Details

Time bar (total: 44.0s)

sample327.0ms

Algorithm
intervals
Results
120.0ms76×body1280valid
98.0ms31×body2560valid
48.0ms49×body640valid
15.0ms104×body80valid
13.0ms24×body320valid
10.0ms75×body80nan
5.0ms14×body160valid

simplify5.1s

Counts
1 → 1
Iterations
IterNodes
67344
51457
4432
3152
257
126
010

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.0b

localize18.0ms

Local error

Found 3 expressions with local error:

1.1b
(fma (pow (+ 1 (/ i n)) n) 100 -100)
8.0b
(pow (+ 1 (/ i n)) n)
10.2b
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
49×*-un-lft-identity
47×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
9×add-exp-log
8×add-cbrt-cube
5×div-inv
4×pow1 unpow-prod-down
3×expm1-log1p-u cbrt-undiv pow-unpow div-exp log1p-expm1-u associate-/l* add-log-exp
1×pow-to-exp clear-num pow-pow frac-2neg pow-exp associate-/r/ fma-udef distribute-lft-out sqr-pow
Counts
3 → 102
Calls
3 calls:
0.0ms
(fma (pow (+ 1 (/ i n)) n) 100 -100)
9.0ms
(pow (+ 1 (/ i n)) n)
6.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

series1.1s

Counts
3 → 9
Calls
3 calls:
306.0ms
(fma (pow (+ 1 (/ i n)) n) 100 -100)
301.0ms
(pow (+ 1 (/ i n)) n)
444.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

simplify3.5s

Counts
111 → 111
Iterations
IterNodes
34900
21581
1502
0219

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize32.0ms

Local error

Found 4 expressions with local error:

2.1b
(fma (exp (* (log1p (/ i n)) n)) 100 -100)
6.8b
(log1p (/ i n))
9.9b
(* (log1p (/ i n)) n)
10.2b
(/ (fma (exp (* (log1p (/ i n)) n)) 100 -100) (/ i n))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
11×add-cbrt-cube add-exp-log
6×pow1
5×expm1-log1p-u div-inv
4×log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
1×log1p-udef clear-num frac-2neg pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 113
Calls
4 calls:
0.0ms
(fma (exp (* (log1p (/ i n)) n)) 100 -100)
0.0ms
(log1p (/ i n))
6.0ms
(* (log1p (/ i n)) n)
6.0ms
(/ (fma (exp (* (log1p (/ i n)) n)) 100 -100) (/ i n))

series853.0ms

Counts
4 → 12
Calls
4 calls:
289.0ms
(fma (exp (* (log1p (/ i n)) n)) 100 -100)
68.0ms
(log1p (/ i n))
119.0ms
(* (log1p (/ i n)) n)
377.0ms
(/ (fma (exp (* (log1p (/ i n)) n)) 100 -100) (/ i n))

simplify3.2s

Counts
125 → 125
Iterations
IterNodes
34839
21610
1498
0218

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize21.0ms

Local error

Found 4 expressions with local error:

2.1b
(+ (* (exp (* (log1p (/ i n)) n)) 100) -100)
6.8b
(log1p (/ i n))
9.9b
(* (log1p (/ i n)) n)
10.2b
(/ (+ (* (exp (* (log1p (/ i n)) n)) 100) -100) (/ i n))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
11×add-cbrt-cube add-exp-log
6×pow1 add-log-exp
5×expm1-log1p-u div-inv
4×log1p-expm1-u
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
2×flip3-+ flip-+ associate-/l/
1×+-commutative log1p-udef clear-num sum-log fma-def frac-2neg pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 119
Calls
4 calls:
13.0ms
(+ (* (exp (* (log1p (/ i n)) n)) 100) -100)
1.0ms
(log1p (/ i n))
11.0ms
(* (log1p (/ i n)) n)
30.0ms
(/ (+ (* (exp (* (log1p (/ i n)) n)) 100) -100) (/ i n))

series833.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(+ (* (exp (* (log1p (/ i n)) n)) 100) -100)
68.0ms
(log1p (/ i n))
94.0ms
(* (log1p (/ i n)) n)
365.0ms
(/ (+ (* (exp (* (log1p (/ i n)) n)) 100) -100) (/ i n))

simplify3.5s

Counts
131 → 131
Iterations
IterNodes
35271
21809
1583
0233

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.1b

localize46.0ms

Local error

Found 4 expressions with local error:

