Details

Time bar (total: 36.4s)

sample118.0ms

Algorithm
intervals
Results
37.0ms96×body10240exit
30.0ms66×body1280valid
20.0ms105×body80valid
14.0ms42×body640valid
7.0ms34×body320valid
1.0ms10×body160valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(/ (exp x) (- (exp x) 1))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize15.0ms

Local error

Found 2 expressions with local error:

3.2b
(- (exp x) 1)
0.0b
(/ (exp x) (- (exp x) 1))

rewrite48.0ms

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
Counts
2 → 80
Calls
2 calls:
Slowest
27.0ms
(/ (exp x) (- (exp x) 1))
19.0ms
(- (exp x) 1)

series53.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
27.0ms
(/ (exp x) (- (exp x) 1))
26.0ms
(- (exp x) 1)

simplify2.3s

Counts
88 → 86
Calls
88 calls:
Slowest
271.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
263.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
87.0ms
(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))
69.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
68.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (sqrt 1) (sqrt 1))))

prune565.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

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
Counts
1 → 30
Calls
1 calls:
Slowest
6.0ms
(/ (exp x) (expm1 x))

series33.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
33.0ms
(/ (exp x) (expm1 x))

simplify688.0ms

Counts
28 → 33
Calls
28 calls:
Slowest
416.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
44.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (expm1 x)) (cbrt (expm1 x))))
29.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (sqrt (expm1 x)))
26.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
22.0ms
(/ (exp x) (- (exp x) 1))

prune230.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
154×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×sqrt-prod
28×associate-/r*
9×add-cbrt-cube add-exp-log div-inv associate-/l*
4×cbrt-undiv div-exp
2×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×div-sub associate-/r/ expm1-udef
Counts
2 → 221
Calls
2 calls:
Slowest
22.0ms
(/ (sqrt (exp x)) (/ (expm1 x) (sqrt (exp x))))
12.0ms
(/ (expm1 x) (sqrt (exp x)))

series131.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
96.0ms
(/ (expm1 x) (sqrt (exp x)))
34.0ms
(/ (sqrt (exp x)) (/ (expm1 x) (sqrt (exp x))))

simplify12.5s

Counts
349 → 227
Calls
349 calls:
Slowest
490.0ms
(/ (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x))) (/ (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x)))))
411.0ms
(/ (* (* (expm1 x) (expm1 x)) (expm1 x)) (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x))))
328.0ms
(+ x (+ (* 1/24 (pow x 3)) (* 1/1920 (pow x 5))))
311.0ms
(/ (sqrt 1) (/ (* (cbrt (expm1 x)) (cbrt (expm1 x))) (* (cbrt (sqrt (exp x))) (cbrt (sqrt (exp x))))))
252.0ms
(/ (* (* (sqrt (exp x)) (sqrt (exp x))) (sqrt (exp x))) (* (* (/ (expm1 x) (sqrt (exp x))) (/ (expm1 x) (sqrt (exp x)))) (/ (expm1 x) (sqrt (exp x)))))

prune2.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (exp x) (sqrt (expm1 x)))
0.1b
(/ (/ (exp x) (sqrt (expm1 x))) (sqrt (expm1 x)))
0.0b
(sqrt (expm1 x))
0.0b
(sqrt (expm1 x))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube
9×add-exp-log div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 252
Calls
4 calls:
Slowest
22.0ms
(/ (/ (exp x) (sqrt (expm1 x))) (sqrt (expm1 x)))
15.0ms
(/ (exp x) (sqrt (expm1 x)))
2.0ms
(sqrt (expm1 x))
2.0ms
(sqrt (expm1 x))

series220.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(/ (exp x) (sqrt (expm1 x)))
46.0ms
(sqrt (expm1 x))
37.0ms
(sqrt (expm1 x))
29.0ms
(/ (/ (exp x) (sqrt (expm1 x))) (sqrt (expm1 x)))

simplify11.1s

Counts
364 → 264
Calls
364 calls:
Slowest
483.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (sqrt (expm1 x)) (sqrt (expm1 x))) (sqrt (expm1 x))))
375.0ms
(/ (/ 1 (sqrt (sqrt (expm1 x)))) (sqrt (* (cbrt (expm1 x)) (cbrt (expm1 x)))))
355.0ms
(/ (/ (* (* (exp x) (exp x)) (exp x)) (* (* (sqrt (expm1 x)) (sqrt (expm1 x))) (sqrt (expm1 x)))) (* (* (sqrt (expm1 x)) (sqrt (expm1 x))) (sqrt (expm1 x))))
290.0ms
(/ (* (* (/ (exp x) (sqrt (expm1 x))) (/ (exp x) (sqrt (expm1 x)))) (/ (exp x) (sqrt (expm1 x)))) (* (* (sqrt (expm1 x)) (sqrt (expm1 x))) (sqrt (expm1 x))))
181.0ms
(/ (/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (sqrt (expm1 x))) (cbrt (sqrt (expm1 x))))) (sqrt (* (cbrt (expm1 x)) (cbrt (expm1 x)))))

prune2.5s

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

sample3.6s

Algorithm
intervals
Results
1.4s2598×body10240exit
1.1s2326×body1280valid
463.0ms1654×body640valid
211.0ms805×body320valid
154.0ms2811×body80valid
48.0ms405×body160valid