-in flip-+
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
2×associate-+r- diff-log rem-log-exp associate-+l-
1×sum-log sub-neg flip3-- associate--l+ flip--
Calls
3 calls:
Slowest
55.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
4.0ms
(log (sqrt (+ 1 (exp x))))
4.0ms
(log (sqrt (+ 1 (exp x))))

series271.0ms

Calls
3 calls:
Slowest
98.0ms
(log (sqrt (+ 1 (exp x))))
87.0ms
(- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y))
86.0ms
(log (sqrt (+ 1 (exp x))))

simplify3.2s

Calls
91 calls:
Slowest
306.0ms
(- (+ (* 1/2 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (* 2 (log (sqrt 2))) (/ x (pow (sqrt 2) 2)))) (* 1/2 (/ (pow x 2) (pow (sqrt 2) 4))))
179.0ms
(- (+ (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (log (sqrt 2)) (* 1/2 (/ x (pow (sqrt 2) 2))))) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 4))))
170.0ms
(- (+ (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))) (+ (log (sqrt 2)) (* 1/2 (/ x (pow (sqrt 2) 2))))) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 4))))
121.0ms
(fma (* (cbrt (log (sqrt (+ 1 (exp x))))) (cbrt (log (sqrt (+ 1 (exp x)))))) (+ (cbrt (log (sqrt (+ 1 (exp x))))) (cbrt (log (sqrt (+ 1 (exp x)))))) (- (* y x)))
113.0ms
(fma (cbrt (log (sqrt (+ 1 (exp x))))) (+ (* (cbrt (log (sqrt (+ 1 (exp x))))) (cbrt (log (sqrt (+ 1 (exp x)))))) (* (cbrt (log (sqrt (+ 1 (exp x))))) (cbrt (log (sqrt (+ 1 (exp x))))))) (- (* y x)))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

15.1b
(/ (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))
1.0b
(log (+ 1 (exp x)))
1.0b
(log (+ 1 (exp x)))
1.0b
(log (+ 1 (exp x)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
28×*-un-lft-identity
24×times-frac
20×add-cube-cbrt
12×difference-of-squares
9×log-prod add-exp-log
8×associate-/l*
7×pow1
6×log-div add-cbrt-cube
4×expm1-log1p-u difference-cubes unpow-prod-down flip3-+ cube-prod flip-+ insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
3×associate-/r* log1p-def rem-log-exp log-pow
2×associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp div-inv flip--
Calls
4 calls:
Slowest
76.0ms
(/ (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))
2.0ms
(log (+ 1 (exp x)))
2.0ms
(log (+ 1 (exp x)))
2.0ms
(log (+ 1 (exp x)))

series376.0ms

Calls
4 calls:
Slowest
145.0ms
(/ (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))
78.0ms
(log (+ 1 (exp x)))
78.0ms
(log (+ 1 (exp x)))
74.0ms
(log (+ 1 (exp x)))

simplify15.7s

Calls
97 calls:
Slowest
644.0ms
(- (* (pow (log (+ 1 (exp x))) 3) (pow (log (+ 1 (exp x))) 3)) (* (pow (* x y) 3) (pow (* x y) 3)))
644.0ms
(/ (* (* (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (* (* (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))))
612.0ms
(/ (+ (pow (sqrt (log (+ 1 (exp x)))) 3) (sqrt (pow (* x y) 3))) (* (cbrt (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))) (cbrt (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))))
390.0ms
(/ (* (cbrt (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3))) (cbrt (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)))) 1)
384.0ms
(- (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))

prune1.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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
9.0ms
(- (fma x (fma 1/8 x 1/2) (log 2)) (* x y))
0.0ms
(fma x (fma 1/8 x 1/2) (log 2))

series56.0ms

Calls
2 calls:
Slowest
40.0ms
(- (fma x (fma 1/8 x 1/2) (log 2)) (* x y))
16.0ms
(fma x (fma 1/8 x 1/2) (log 2))

simplify1.5s

Calls
16 calls:
Slowest
249.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
194.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
156.0ms
(fma 1 (fma x (fma 1/8 x 1/2) (log 2)) (- (* y x)))
150.0ms
(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))) (- (* y x)))
147.0ms
(/ (exp (fma x (fma 1/8 x 1/2) (log 2))) (exp (* x y)))

prune445.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes100.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 1.0b

bsearch3.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.2s2427×body10240exit
1.4s8356×body80valid
145.0ms123×body1280valid
138.0ms251×body640valid
66.0ms189×body320valid
24.0ms115×body160valid