Details

Time bar (total: 1.8m)

sample102.0ms

Algorithm
intervals
Results
51.0ms380×body80valid
29.0ms139×body80nan

simplify291.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
291.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
14×add-sqr-sqrt
10×add-cbrt-cube
9×*-un-lft-identity add-cube-cbrt
8×add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×expm1-log1p-u pow1 associate-/r* sum-log fma-def times-frac associate-*l* insert-posit16 log1p-expm1-u unswap-sqr
2×pow-to-exp cbrt-undiv flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ clear-num frac-2neg *-commutative div-inv associate-/l*
Counts
3 → 75
Calls
3 calls:
Slowest
47.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))
40.0ms
(+ (+ 1 (* 10 k)) (* k k))
18.0ms
(* a (pow k m))

series282.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
150.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))
102.0ms
(* a (pow k m))
30.0ms
(+ (+ 1 (* 10 k)) (* k k))

simplify7.2s

Counts
49 → 84
Calls
49 calls:
Slowest
688.0ms
(- (+ a (* (log k) (* m a))) (* 10 (* a k)))
576.0ms
(/ (* (* (* a (pow k m)) (* a (pow k m))) (* a (pow k m))) (* (* (+ (+ 1 (* 10 k)) (* k k)) (+ (+ 1 (* 10 k)) (* k k))) (+ (+ 1 (* 10 k)) (* k k))))
505.0ms
(/ (* (* (* a a) a) (* (* (pow k m) (pow k m)) (pow k m))) (* (* (+ (+ 1 (* 10 k)) (* k k)) (+ (+ 1 (* 10 k)) (* k k))) (+ (+ 1 (* 10 k)) (* k k))))
460.0ms
(* (* (* a a) a) (* (* (pow k m) (pow k m)) (pow k m)))
391.0ms
(/ (pow k m) (sqrt (+ (+ 1 (* 10 k)) (* k k))))

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

13.6b
(sqrt (+ (+ 1 (* 10 k)) (* k k)))
13.6b
(sqrt (+ (+ 1 (* 10 k)) (* k k)))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
0.0b
(+ (+ 1 (* 10 k)) (* k k))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
58×add-sqr-sqrt
54×*-un-lft-identity add-cube-cbrt
20×sqrt-div add-exp-log
16×associate-/r/
13×add-cbrt-cube
12×associate-/l*
11×flip3-+ flip-+
9×div-exp add-log-exp
8×div-inv
6×pow1 associate-/r*
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×sum-log fma-def prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×pow-to-exp +-commutative associate-+l+ clear-num frac-2neg pow-exp cbrt-unprod associate-/l/
Counts
4 → 171
Calls
4 calls:
Slowest
71.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
34.0ms
(+ (+ 1 (* 10 k)) (* k k))
23.0ms
(sqrt (+ (+ 1 (* 10 k)) (* k k)))
15.0ms
(sqrt (+ (+ 1 (* 10 k)) (* k k)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
47.0ms
(sqrt (+ (+ 1 (* 10 k)) (* k k)))
39.0ms
(sqrt (+ (+ 1 (* 10 k)) (* k k)))
25.0ms
(+ (+ 1 (* 10 k)) (* k k))

simplify42.8s

Counts
204 → 183
Calls
204 calls:
Slowest
900.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
702.0ms
(/ (/ (* (* (* a (pow k m)) (* a (pow k m))) (* a (pow k m))) (* (* (sqrt (+ (+ 1 (* 10 k)) (* k k))) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))) (* (* (sqrt (+ (+ 1 (* 10 k)) (* k k))) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k)))))
610.0ms
(- (- (+ (log a) (log (pow k m))) (log (sqrt (+ (+ 1 (* 10 k)) (* k k))))) (log (sqrt (+ (+ 1 (* 10 k)) (* k k)))))
575.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
554.0ms
(- (- (log (* a (pow k m))) (log (sqrt (+ (+ 1 (* 10 k)) (* k k))))) (log (sqrt (+ (+ 1 (* 10 k)) (* k k)))))

