Details

Time bar (total: 13.9s)

sample113.0ms

Algorithm
intervals
Results
67.0ms76×body10240exit
23.0ms269×body80valid
5.0ms9×body640valid
4.0ms5×body1280valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (log (+ 1 (exp x))) (* x y))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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
17.0ms
(- (log1p (exp x)) (* y x))
0.0ms
(log1p (exp x))

series154.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
82.0ms
(- (log1p (exp x)) (* y x))
72.0ms
(log1p (exp x))

simplify704.0ms

Counts
17 → 40
Calls
17 calls:
Slowest
123.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
96.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
95.0ms
(/ (exp (log1p (exp x))) (exp (* y x)))
71.0ms
(/ (+ 1 (exp x)) (exp (* y x)))
56.0ms
(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))

prune419.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize19.0ms

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))

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--
Counts
2 → 33
Calls
2 calls:
Slowest
5.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0ms
(fma (fma 1/8 x 1/2) x (log 2))

series119.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
70.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
49.0ms
(fma (fma 1/8 x 1/2) x (log 2))

simplify1.6s

Counts
16 → 39
Calls
16 calls:
Slowest
220.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
218.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
203.0ms
(/ (exp (fma (fma 1/8 x 1/2) x (log 2))) (exp (* y x)))
191.0ms
(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* x y)))
153.0ms
(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)))

prune461.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
1 → 11
Calls
1 calls:
Slowest
1.0ms
(fma x (- (fma x 1/8 1/2) y) (log 2))

series63.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
62.0ms
(fma x (- (fma x 1/8 1/2) y) (log 2))

simplify586.0ms

Counts
3 → 14
Calls
3 calls:
Slowest
239.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
236.0ms
(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
110.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune155.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

5.4b
(log1p (- (fma (fma 1/8 x 1/2) x (log 2)) (* y x)))
1.3b
(expm1 (log1p (- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))))
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))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
5×expm1-log1p-u
4×pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×fma-neg prod-diff
2×fma-udef
1×log1p-udef expm1-log1p sub-neg flip3-- diff-log associate--l+ log1p-expm1 flip-- expm1-udef
Counts
4 → 57
Calls
4 calls:
Slowest
5.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
1.0ms
(log1p (- (fma (fma 1/8 x 1/2) x (log 2)) (* y x)))
0.0ms
(expm1 (log1p (- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))))
0.0ms
(fma (fma 1/8 x 1/2) x (log 2))

series549.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(expm1 (log1p (- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))))
218.0ms
(log1p (- (fma (fma 1/8 x 1/2) x (log 2)) (* y x)))
64.0ms
(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
30.0ms
(fma (fma 1/8 x 1/2) x (log 2))

simplify3.4s

Counts
24 → 69
Calls
24 calls:
Slowest
379.0ms
(- (+ (log 1/8) (+ (* 8 (/ (log 2) (pow x 2))) (* 4 (/ 1 x)))) (* 2 (log (/ 1 x))))
323.0ms
(+ (log 2) (+ (* 1/8 (pow x 2)) (+ (* 1/2 (/ (* (log 2) x) (+ (log 2) 1))) (* 1/2 (/ x (+ (log 2) 1))))))
304.0ms
(- (+ (* 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))))
259.0ms
(- (+ (log 1/8) (+ (* 8 (/ (log 2) (pow x 2))) (* 4 (/ 1 x)))) (* 2 (log (/ -1 x))))
252.0ms
(/ (exp (fma (fma 1/8 x 1/2) x (log 2))) (exp (* y x)))

prune864.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes88.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.5s2438×body10240exit
884.0ms8359×body80valid
585.0ms276×body640valid
123.0ms124×body1280valid
67.0ms186×body320valid
29.0ms125×body160valid