Details

Time bar (total: 38.5s)

sample122.0ms

Algorithm
intervals
Results
71.0ms73×body10240exit
24.0ms268×body80valid
8.0ms8×body1280valid
3.0ms5×body640valid
2.0ms6×body320valid
1.0ms2×body160valid

simplify43.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
42.0ms
(- (log (+ 1 (exp x))) (* x y))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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
83.0ms
(log1p (exp x))
69.0ms
(- (log1p (exp x)) (* y x))

simplify620.0ms

Counts
17 → 40
Calls
17 calls:
Slowest
116.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
116.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
81.0ms
(/ (exp (log1p (exp x))) (exp (* y x)))
69.0ms
(/ (+ 1 (exp x)) (exp (* y x)))
65.0ms
(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))

prune360.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize49.0ms

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
23×pow1
14×associate-*l/
13×cbrt-prod
12×pow1/3
11×add-sqr-sqrt
9×*-un-lft-identity add-exp-log pow-prod-up add-cube-cbrt
8×associate-*r/
6×pow-plus associate-*r*
5×add-cbrt-cube pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp pow-sqr cbrt-unprod
2×pow2 unswap-sqr
1×associate-*l* pow3 *-commutative
Counts
4 → 112
Calls
4 calls:
Slowest
63.0ms
(* (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))) (cbrt (- (log1p (exp x)) (* y x))))
5.0ms
(cbrt (- (log1p (exp x)) (* y x)))
3.0ms
(cbrt (- (log1p (exp x)) (* y x)))
2.0ms
(cbrt (- (log1p (exp x)) (* y x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
345.0ms
(cbrt (- (log1p (exp x)) (* y x)))
327.0ms
(cbrt (- (log1p (exp x)) (* y x)))
322.0ms
(cbrt (- (log1p (exp x)) (* y x)))
58.0ms
(* (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))) (cbrt (- (log1p (exp x)) (* y x))))

simplify17.0s

Counts
104 → 124
Calls
104 calls:
Slowest
796.0ms
(* (* (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (cbrt (- (log1p (exp x)) (* y x)))) (cbrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))
556.0ms
(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
526.0ms
(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
477.0ms
(- (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))))))
466.0ms
(* (* (* (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))) (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x))))) (- (log1p (exp x)) (* y x)))

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize59.0ms

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
Counts
4 → 64
Calls
4 calls:
Slowest
5.0ms
(cbrt (- (log1p (exp x)) (* y x)))
3.0ms
(cbrt (- (log1p (exp x)) (* y x)))
3.0ms
(cbrt (- (log1p (exp x)) (* y x)))
2.0ms
(cbrt (- (log1p (exp x)) (* y x)))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
436.0ms
(cbrt (- (log1p (exp x)) (* y x)))
407.0ms
(cbrt (- (log1p (exp x)) (* y x)))
369.0ms
(cbrt (- (log1p (exp x)) (* y x)))
361.0ms
(cbrt (- (log1p (exp x)) (* y x)))

simplify8.1s

Counts
32 → 76
Calls
32 calls:
Slowest
568.0ms
(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
542.0ms
(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
534.0ms
(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
504.0ms
(- (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 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)))) (* 1/3 (/ (* (log (+ (exp x) 1)) (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))))) (* x y)))))
485.0ms
(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))

prune956.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

localize18.0ms

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))

rewrite11.0ms

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
10.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0ms
(fma (fma 1/8 x 1/2) x (log 2))

series95.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
48.0ms
(fma (fma 1/8 x 1/2) x (log 2))
47.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))

simplify1.8s

Counts
16 → 39
Calls
16 calls:
Slowest
285.0ms
(/ (exp (fma (fma 1/8 x 1/2) x (log 2))) (exp (* y x)))
268.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
235.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
189.0ms
(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* x y)))
163.0ms
(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)))

prune445.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes144.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.7s2352×body10240exit
977.0ms8347×body80valid
146.0ms261×body640valid
137.0ms144×body1280valid
72.0ms194×body320valid
23.0ms112×body160valid