Details

Time bar (total: 42.2s)

sample103.0ms

Algorithm
intervals
Results
43.0ms82×body1280valid
27.0ms78×body10240exit
9.0ms32×body640valid
6.0ms102×body80valid
6.0ms26×body320valid
2.0ms14×body160valid

simplify17.0ms

Calls
1 calls:
Slowest
17.0ms
(/ (exp x) (- (exp x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize7.0ms

Local error

Found 2 expressions with local error:

4.1b
(- (exp x) 1)
0.0b
(/ (exp x) (- (exp x) 1))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
36×*-un-lft-identity
21×times-frac add-cube-cbrt
10×difference-of-squares
9×prod-diff
7×associate-/r*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-log-exp
3×fma-neg add-exp-log associate-/l*
2×expm1-log1p-u pow1 flip3-- associate-/r/ insert-posit16 log1p-expm1-u flip--
1×cbrt-undiv expm1-def clear-num sub-neg frac-2neg diff-log div-exp div-inv
Calls
2 calls:
Slowest
18.0ms
(/ (exp x) (- (exp x) 1))
9.0ms
(- (exp x) 1)

series58.0ms

Calls
2 calls:
Slowest
32.0ms
(- (exp x) 1)
26.0ms
(/ (exp x) (- (exp x) 1))

simplify2.4s

Calls
88 calls:
Slowest
264.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
254.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
87.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (sqrt 1) (sqrt 1))))
79.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
76.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (sqrt 1) (sqrt 1))))

prune586.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (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))

series38.0ms

Calls
1 calls:
Slowest
38.0ms
(/ (exp x) (expm1 x))

simplify748.0ms

Calls
28 calls:
Slowest
410.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
45.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
42.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
30.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) 1)
29.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (sqrt (expm1 x)))

prune283.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (expm1 x) (sqrt (exp x)))
0.0b
(/ (sqrt (exp x)) (/ (expm1 x) (sqrt (exp x))))
0.0b
(sqrt (exp x))
0.0b
(sqrt (exp x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
162×add-sqr-sqrt
160×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
28×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv associate-/l*
8×sqrt-pow1
6×pow1 exp-prod
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg pow1/2
1×div-sub associate-/r/ expm1-udef
Calls
4 calls:
Slowest
13.0ms
(/ (sqrt (exp x)) (/ (expm1 x) (sqrt (exp x))))
13.0ms
(/ (expm1 x) (sqrt (exp x)))
2.0ms
(sqrt (exp x))
2.0ms
(sqrt (exp x))

series175.0ms

Calls
4 calls:
Slowest
107.0ms
(/ (expm1 x) (sqrt (exp x)))
29.0ms
(/ (sqrt (exp x)) (/ (expm1 x) (sqrt (exp x))))
26.0ms
(sqrt (exp x))
13.0ms
(sqrt (exp x))

simplify13.2s

Calls
371 calls:
Slowest
464.0ms
(/ (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x))) (/ (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x)))))
402.0ms
(/ (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x))))
343.0ms
(+ x (+ (* 1/24 (pow x 3)) (* 1/1920 (pow x 5))))
294.0ms
(/ (sqrt 1) (/ (* (cbrt (expm1 x)) (cbrt (expm1 x))) (* (cbrt (sqrt (exp x))) (cbrt (sqrt (exp x))))))
279.0ms
(/ (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x))) (* (* (/ (expm1 x) (sqrt (exp x))) (/ (expm1 x) (sqrt (exp x)))) (/ (expm1 x) (sqrt (exp x)))))

prune3.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))
0.2b
(* 1/24 (* x x))
0.0b
(fma (* 1/24 (* x x)) x x)
0.0b
(/ (sqrt (exp x)) (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
12×sqrt-prod
11×add-cbrt-cube add-exp-log
9×pow1
6×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l* pow-prod-down prod-exp cbrt-unprod
2×fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp associate-*r* *-commutative div-inv unswap-sqr
Calls
4 calls:
Slowest
27.0ms
(* 1/24 (* x x))
13.0ms
(/ (sqrt (exp x)) (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x)))
1.0ms
(fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))
0.0ms
(fma (* 1/24 (* x x)) x x)

series346.0ms

Calls
4 calls:
Slowest
111.0ms
(fma (* 1/24 (* x x)) x x)
107.0ms
(fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))
100.0ms
(/ (sqrt (exp x)) (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x)))
28.0ms
(* 1/24 (* x x))

simplify16.0s

Calls
68 calls:
Slowest
658.0ms
(/ (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x))) (* (* (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x)) (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))) (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))))
615.0ms
(/ 1 (* (cbrt (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))) (cbrt (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x)))))
507.0ms
(/ (sqrt (cbrt (exp x))) (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x)))
504.0ms
(/ (sqrt 1) (* (cbrt (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))) (cbrt (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x)))))
501.0ms
(/ (cbrt (sqrt (exp x))) (sqrt (fma 1/1920 (pow x 5) (fma (* 1/24 (* x x)) x x))))

prune1.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.5s2336×body1280valid
1.1s2576×body10240exit
536.0ms1530×body640valid
177.0ms882×body320valid
174.0ms2857×body80valid
89.0ms395×body160valid