Details

Time bar (total: 7.1m)

sample106.0ms

Algorithm
intervals
Results
59.0ms379×body80valid
21.0ms141×body80nan

simplify309.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
309.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize40.0ms

Local error

Found 3 expressions with local error:

2.2b
(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))
0.0b
(* k (+ k 10))
0.0b
(* (pow k m) a)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
17×add-sqr-sqrt
12×*-un-lft-identity add-cbrt-cube
10×associate-*l* add-cube-cbrt
7×associate-*r* prod-exp
5×pow1
4×unpow-prod-down div-exp unswap-sqr
3×associate-/r* times-frac cbrt-unprod insert-posit16 add-log-exp
2×pow-to-exp cbrt-undiv flip3-+ pow-exp associate-*r/ associate-/r/ *-commutative flip-+ sqr-pow
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow-prod-down div-inv distribute-lft-out associate-/l*
Counts
3 → 76
Calls
3 calls:
Slowest
27.0ms
(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))
13.0ms
(* k (+ k 10))
12.0ms
(* (pow k m) a)

series346.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
144.0ms
(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))
125.0ms
(* (pow k m) a)
77.0ms
(* k (+ k 10))

simplify5.5s

Counts
60 → 85
Calls
60 calls:
Slowest
607.0ms
(/ (* (* (* (pow k m) a) (* (pow k m) a)) (* (pow k m) a)) (* (* (+ (* k (+ k 10)) 1) (+ (* k (+ k 10)) 1)) (+ (* k (+ k 10)) 1)))
477.0ms
(/ (* (* (* (pow k m) (pow k m)) (pow k m)) (* (* a a) a)) (* (* (+ (* k (+ k 10)) 1) (+ (* k (+ k 10)) 1)) (+ (* k (+ k 10)) 1)))
441.0ms
(* (* (* (pow k m) (pow k m)) (pow k m)) (* (* a a) a))
436.0ms
(/ (pow k m) (sqrt (+ (* k (+ k 10)) 1)))
305.0ms
(- (log (* (pow k m) a)) (log (+ (* k (+ k 10)) 1)))

prune930.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

2.2b
(/ (* (pow k m) a) (+ (* (+ 10 k) k) 1))
0.0b
(* (+ 10 k) k)
0.0b
(* (pow k m) a)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
17×add-sqr-sqrt
12×*-un-lft-identity add-cbrt-cube
11×associate-*l*
10×add-cube-cbrt
7×prod-exp
6×associate-*r*
5×pow1
4×unpow-prod-down div-exp unswap-sqr
3×associate-/r* times-frac cbrt-unprod insert-posit16 add-log-exp
2×pow-to-exp cbrt-undiv flip3-+ associate-*l/ pow-exp associate-/r/ *-commutative flip-+ sqr-pow
1×clear-num frac-2neg pow-prod-down div-inv distribute-lft-out associate-/l*
Counts
3 → 74
Calls
3 calls:
Slowest
39.0ms
(/ (* (pow k m) a) (+ (* (+ 10 k) k) 1))
32.0ms
(* (+ 10 k) k)
17.0ms
(* (pow k m) a)

series329.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
142.0ms
(* (pow k m) a)
129.0ms
(/ (* (pow k m) a) (+ (* (+ 10 k) k) 1))
59.0ms
(* (+ 10 k) k)

simplify6.9s

Counts
56 → 83
Calls
56 calls:
Slowest
615.0ms
(- (+ a (* (log k) (* m a))) (* 10 (* a k)))
565.0ms
(/ (* (* (* (pow k m) a) (* (pow k m) a)) (* (pow k m) a)) (* (* (+ (* (+ 10 k) k) 1) (+ (* (+ 10 k) k) 1)) (+ (* (+ 10 k) k) 1)))
527.0ms
(* (* (* (+ 10 k) (+ 10 k)) (+ 10 k)) (* (* k k) k))
471.0ms
(/ (* (* (* (pow k m) (pow k m)) (pow k m)) (* (* a a) a)) (* (* (+ (* (+ 10 k) k) 1) (+ (* (+ 10 k) k) 1)) (+ (* (+ 10 k) k) 1)))
440.0ms
(* (* (* (pow k m) (pow k m)) (pow k m)) (* (* a a) a))

prune963.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

15.0b
(sqrt (+ (* (+ 10 k) k) 1))
15.0b
(sqrt (+ (* (+ 10 k) k) 1))
0.0b
(* (/ (pow k m) (sqrt (+ (* (+ 10 k) k) 1))) (/ a (sqrt (+ (* (+ 10 k) k) 1))))
0.0b
(/ (pow k m) (sqrt (+ (* (+ 10 k) k) 1)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
146×add-sqr-sqrt
134×times-frac
76×*-un-lft-identity add-cube-cbrt sqrt-prod
48×associate-*l*
45×unpow-prod-down
33×add-exp-log
24×associate-*r*
21×unswap-sqr
19×sqr-pow
18×add-cbrt-cube
13×div-exp
10×sqrt-div
8×pow1 prod-exp
7×associate-/l*
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod insert-posit16 add-log-exp
3×pow-to-exp pow-exp div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 222
Calls
4 calls:
Slowest
84.0ms
(* (/ (pow k m) (sqrt (+ (* (+ 10 k) k) 1))) (/ a (sqrt (+ (* (+ 10 k) k) 1))))
17.0ms
(/ (pow k m) (sqrt (+ (* (+ 10 k) k) 1)))
14.0ms
(sqrt (+ (* (+ 10 k) k) 1))
11.0ms
(sqrt (+ (* (+ 10 k) k) 1))

