Details

Time bar (total: 1.2m)

sample100.0ms

Algorithm
intervals
Results
30.0ms53×body1280valid
20.0ms285×body80nan
17.0ms46×body640valid
12.0ms125×body80valid
5.0ms20×body320valid
2.0ms12×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(- (log (+ N 1)) (log N))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize31.0ms

Local error

Found 1 expressions with local error:

2.7b
(- (log1p N) (log N))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt prod-diff
10×add-cube-cbrt
5×pow1
4×log-pow
3×log-prod fma-neg associate--r+
2×diff-log distribute-lft-out-- add-log-exp
1×expm1-log1p-u log1p-udef sub-neg flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
Counts
1 → 37
Calls
1 calls:
Slowest
11.0ms
(- (log1p N) (log N))

series71.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
71.0ms
(- (log1p N) (log N))

simplify2.1s

Counts
38 → 40
Calls
38 calls:
Slowest
204.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
159.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
157.0ms
(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))
155.0ms
(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
151.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune277.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

13.6b
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
0.3b
(/ -1/2 (* N N))
0.2b
(/ -1/3 (* (* N N) N))
0.1b
(* (* N N) N)

rewrite291.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
35×prod-diff
30×add-sqr-sqrt
27×add-cube-cbrt
23×pow1 add-cbrt-cube add-exp-log
21×times-frac
18×distribute-lft-out
16×div-inv
9×add-log-exp
7×prod-exp cbrt-unprod
6×pow-plus pow-prod-up associate-/l*
5×cbrt-undiv fma-neg div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* pow-prod-down frac-sub distribute-lft-out--
2×pow2 clear-num associate-/r* frac-2neg diff-log frac-add pow-sqr
1×sum-log sub-neg flip3-+ flip3-- associate-*l* pow3 associate--l+ *-commutative flip-+ flip-- sub-div difference-of-squares unswap-sqr
Counts
4 → 146
Calls
4 calls:
Slowest
237.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
25.0ms
(/ -1/3 (* (* N N) N))
14.0ms
(* (* N N) N)
12.0ms
(/ -1/2 (* N N))

series162.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
48.0ms
(* (* N N) N)
47.0ms
(/ -1/3 (* (* N N) N))
33.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
33.0ms
(/ -1/2 (* N N))

simplify24.1s

Counts
140 → 158
Calls
140 calls:
Slowest
680.0ms
(* (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ 1 N)))) (* (* N N) N))
635.0ms
(- (* (+ (pow (/ -1/2 (* N N)) 3) (pow (/ 1 N) 3)) (* (* N N) N)) (* (+ (* (/ -1/2 (* N N)) (/ -1/2 (* N N))) (- (* (/ 1 N) (/ 1 N)) (* (/ -1/2 (* N N)) (/ 1 N)))) -1/3))
556.0ms
(fma (* (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N)))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (* (/ -1/3 N) (/ 1 (* N N)))))
498.0ms
(* (* (* (* N N) (* N N)) (* N N)) (* (* N N) N))
474.0ms
(fma (* (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N)))) (cbrt (+ (/ -1/2 (* N N)) (/ 1 N))) (- (* (/ (cbrt -1/3) N) (/ (* (cbrt -1/3) (cbrt -1/3)) (* N N)))))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

20.8b
(- (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N)) (/ -1/3 (* (* N N) N)))
2.4b
(log (exp (/ -1/2 (* N N))))
0.3b
(/ -1/2 (* N N))
0.2b
(/ -1/3 (* (* N N) N))

rewrite495.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
49×prod-diff
36×distribute-lft-out
35×add-sqr-sqrt
33×add-cube-cbrt
30×times-frac
28×div-inv
26×log-pow
23×pow1
18×add-cbrt-cube add-exp-log
8×add-log-exp
7×exp-prod fma-neg
6×associate-/l*
5×cbrt-undiv div-exp distribute-lft-out--
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×log-prod
2×clear-num associate-/r* frac-2neg diff-log frac-sub
1×sum-log sub-neg flip3-+ flip3-- rem-log-exp associate--l+ flip-+ flip-- difference-of-squares
Counts
4 → 153
Calls
4 calls:
Slowest
454.0ms
(- (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N)) (/ -1/3 (* (* N N) N)))
17.0ms
(log (exp (/ -1/2 (* N N))))
14.0ms
(/ -1/3 (* (* N N) N))
9.0ms
(/ -1/2 (* N N))

