Details

Time bar (total: 1.2m)

sample89.0ms

Algorithm
intervals
Results
47.0ms72×body10240exit
20.0ms271×body80valid
6.0ms7×body1280valid
4.0ms10×body640valid
1.0ms5×body160valid
0.0ms1×body320valid

simplify41.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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
5.0ms
(- (log1p (exp x)) (* y x))
0.0ms
(log1p (exp x))

series124.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(log1p (exp x))
59.0ms
(- (log1p (exp x)) (* y x))

simplify2.2s

Counts
44 → 40
Calls
44 calls:
Slowest
507.0ms
(- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))
324.0ms
(- (pow (log1p (exp x)) 3) (pow (* y x) 3))
156.0ms
(* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x)))
128.0ms
(+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))
99.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune362.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))
0.5b
(sqrt (- (log1p (exp x)) (* y x)))
0.5b
(sqrt (- (log1p (exp x)) (* y x)))
0.0b
(- (log1p (exp x)) (* y x))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×*-un-lft-identity sqrt-div add-cube-cbrt
10×sqrt-pow1 pow1/2
9×flip3-- flip--
8×swap-sqr
7×add-log-exp
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u unswap-sqr
3×fma-neg prod-diff pow-prod-down pow-sqr
2×rem-sqrt-square diff-log associate-*l/ associate-*r/
1×pow2 log1p-udef sub-neg rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 118
Calls
4 calls:
Slowest
27.0ms
(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))
10.0ms
(- (log1p (exp x)) (* y x))
5.0ms
(sqrt (- (log1p (exp x)) (* y x)))
5.0ms
(sqrt (- (log1p (exp x)) (* y x)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(sqrt (- (log1p (exp x)) (* y x)))
160.0ms
(sqrt (- (log1p (exp x)) (* y x)))
87.0ms
(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))
60.0ms
(- (log1p (exp x)) (* y x))

simplify12.4s

Counts
154 → 130
Calls
154 calls:
Slowest
526.0ms
(- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))
516.0ms
(sqrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
467.0ms
(- (+ (* 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))))
454.0ms
(sqrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
442.0ms
(* (sqrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))) (sqrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.1b
(cbrt (- (log1p (exp x)) (* y x)))
1.1b
(cbrt (- (log1p (exp x)) (* y x)))
1.1b
(cbrt (- (log1p (exp x)) (* y x)))
0.6b
(* (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x)))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
180×sqrt-div
168×cbrt-div
136×frac-times
111×flip3-- flip--
44×associate-*l/ associate-*r/
18×pow1
16×sqrt-pow1
15×pow1/3
10×pow-prod-down pow-prod-up
9×cbrt-prod add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1/2
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod
2×sqrt-unprod pow-sqr
1×associate-*r* *-commutative sqrt-prod
Counts
4 → 158
Calls
4 calls:
Slowest
116.0ms
(* (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x)))))
3.0ms
(cbrt (- (log1p (exp x)) (* y x)))
2.0ms
(cbrt (- (log1p (exp x)) (* y x)))
2.0ms
(cbrt (- (log1p (exp x)) (* y x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
394.0ms
(cbrt (- (log1p (exp x)) (* y x)))
370.0ms
(cbrt (- (log1p (exp x)) (* y x)))
351.0ms
(cbrt (- (log1p (exp x)) (* y x)))
74.0ms
(* (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x)))))

simplify43.7s

Counts
245 → 170
Calls
245 calls:
Slowest
978.0ms
(* (* (* (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))))) (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))))) (* (* (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x)))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x))))))
864.0ms
(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
605.0ms
(* (* (* (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x))))) (* (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x)))))) (* (sqrt (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (log1p (exp x)) (* y x)))) (sqrt (- (log1p (exp x)) (* y x))))))
522.0ms
(- (exp (* 1/3 (- (log -1) (+ (log (/ 1 x)) (log (/ 1 y)))))) (+ (* 1/3 (/ (* (log (+ (exp x) 1)) (exp (* 1/3 (- (log -1) (+ (log (/ 1 x)) (log (/ 1 y))))))) (* x y))) (* 1/9 (/ (* (pow (log (+ (exp x) 1)) 2) (exp (* 1/3 (- (log -1) (+ (log (/ 1 x)) (log (/ 1 y))))))) (* (pow x 2) (pow y 2))))))
514.0ms
(* (sqrt (* (cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x)))) (cbrt (- (log1p (exp x)) (* y x))))) (* (sqrt (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))) (sqrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))))

prune2.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes90.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.7s2427×body10240exit
845.0ms8355×body80valid
158.0ms254×body640valid
120.0ms132×body1280valid
67.0ms199×body320valid
24.0ms116×body160valid