Details

Time bar (total: 2.0m)

sample210.0ms

Algorithm
intervals
Results
156.0ms385×body80valid
31.0ms165×body80nan

simplify122.0ms

Calls
1 calls:
Slowest
122.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize32.0ms

Local error

Found 2 expressions with local error:

3.0b
(/ a (/ (fma k (+ k 10) 1) (pow k m)))
0.0b
(fma k (+ k 10) 1)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
13×associate-/r*
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv add-log-exp
1×clear-num frac-2neg associate-/r/ fma-udef
Calls
2 calls:
Slowest
2.0ms
(/ a (/ (fma k (+ k 10) 1) (pow k m)))
0.0ms
(fma k (+ k 10) 1)

series160.0ms

Calls
2 calls:
Slowest
146.0ms
(/ a (/ (fma k (+ k 10) 1) (pow k m)))
14.0ms
(fma k (+ k 10) 1)

simplify2.3s

Calls
20 calls:
Slowest
385.0ms
(- (+ a (* (log k) (* m a))) (* 10 (* a k)))
268.0ms
(+ (pow k 2) (+ 1 (* 10 k)))
225.0ms
(- (+ (* 99 (/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 4))) (/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 2))) (* 10 (/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 3))))
208.0ms
(- (+ (* 99 (/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 4))) (/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 2))) (* 10 (/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 3))))
122.0ms
(+ (pow k 2) (+ 1 (* 10 k)))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 3 expressions with local error:

2.8b
(* a (/ 1 (/ (fma k (+ k 10) 1) (pow k m))))
0.1b
(/ 1 (/ (fma k (+ k 10) 1) (pow k m)))
0.0b
(fma k (+ k 10) 1)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
13×associate-/r*
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-exp-log
5×associate-*r*
4×pow1
3×expm1-log1p-u rec-exp add-cbrt-cube insert-posit16 log1p-expm1-u div-inv add-log-exp
2×div-exp associate-/r/
1×pow-to-exp clear-num frac-2neg associate-*r/ un-div-inv *-commutative fma-udef pow-flip inv-pow
Calls
3 calls:
Slowest
3.0ms
(/ 1 (/ (fma k (+ k 10) 1) (pow k m)))
2.0ms
(* a (/ 1 (/ (fma k (+ k 10) 1) (pow k m))))
0.0ms
(fma k (+ k 10) 1)

series236.0ms

Calls
3 calls:
Slowest
144.0ms
(* a (/ 1 (/ (fma k (+ k 10) 1) (pow k m))))
78.0ms
(/ 1 (/ (fma k (+ k 10) 1) (pow k m)))
13.0ms
(fma k (+ k 10) 1)

simplify3.6s

Calls
31 calls:
Slowest
393.0ms
(- (+ a (* (log k) (* m a))) (* 10 (* a k)))
338.0ms
(- (+ (/ (exp (* -1 (* (log (/ 1 k)) m))) (pow k 2)) (* 99 (/ (exp (* -1 (* (log (/ 1 k)) m))) (pow k 4)))) (* 10 (/ (exp (* -1 (* (log (/ 1 k)) m))) (pow k 3))))
312.0ms
(- (+ (* 99 (/ (exp (* m (- (log -1) (log (/ -1 k))))) (pow k 4))) (/ (exp (* m (- (log -1) (log (/ -1 k))))) (pow k 2))) (* 10 (/ (exp (* m (- (log -1) (log (/ -1 k))))) (pow k 3))))
231.0ms
(- (+ (* 99 (/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 4))) (/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 2))) (* 10 (/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 3))))
221.0ms
(- (+ (* 99 (/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 4))) (/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 2))) (* 10 (/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 3))))

