Details

Time bar (total: 1.3m)

sample106.0ms

Algorithm
intervals
Results
34.0ms54×body1280valid
18.0ms261×body80nan
18.0ms43×body640valid
15.0ms131×body80valid
5.0ms18×body320valid
2.0ms10×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: 29.2b

localize21.0ms

Local error

Found 2 expressions with local error:

2.4b
(- (log (+ N 1)) (log N))
2.4b
(log (+ N 1))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×add-sqr-sqrt pow1 prod-diff
14×log-pow add-cube-cbrt
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 67
Calls
2 calls:
Slowest
24.0ms
(- (log (+ N 1)) (log N))
3.0ms
(log (+ N 1))

series100.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
73.0ms
(- (log (+ N 1)) (log N))
27.0ms
(log (+ N 1))

simplify4.4s

Counts
63 → 73
Calls
63 calls:
Slowest
386.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
297.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
236.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
229.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
213.0ms
(fma 1 (log (+ N 1)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune639.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

2.2b
(log (/ (+ N 1) N))
0.0b
(/ (+ N 1) N)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×expm1-log1p-u div-exp rem-log-exp insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-+ log-pow flip-+
Counts
2 → 66
Calls
2 calls:
Slowest
34.0ms
(/ (+ N 1) N)
8.0ms
(log (/ (+ N 1) N))

series126.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
74.0ms
(/ (+ N 1) N)
52.0ms
(log (/ (+ N 1) N))

simplify2.2s

Counts
57 → 72
Calls
57 calls:
Slowest
416.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
263.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
233.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
165.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
157.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))

prune555.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

20.9b
(/ (fma (* N N) N 1) (* N (+ (* N N) (- (* 1 1) (* N 1)))))
2.2b
(log (/ (fma (* N N) N 1) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
0.0b
(* N (+ (* N N) (- (* 1 1) (* N 1))))
0.0b
(fma (* N N) N 1)

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
12×add-sqr-sqrt
11×add-cbrt-cube
10×*-un-lft-identity add-cube-cbrt
9×log-prod
7×pow1
6×times-frac associate-*r/
4×expm1-log1p-u div-exp associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ rem-log-exp associate-*r* associate-*l* prod-exp flip-+ associate-/l*
2×cbrt-undiv cbrt-unprod div-inv
1×distribute-rgt-in log-div clear-num associate-/r* frac-2neg distribute-lft-in pow-prod-down log-pow *-commutative fma-udef unswap-sqr
Counts
4 → 86
Calls
4 calls:
Slowest
116.0ms
(* N (+ (* N N) (- (* 1 1) (* N 1))))
52.0ms
(/ (fma (* N N) N 1) (* N (+ (* N N) (- (* 1 1) (* N 1)))))
23.0ms
(log (/ (fma (* N N) N 1) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
0.0ms
(fma (* N N) N 1)

series488.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
225.0ms
(/ (fma (* N N) N 1) (* N (+ (* N N) (- (* 1 1) (* N 1)))))
137.0ms
(log (/ (fma (* N N) N 1) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
94.0ms
(fma (* N N) N 1)
32.0ms
(* N (+ (* N N) (- (* 1 1) (* N 1))))

simplify7.4s

Counts
54 → 98
Calls
54 calls:
Slowest
461.0ms
(/ (* (* (fma (* N N) N 1) (fma (* N N) N 1)) (fma (* N N) N 1)) (* (* (* N N) N) (* (* (+ (* N N) (- (* 1 1) (* N 1))) (+ (* N N) (- (* 1 1) (* N 1)))) (+ (* N N) (- (* 1 1) (* N 1))))))
451.0ms
(/ (* (* (fma (* N N) N 1) (fma (* N N) N 1)) (fma (* N N) N 1)) (* (* (* N (+ (* N N) (- (* 1 1) (* N 1)))) (* N (+ (* N N) (- (* 1 1) (* N 1))))) (* N (+ (* N N) (- (* 1 1) (* N 1))))))
357.0ms
(* (* (* N N) N) (* (* (+ (* N N) (- (* 1 1) (* N 1))) (+ (* N N) (- (* 1 1) (* N 1)))) (+ (* N N) (- (* 1 1) (* N 1)))))
311.0ms
(- (log (fma (* N N) N 1)) (log (* N (+ (* N N) (- (* 1 1) (* N 1))))))
310.0ms
(+ (* (* N N) (* N N)) (- (* (- (* 1 1) (* N 1)) (- (* 1 1) (* N 1))) (* (* N N) (- (* 1 1) (* N 1)))))

prune954.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

13.0b
(- (/ (/ 1/3 N) (* N N)) (/ 1/2 (* N N)))
0.6b
(/ 1/2 (* N N))
0.4b
(/ 1/3 N)
0.1b
(/ (/ 1/3 N) (* N N))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
281×times-frac
140×add-sqr-sqrt
130×*-un-lft-identity
126×add-cube-cbrt
119×prod-diff
40×div-inv
23×add-cbrt-cube add-exp-log
19×associate-/l*
17×fma-neg
9×cbrt-undiv div-exp
6×add-log-exp difference-of-squares
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg prod-exp cbrt-unprod
2×distribute-lft-out--
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div associate-/l/
Counts
4 → 265
Calls
4 calls:
Slowest
81.0ms
(- (/ (/ 1/3 N) (* N N)) (/ 1/2 (* N N)))
18.0ms
(/ (/ 1/3 N) (* N N))
13.0ms
(/ 1/2 (* N N))
7.0ms
(/ 1/3 N)

series275.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(- (/ (/ 1/3 N) (* N N)) (/ 1/2 (* N N)))
79.0ms
(/ (/ 1/3 N) (* N N))
51.0ms
(/ 1/2 (* N N))
31.0ms
(/ 1/3 N)

simplify53.5s

Counts
369 → 277
Calls
369 calls:
Slowest
759.0ms
(fma (/ (/ (* (cbrt 1/3) (cbrt 1/3)) (sqrt N)) N) (/ (/ (cbrt 1/3) (sqrt N)) N) (- (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N))))
613.0ms
(fma (/ (/ 1 (* (cbrt N) (cbrt N))) N) (/ (/ 1/3 (cbrt N)) N) (- (* (sqrt (/ 1/2 (* N N))) (sqrt (/ 1/2 (* N N))))))
524.0ms
(fma (/ (/ (* (cbrt 1/3) (cbrt 1/3)) 1) N) (/ (/ (cbrt 1/3) N) N) (- (* (/ 1 (* N N)) 1/2)))
496.0ms
(fma (/ (/ 1 (sqrt N)) N) (/ (/ 1/3 (sqrt N)) N) (- (* (/ 1 (* N N)) 1/2)))
486.0ms
(fma (/ (/ 1 (sqrt N)) N) (/ (/ 1/3 (sqrt N)) N) (- (* (/ 1/2 N) (/ 1 N))))

prune2.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.4b

bsearch55.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s1706×body1280valid
569.0ms8167×body80nan
504.0ms1277×body640valid
449.0ms4075×body80valid
202.0ms654×body320valid
44.0ms288×body160valid