Details

Time bar (total: 8.8s)

sample100.0ms

Algorithm
intervals
Results
27.0ms69×body1280valid
26.0ms76×body10240exit
19.0ms56×body640valid
12.0ms91×body80valid
5.0ms24×body320valid
2.0ms17×body160valid

simplify13.0ms

Calls
1 calls:
Slowest
13.0ms
(/ (exp x) (- (exp x) 1))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize16.0ms

Local error

Found 2 expressions with local error:

4.1b
(- (exp x) 1)
0.5b
(/ (exp x) (- (exp x) 1))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×*-un-lft-identity times-frac add-cube-cbrt
5×difference-of-sqr-1
4×associate-/r* add-cbrt-cube
3×fma-neg add-exp-log associate-/l*
2×expm1-log1p-u pow1 flip3-- associate-/r/ insert-posit16 log1p-expm1-u flip-- add-log-exp
1×cbrt-undiv expm1-def clear-num sub-neg frac-2neg div-exp div-inv
Calls
2 calls:
Slowest
14.0ms
(/ (exp x) (- (exp x) 1))
8.0ms
(- (exp x) 1)

series52.0ms

Calls
2 calls:
Slowest
36.0ms
(/ (exp x) (- (exp x) 1))
16.0ms
(- (exp x) 1)

simplify1.3s

Calls
43 calls:
Slowest
391.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
189.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
77.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
65.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
37.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (sqrt (exp x)) 1))

prune460.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 1 expressions with local error:

0.5b
(/ (exp x) (expm1 x))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube associate-/l*
2×add-exp-log
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Calls
1 calls:
Slowest
6.0ms
(/ (exp x) (expm1 x))

series25.0ms

Calls
1 calls:
Slowest
25.0ms
(/ (exp x) (expm1 x))

simplify485.0ms

Calls
28 calls:
Slowest
157.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
55.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
45.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
30.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) 1)
27.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (sqrt (expm1 x)))

prune242.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma x 1/12 (+ 1/2 (/ 1 x)))

rewrite0.0ms

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
Calls
1 calls:
Slowest
0.0ms
(fma x 1/12 (+ 1/2 (/ 1 x)))

series10.0ms

Calls
1 calls:
Slowest
10.0ms
(fma x 1/12 (+ 1/2 (/ 1 x)))

simplify98.0ms

Calls
3 calls:
Slowest
48.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
25.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
24.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune66.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 3 expressions with local error:

1.8b
(expm1 (log1p (fma x 1/12 (+ 1/2 (/ 1 x)))))
0.1b
(fma x 1/12 (+ 1/2 (/ 1 x)))
0.0b
(log1p (fma x 1/12 (+ 1/2 (/ 1 x))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
4×expm1-log1p-u
3×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 fma-udef expm1-udef
Calls
3 calls:
Slowest
0.0ms
(expm1 (log1p (fma x 1/12 (+ 1/2 (/ 1 x)))))
0.0ms
(log1p (fma x 1/12 (+ 1/2 (/ 1 x))))
0.0ms
(fma x 1/12 (+ 1/2 (/ 1 x)))

series71.0ms

Calls
3 calls:
Slowest
40.0ms
(expm1 (log1p (fma x 1/12 (+ 1/2 (/ 1 x)))))
24.0ms
(log1p (fma x 1/12 (+ 1/2 (/ 1 x))))
7.0ms
(fma x 1/12 (+ 1/2 (/ 1 x)))

simplify2.0s

Calls
10 calls:
Slowest
540.0ms
(- (+ (* 18 (/ (exp (- (log 1/12) (log (/ 1 x)))) x)) (+ (exp (- (log 1/12) (log (/ 1 x)))) (* 12 (/ (exp (- (log 1/12) (log (/ 1 x)))) (pow x 2))))) 1)
377.0ms
(- (+ (* 18 (/ 1 x)) (log 1/12)) (+ (log (/ 1 x)) (* 150 (/ 1 (pow x 2)))))
282.0ms
(- (+ (* 3/2 (* x (exp (- (log x))))) (+ (* 1/12 (* (pow x 2) (exp (- (log x))))) (exp (- (log x))))) 1)
250.0ms
(- (+ (* 18 (/ (exp (- (log -1/12) (log (/ -1 x)))) x)) (+ (* 12 (/ (exp (- (log -1/12) (log (/ -1 x)))) (pow x 2))) (exp (- (log -1/12) (log (/ -1 x)))))) 1)
233.0ms
(- (+ (log -1/12) (* 18 (/ 1 x))) (+ (log (/ -1 x)) (* 150 (/ 1 (pow x 2)))))

prune359.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes52.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2561×body10240exit
1.0s2267×body1280valid
557.0ms1646×body640valid
191.0ms2844×body80valid
160.0ms832×body320valid
49.0ms412×body160valid