series163.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
51.0ms
(log (exp (/ -1/2 (* N N))))
46.0ms
(/ -1/3 (* (* N N) N))
37.0ms
(/ -1/2 (* N N))
29.0ms
(- (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N)) (/ -1/3 (* (* N N) N)))

simplify31.1s

Counts
162 → 165
Calls
162 calls:
Slowest
697.0ms
(- (* (- (* (log (exp (/ -1/2 (* N N)))) (log (exp (/ -1/2 (* N N))))) (* (/ 1 N) (/ 1 N))) (* (* N N) N)) (* (- (log (exp (/ -1/2 (* N N)))) (/ 1 N)) -1/3))
665.0ms
(fma 1 (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N)) (- (* (/ 1 (* (* N N) N)) -1/3)))
514.0ms
(fma (* (cbrt (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N))) (cbrt (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N)))) (cbrt (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N))) (- (* (/ -1/3 N) (/ 1 (* N N)))))
469.0ms
(fma (- (/ -1/3 N)) (/ 1 (* N N)) (* (/ -1/3 N) (/ 1 (* N N))))
456.0ms
(* (+ (* (log (exp (/ -1/2 (* N N)))) (log (exp (/ -1/2 (* N N))))) (- (* (/ 1 N) (/ 1 N)) (* (log (exp (/ -1/2 (* N N)))) (/ 1 N)))) (* (* N N) N))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1/3 N)
0.1b
(fma (/ 1 N) (/ 1/3 N) 1)
0.0b
(* (/ 1 N) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)))
0.0b
(+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
32×*-un-lft-identity
29×times-frac
27×add-cube-cbrt
15×add-exp-log
13×fma-def associate-*l*
11×add-cbrt-cube
6×pow1 add-log-exp
4×expm1-log1p-u associate-*r* prod-exp insert-posit16 log1p-expm1-u
3×associate-/r* flip3-+ div-exp flip-+ div-inv associate-/l* unswap-sqr
2×frac-times cbrt-undiv associate-*r/ cbrt-unprod fma-udef distribute-lft-out
1×distribute-rgt-in +-commutative rec-exp associate-+r+ clear-num sum-log frac-2neg distribute-lft-in 1-exp pow-prod-down associate-*l/ *-commutative
Counts
4 → 115
Calls
4 calls:
Slowest
51.0ms
(* (/ 1 N) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)))
18.0ms
(+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1))
8.0ms
(/ 1/3 N)
0.0ms
(fma (/ 1 N) (/ 1/3 N) 1)

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(fma (/ 1 N) (/ 1/3 N) 1)
57.0ms
(* (/ 1 N) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)))
33.0ms
(/ 1/3 N)
27.0ms
(+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1))

simplify7.3s

Counts
86 → 127
Calls
86 calls:
Slowest
493.0ms
(* (* (* (/ 1 N) (/ 1 N)) (/ 1 N)) (* (* (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1))) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1))))
440.0ms
(* (/ (* (* 1 1) 1) (* (* N N) N)) (* (* (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1))) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1))))
432.0ms
(* N (+ (* (/ -1/2 N) (/ -1/2 N)) (- (* (fma (/ 1 N) (/ 1/3 N) 1) (fma (/ 1 N) (/ 1/3 N) 1)) (* (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)))))
419.0ms
(* N (- (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)))
369.0ms
(* (/ 1 N) (+ (/ -1/2 N) (fma (/ 1 N) (/ 1/3 N) 1)))

prune946.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.2b

bsearch89.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.5s1721×body1280valid
628.0ms7851×body80nan
474.0ms4115×body80valid
472.0ms1254×body640valid
163.0ms633×body320valid
46.0ms277×body160valid