Details

Time bar (total: 27.9s)

sample98.0ms

Algorithm
intervals
Results
60.0ms385×body80valid
18.0ms151×body80nan

simplify77.0ms

Calls
1 calls:
Slowest
77.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 2 expressions with local error:

3.1b
(/ a (/ (fma k (+ k 10) 1) (pow k m)))
0.0b
(/ (fma k (+ k 10) 1) (pow k m))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r*
5×add-exp-log
4×add-cbrt-cube
3×div-inv associate-/l*
2×expm1-log1p-u pow1 clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u add-log-exp
1×pow-to-exp cbrt-undiv associate-/r/
Calls
2 calls:
Slowest
4.0ms
(/ (fma k (+ k 10) 1) (pow k m))
2.0ms
(/ a (/ (fma k (+ k 10) 1) (pow k m)))

series273.0ms

Calls
2 calls:
Slowest
169.0ms
(/ a (/ (fma k (+ k 10) 1) (pow k m)))
104.0ms
(/ (fma k (+ k 10) 1) (pow k m))

simplify3.6s

Calls
46 calls:
Slowest
382.0ms
(/ (* (* (fma k (+ k 10) 1) (fma k (+ k 10) 1)) (fma k (+ k 10) 1)) (* (* (pow k m) (pow k m)) (pow k m)))
329.0ms
(+ (* 10 (/ k (exp (* m (- (log -1) (log (/ -1 k))))))) (+ (/ (pow k 2) (exp (* m (- (log -1) (log (/ -1 k)))))) (/ 1 (exp (* m (- (log -1) (log (/ -1 k))))))))
299.0ms
(- (+ a (* (log k) (* m a))) (* 10 (* a k)))
293.0ms
(+ (* 10 (/ k (exp (* -1 (* (log (/ 1 k)) m))))) (+ (/ (pow k 2) (exp (* -1 (* (log (/ 1 k)) m)))) (/ 1 (exp (* -1 (* (log (/ 1 k)) m))))))
176.0ms
(- (+ (* 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))))

prune746.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

2.5b
(* a (/ 1 (/ (fma k (+ k 10) 1) (pow k m))))
0.5b
(/ 1 (/ (fma k (+ k 10) 1) (pow k m)))
0.0b
(/ (fma k (+ k 10) 1) (pow k m))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
16×associate-/r*
10×add-exp-log
5×add-cbrt-cube associate-*r*
4×pow1 div-exp div-inv
3×expm1-log1p-u rec-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×pow-to-exp clear-num frac-2neg associate-/r/
1×cbrt-undiv associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Calls
3 calls:
Slowest
4.0ms
(/ (fma k (+ k 10) 1) (pow k m))
2.0ms
(/ 1 (/ (fma k (+ k 10) 1) (pow k m)))
1.0ms
(* a (/ 1 (/ (fma k (+ k 10) 1) (pow k m))))

series346.0ms

Calls
3 calls:
Slowest
146.0ms
(* a (/ 1 (/ (fma k (+ k 10) 1) (pow k m))))
105.0ms
(/ (fma k (+ k 10) 1) (pow k m))
95.0ms
(/ 1 (/ (fma k (+ k 10) 1) (pow k m)))

simplify4.5s

Calls
57 calls:
Slowest
384.0ms
(/ (* (* (fma k (+ k 10) 1) (fma k (+ k 10) 1)) (fma k (+ k 10) 1)) (* (* (pow k m) (pow k m)) (pow k m)))
327.0ms
(+ (* 10 (/ k (exp (* m (- (log -1) (log (/ -1 k))))))) (+ (/ (pow k 2) (exp (* m (- (log -1) (log (/ -1 k)))))) (/ 1 (exp (* m (- (log -1) (log (/ -1 k))))))))
260.0ms
(- (+ a (* (log k) (* m a))) (* 10 (* a k)))
242.0ms
(- (+ (/ (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))))
220.0ms
(+ (* 10 (/ k (exp (* -1 (* (log (/ 1 k)) m))))) (+ (/ (pow k 2) (exp (* -1 (* (log (/ 1 k)) m)))) (/ 1 (exp (* -1 (* (log (/ 1 k)) m))))))