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (fma k (+ k 10) 1))
16.8b
(sqrt (fma k (+ k 10) 1))
2.8b
(* a (/ (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)) (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))
0.1b
(/ (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)) (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
418×times-frac
197×add-sqr-sqrt
195×*-un-lft-identity add-cube-cbrt
115×associate-*r*
105×sqrt-prod
58×div-inv
47×associate-/r/
22×associate-/r*
18×add-exp-log
10×div-exp
9×add-cbrt-cube
5×associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp
2×pow-to-exp rem-sqrt-square pow1/2
1×clear-num frac-2neg associate-*r/ *-commutative associate-/l/
Calls
4 calls:
Slowest
14.0ms
(/ (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)) (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))
9.0ms
(* a (/ (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)) (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))
2.0ms
(sqrt (fma k (+ k 10) 1))
2.0ms
(sqrt (fma k (+ k 10) 1))

series290.0ms

Calls
4 calls:
Slowest
150.0ms
(* a (/ (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)) (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))
81.0ms
(/ (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)) (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))
25.0ms
(sqrt (fma k (+ k 10) 1))
24.0ms
(sqrt (fma k (+ k 10) 1))

simplify1.3m

Calls
390 calls:
Slowest
1.9s
(/ (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))
1.3s
(/ (/ 1 (sqrt (fma k (+ k 10) 1))) (/ (* (cbrt (sqrt (fma k (+ k 10) 1))) (cbrt (sqrt (fma k (+ k 10) 1)))) (sqrt (pow k m))))
963.0ms
(/ (/ 1 (sqrt (fma k (+ k 10) 1))) (/ (sqrt (* (cbrt (fma k (+ k 10) 1)) (cbrt (fma k (+ k 10) 1)))) (* (cbrt (pow k m)) (cbrt (pow k m)))))
840.0ms
(/ (/ 1 (sqrt (fma k (+ k 10) 1))) (/ (sqrt (sqrt (fma k (+ k 10) 1))) (* (cbrt (pow k m)) (cbrt (pow k m)))))
686.0ms
(/ (* (cbrt (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1))) (cbrt (/ 1 (/ (sqrt (fma k (+ k 10) 1)) 1)))) (/ (* (cbrt (sqrt (fma k (+ k 10) 1))) (cbrt (sqrt (fma k (+ k 10) 1)))) (* (cbrt (pow k m)) (cbrt (pow k m)))))

prune5.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (fma k (+ k 10) 1))
16.8b
(sqrt (fma k (+ k 10) 1))
16.8b
(sqrt (fma k (+ k 10) 1))
1.6b
(* (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))) (/ (/ 1 (sqrt (fma k (+ k 10) 1))) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
133×sqrt-prod
105×associate-*r*
92×add-sqr-sqrt
89×*-un-lft-identity add-cube-cbrt
30×div-inv
12×add-exp-log
9×add-cbrt-cube
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2 prod-exp associate-*r/
2×frac-times div-exp associate-*l/ un-div-inv cbrt-unprod
1×cbrt-undiv rec-exp sqrt-div associate-*l* pow-prod-down associate-/r/ *-commutative
Calls
4 calls:
Slowest
23.0ms
(* (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))) (/ (/ 1 (sqrt (fma k (+ k 10) 1))) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))
2.0ms
(sqrt (fma k (+ k 10) 1))
2.0ms
(sqrt (fma k (+ k 10) 1))
2.0ms
(sqrt (fma k (+ k 10) 1))

series228.0ms

Calls
4 calls:
Slowest
152.0ms
(* (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))) (/ (/ 1 (sqrt (fma k (+ k 10) 1))) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))
26.0ms
(sqrt (fma k (+ k 10) 1))
25.0ms
(sqrt (fma k (+ k 10) 1))
24.0ms
(sqrt (fma k (+ k 10) 1))

simplify18.4s

Calls
142 calls:
Slowest
664.0ms
(* (* (* (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))) (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))) (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))) (/ (* (* (/ 1 (sqrt (fma k (+ k 10) 1))) (/ 1 (sqrt (fma k (+ k 10) 1)))) (/ 1 (sqrt (fma k (+ k 10) 1)))) (* (* (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))))
565.0ms
(+ (log (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))) (log (/ (/ 1 (sqrt (fma k (+ k 10) 1))) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))))
545.0ms
(+ (log (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))) (- (- (log (sqrt (fma k (+ k 10) 1)))) (log (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))))
469.0ms
(+ (log (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))) (- (log (/ 1 (sqrt (fma k (+ k 10) 1)))) (log (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))))
458.0ms
(* (* a (/ 1 (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m))))) (/ (/ 1 (sqrt (fma k (+ k 10) 1))) (sqrt (/ (sqrt (fma k (+ k 10) 1)) (pow k m)))))

prune4.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes267.0ms

Accuracy

96.2% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.2b

bsearch94.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.8s11907×body80valid
710.0ms4178×body80nan