9.9b
(* (log1p (/ i n)) n)
9.9b
(* (log1p (/ i n)) n)
9.9b
(* (log1p (/ i n)) (+ n n))
10.2b
(/ (/ (fma (exp (+ (* (log1p (/ i n)) n) (* (log1p (/ i n)) (+ n n)))) 1000000 -1000000) (fma (exp (* (log1p (/ i n)) n)) (* (exp (* (log1p (/ i n)) n)) 10000) (+ (* (exp (* (log1p (/ i n)) n)) 10000) 10000))) (/ i n))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
421×times-frac
216×add-sqr-sqrt
212×*-un-lft-identity
210×add-cube-cbrt
29×div-inv
22×add-cbrt-cube add-exp-log
18×associate-*r*
13×associate-/r* associate-/l*
10×pow1
9×associate-*l*
8×cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-out pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
2×associate-*r/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in distribute-lft1-in flip3-+ count-2 distribute-rgt1-in associate-/r/ flip-+ associate-/l/
Counts
4 → 290
Calls
4 calls:
5.0ms
(* (log1p (/ i n)) n)
5.0ms
(* (log1p (/ i n)) n)
19.0ms
(* (log1p (/ i n)) (+ n n))
10.0ms
(/ (/ (fma (exp (+ (* (log1p (/ i n)) n) (* (log1p (/ i n)) (+ n n)))) 1000000 -1000000) (fma (exp (* (log1p (/ i n)) n)) (* (exp (* (log1p (/ i n)) n)) 10000) (+ (* (exp (* (log1p (/ i n)) n)) 10000) 10000))) (/ i n))

series7.9s

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (log1p (/ i n)) n)
80.0ms
(* (log1p (/ i n)) n)
83.0ms
(* (log1p (/ i n)) (+ n n))
7.7s
(/ (/ (fma (exp (+ (* (log1p (/ i n)) n) (* (log1p (/ i n)) (+ n n)))) 1000000 -1000000) (fma (exp (* (log1p (/ i n)) n)) (* (exp (* (log1p (/ i n)) n)) 10000) (+ (* (exp (* (log1p (/ i n)) n)) 10000) 10000))) (/ i n))

simplify2.5s

Counts
302 → 302
Iterations
IterNodes
25027
11629
0542

prune3.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.1b

regimes199.0ms

Accuracy

41.7% (13.3b remaining)

Error of 29.4b against oracle of 16.2b and baseline of 38.9b

bsearch689.0ms

Steps
ItersRangePoint
4
1.6082570930759333e+147
2.5209115378479715e+147
2.3783092808523403e+147
7
1.4604094432221333e-135
6.06229621642618e-134
1.8317810149458703e-135
10
-3.3361098338481354e-09
-9.773814465833408e-23
-3.9175258711905035e-19
8
-3.952242572080396e+27
-1.0293047184176334e+23
-2.81251599798957e+26
8
-2.8945583997465117e+50
-1.0151626126287093e+46
-6.741071980134238e+48
8
-2.369259881398571e+131
-6.226433034214745e+127
-2.8503749344901687e+128

simplify23.0ms

Iterations
IterNodes
290
190
076

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.6s2391×body1280valid
2.2s1010×body2560valid
942.0ms1666×body640valid
359.0ms446×body160valid
298.0ms3060×body80valid
289.0ms866×body320valid
162.0ms2217×body80nan
22.0ms6×body5120valid