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

6.9b
(/ (exp (* (log k) m)) (/ (pow k 4) a))
6.7b
(fma (/ (/ (exp (* (log k) m)) (* (/ k a) k)) k) -10 (fma 99 (/ (exp (* (log k) m)) (/ (pow k 4) a)) (/ (exp (* (log k) m)) (* (/ k a) k))))
4.3b
(/ (pow k 4) a)
3.8b
(/ (exp (* (log k) m)) (* (/ k a) k))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×times-frac
9×associate-/l*
8×add-cbrt-cube
7×div-inv
6×add-exp-log
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×cbrt-undiv div-exp associate-/r/
1×associate-*l/ fma-udef
Calls
4 calls:
Slowest
15.0ms
(/ (exp (* (log k) m)) (* (/ k a) k))
14.0ms
(/ (exp (* (log k) m)) (/ (pow k 4) a))
6.0ms
(/ (pow k 4) a)
0.0ms
(fma (/ (/ (exp (* (log k) m)) (* (/ k a) k)) k) -10 (fma 99 (/ (exp (* (log k) m)) (/ (pow k 4) a)) (/ (exp (* (log k) m)) (* (/ k a) k))))

series587.0ms

Calls
4 calls:
Slowest
240.0ms
(fma (/ (/ (exp (* (log k) m)) (* (/ k a) k)) k) -10 (fma 99 (/ (exp (* (log k) m)) (/ (pow k 4) a)) (/ (exp (* (log k) m)) (* (/ k a) k))))
163.0ms
(/ (exp (* (log k) m)) (/ (pow k 4) a))
140.0ms
(/ (exp (* (log k) m)) (* (/ k a) k))
44.0ms
(/ (pow k 4) a)

simplify4.7s

Calls
56 calls:
Slowest
495.0ms
(/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 2))
495.0ms
(/ (* (* (exp (* (log k) m)) (exp (* (log k) m))) (exp (* (log k) m))) (* (* (/ (pow k 4) a) (/ (pow k 4) a)) (/ (pow k 4) a)))
360.0ms
(/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 2))
301.0ms
(/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 4))
272.0ms
(+ (/ (* (log k) (* m a)) (pow k 4)) (+ (* 1/2 (/ (* (pow (log k) 2) (* (pow m 2) a)) (pow k 4))) (/ a (pow k 4))))

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

6.9b
(/ (exp (* (log k) m)) (/ (pow k 4) a))
6.7b
(fma (/ (/ (exp (* (log k) m)) (* (/ k a) k)) k) -10 (fma 99 (/ (exp (* (log k) m)) (/ (pow k 4) a)) (* (exp (* (log k) m)) (/ (/ a k) k))))
4.3b
(/ (pow k 4) a)
4.2b
(* (exp (* (log k) m)) (/ (/ a k) k))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
8×add-cbrt-cube
7×div-inv
6×pow1 add-exp-log associate-/l*
4×expm1-log1p-u associate-/r* associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×clear-num frac-2neg
1×cbrt-undiv div-exp pow-prod-down prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod fma-udef
Calls
4 calls:
Slowest
17.0ms
(* (exp (* (log k) m)) (/ (/ a k) k))
13.0ms
(/ (exp (* (log k) m)) (/ (pow k 4) a))
6.0ms
(/ (pow k 4) a)
0.0ms
(fma (/ (/ (exp (* (log k) m)) (* (/ k a) k)) k) -10 (fma 99 (/ (exp (* (log k) m)) (/ (pow k 4) a)) (* (exp (* (log k) m)) (/ (/ a k) k))))

series529.0ms

Calls
4 calls:
Slowest
201.0ms
(fma (/ (/ (exp (* (log k) m)) (* (/ k a) k)) k) -10 (fma 99 (/ (exp (* (log k) m)) (/ (pow k 4) a)) (* (exp (* (log k) m)) (/ (/ a k) k))))
155.0ms
(/ (exp (* (log k) m)) (/ (pow k 4) a))
129.0ms
(* (exp (* (log k) m)) (/ (/ a k) k))
44.0ms
(/ (pow k 4) a)

simplify4.5s

Calls
55 calls:
Slowest
576.0ms
(* (* (* (exp (* (log k) m)) (exp (* (log k) m))) (exp (* (log k) m))) (* (* (/ (/ a k) k) (/ (/ a k) k)) (/ (/ a k) k)))
484.0ms
(/ (* (* (exp (* (log k) m)) (exp (* (log k) m))) (exp (* (log k) m))) (* (* (/ (pow k 4) a) (/ (pow k 4) a)) (/ (pow k 4) a)))
379.0ms
(/ (* a (exp (* m (- (log -1) (log (/ -1 k)))))) (pow k 2))
329.0ms
(/ (* (exp (* -1 (* (log (/ 1 k)) m))) a) (pow k 2))
317.0ms
(+ (/ (* (log k) (* m a)) (pow k 4)) (+ (* 1/2 (/ (* (pow (log k) 2) (* (pow m 2) a)) (pow k 4))) (/ a (pow k 4))))

prune1.6s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes179.0ms

Accuracy

98.6% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.2b

bsearch83.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.1s11974×body80valid
521.0ms4335×body80nan