prune2.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

2.7b
(* a (/ (pow k m) (fma k (+ k 10) 1)))
0.4b
(/ (pow k m) (fma k (+ k 10) 1))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
43×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
25×associate-*r*
22×unpow-prod-down
17×add-exp-log
9×add-cbrt-cube
8×sqr-pow
7×associate-/l*
6×div-exp
4×pow1 prod-exp unswap-sqr
3×associate-/r* associate-*l*
2×expm1-log1p-u pow-to-exp cbrt-undiv pow-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
2 → 99
Calls
2 calls:
Slowest
12.0ms
(/ (pow k m) (fma k (+ k 10) 1))
11.0ms
(* a (/ (pow k m) (fma k (+ k 10) 1)))

series271.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
159.0ms
(* a (/ (pow k m) (fma k (+ k 10) 1)))
111.0ms
(/ (pow k m) (fma k (+ k 10) 1))

simplify23.6s

Counts
104 → 105
Calls
104 calls:
Slowest
804.0ms
(* (* (* a a) a) (* (* (/ (pow k m) (fma k (+ k 10) 1)) (/ (pow k m) (fma k (+ k 10) 1))) (/ (pow k m) (fma k (+ k 10) 1))))
601.0ms
(/ (pow (* (cbrt k) (cbrt k)) m) (* (cbrt (fma k (+ k 10) 1)) (cbrt (fma k (+ k 10) 1))))
474.0ms
(- (+ (* 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))))
426.0ms
(+ (log a) (log (/ (pow k m) (fma k (+ k 10) 1))))
423.0ms
(cbrt (/ (pow k m) (fma k (+ k 10) 1)))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

2.6b
(/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m)))
0.3b
(/ 1 (/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m))))
0.0b
(+ (+ 1 (* 10 k)) (* k k))
0.0b
(* a (pow k m))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
57×add-exp-log
36×times-frac
31×add-sqr-sqrt
26×*-un-lft-identity div-exp add-cube-cbrt
20×add-cbrt-cube
15×prod-exp
9×add-log-exp
8×associate-/r*
7×cbrt-undiv associate-*r*
6×div-inv associate-/l*
5×pow-to-exp pow1 rec-exp 1-exp pow-exp
4×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u
3×sum-log fma-def associate-*l* cbrt-unprod unswap-sqr
2×clear-num frac-2neg flip3-+ flip-+ sqr-pow associate-/l/
1×+-commutative associate-+l+ associate-/r/ *-commutative pow-flip inv-pow
Counts
4 → 140
Calls
4 calls:
Slowest
84.0ms
(/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m)))
53.0ms
(/ 1 (/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m))))
35.0ms
(+ (+ 1 (* 10 k)) (* k k))
18.0ms
(* a (pow k m))

series403.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ 1 (/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m))))
142.0ms
(/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m)))
87.0ms
(* a (pow k m))
26.0ms
(+ (+ 1 (* 10 k)) (* k k))

simplify22.6s

Counts
118 → 152
Calls
118 calls:
Slowest
850.0ms
(/ 1 (/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m))))
622.0ms
(/ (* (* 1 1) 1) (/ (* (* (+ (+ 1 (* 10 k)) (* k k)) (+ (+ 1 (* 10 k)) (* k k))) (+ (+ 1 (* 10 k)) (* k k))) (* (* (* a (pow k m)) (* a (pow k m))) (* a (pow k m)))))
620.0ms
(/ (sqrt 1) (/ (+ (+ 1 (* 10 k)) (* k k)) (* a (pow k m))))
617.0ms
(/ (* (* (+ (+ 1 (* 10 k)) (* k k)) (+ (+ 1 (* 10 k)) (* k k))) (+ (+ 1 (* 10 k)) (* k k))) (* (* (* a (pow k m)) (* a (pow k m))) (* a (pow k m))))
586.0ms
(/ (* (* 1 1) 1) (/ (* (* (+ (+ 1 (* 10 k)) (* k k)) (+ (+ 1 (* 10 k)) (* k k))) (+ (+ 1 (* 10 k)) (* k k))) (* (* (* a a) a) (* (* (pow k m) (pow k m)) (pow k m)))))

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes183.0ms

Accuracy

96.4% (0.1b remaining)

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

bsearch101.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s11998×body80valid
580.0ms4167×body80nan