series338.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(* (/ (pow k m) (sqrt (+ (* (+ 10 k) k) 1))) (/ a (sqrt (+ (* (+ 10 k) k) 1))))
116.0ms
(/ (pow k m) (sqrt (+ (* (+ 10 k) k) 1)))
50.0ms
(sqrt (+ (* (+ 10 k) k) 1))
49.0ms
(sqrt (+ (* (+ 10 k) k) 1))

simplify1.1m

Counts
258 → 234
Calls
258 calls:
Slowest
1.1s
(/ (* (* (pow k m) (pow k m)) (pow k m)) (* (* (sqrt (+ (* (+ 10 k) k) 1)) (sqrt (+ (* (+ 10 k) k) 1))) (sqrt (+ (* (+ 10 k) k) 1))))
753.0ms
(/ (pow k (/ m 2)) (sqrt (cbrt (+ (* (+ 10 k) k) 1))))
719.0ms
(/ (pow (sqrt k) m) (sqrt (sqrt (+ (* (+ 10 k) k) 1))))
551.0ms
(/ (pow (* (cbrt k) (cbrt k)) m) 1)
533.0ms
(* (/ (pow (sqrt k) m) (sqrt (sqrt (+ (* (+ 10 k) k) 1)))) (/ (sqrt a) (sqrt (sqrt (+ (* (+ 10 k) k) 1)))))

prune3.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

9.7b
(+ (* 99 (/ (* (exp (* m (+ 0 (log k)))) a) (* (* k k) (* k k)))) (+ (* (/ (/ a k) k) (exp (* m (+ 0 (log k))))) (/ -10 (/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k))))))))
8.2b
(+ (* (/ (/ a k) k) (exp (* m (+ 0 (log k))))) (/ -10 (/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k)))))))
7.5b
(/ (* (exp (* m (+ 0 (log k)))) a) (* (* k k) (* k k)))
3.7b
(/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k)))))

rewrite553.0ms

Algorithm
rewrite-expression-head
Rules
2633×times-frac
1033×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
270×exp-sum
135×distribute-rgt-in distribute-lft-in associate-/l*
80×div-inv
59×add-cbrt-cube
50×add-exp-log
21×prod-exp cbrt-unprod
20×cbrt-undiv div-exp
11×add-log-exp
7×associate-/r/
6×associate-/r*
5×frac-add
4×pow1 sum-log insert-posit16
3×flip3-+ associate-*r/ flip-+
2×+-commutative clear-num frac-2neg associate-*l/
1×associate-+r+ distribute-rgt-out associate-/l/
Counts
4 → 894
Calls
4 calls:
Slowest
342.0ms
(+ (* 99 (/ (* (exp (* m (+ 0 (log k)))) a) (* (* k k) (* k k)))) (+ (* (/ (/ a k) k) (exp (* m (+ 0 (log k))))) (/ -10 (/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k))))))))
84.0ms
(+ (* (/ (/ a k) k) (exp (* m (+ 0 (log k))))) (/ -10 (/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k)))))))
43.0ms
(/ (* (exp (* m (+ 0 (log k)))) a) (* (* k k) (* k k)))
33.0ms
(/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k)))))

series661.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(+ (* 99 (/ (* (exp (* m (+ 0 (log k)))) a) (* (* k k) (* k k)))) (+ (* (/ (/ a k) k) (exp (* m (+ 0 (log k))))) (/ -10 (/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k))))))))
192.0ms
(+ (* (/ (/ a k) k) (exp (* m (+ 0 (log k))))) (/ -10 (/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k)))))))
138.0ms
(/ (* (exp (* m (+ 0 (log k)))) a) (* (* k k) (* k k)))
108.0ms
(/ (/ k (/ (/ a k) k)) (exp (* m (+ 0 (log k)))))

simplify5.5m

Counts
1535 → 906
Calls
1535 calls:
Slowest
1.8s
(/ (* (* (* (exp (* m (+ 0 (log k)))) a) (* (exp (* m (+ 0 (log k)))) a)) (* (exp (* m (+ 0 (log k)))) a)) (* (* (* (* k k) (* k k)) (* k k)) (* (* (* k k) k) (* (* k k) k))))
1.6s
(/ (* (* (* (exp (* m (+ 0 (log k)))) a) (* (exp (* m (+ 0 (log k)))) a)) (* (exp (* m (+ 0 (log k)))) a)) (* (* (* (* k k) k) (* (* k k) k)) (* (* (* k k) (* k k)) (* k k))))
1.5s
(/ (* (* (* (exp (* m (+ 0 (log k)))) a) (* (exp (* m (+ 0 (log k)))) a)) (* (exp (* m (+ 0 (log k)))) a)) (* (* (* (* k k) (* k k)) (* k k)) (* (* (* k k) (* k k)) (* k k))))
1.4s
(/ (* (* (* (exp (* m (+ 0 (log k)))) a) (* (exp (* m (+ 0 (log k)))) a)) (* (exp (* m (+ 0 (log k)))) a)) (* (* (* (* k k) k) (* (* k k) k)) (* (* (* k k) k) (* (* k k) k))))
1.3s
(/ (* (* (* (exp (* m (+ 0 (log k)))) (exp (* m (+ 0 (log k))))) (exp (* m (+ 0 (log k))))) (* (* a a) a)) (* (* (* (* k k) k) (* (* k k) k)) (* (* (* k k) (* k k)) (* k k))))

prune10.7s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes106.0ms

Accuracy

98.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch16.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s12000×body80valid
404.0ms4232×body80nan