Details

sample307.0ms

Algorithm

intervals

Results

135.0ms	86×	body	1280	valid
86.0ms	25×	body	2560	valid
36.0ms	52×	body	640	valid
12.0ms	101×	body	80	valid
9.0ms	23×	body	320	valid
8.0ms	76×	body	80	nan
5.0ms	18×	body	160	valid

simplify5.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	7344
5	1457
4	432
3	152
2	57
1	26
0	10

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (/ i n))
2.0b	(fma (pow (+ 1 (/ i n)) n) 100 -100)
5.6b	(pow (+ 1 (/ i n)) n)
8.0b	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
53×	`*-un-lft-identity`
49×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/r*`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `unpow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `fma-def` `div-exp` `associate-/l*`
2×	`distribute-lft-out`
1×	`pow-to-exp` `+-commutative` `clear-num` `sum-log` `pow-pow` `frac-2neg` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `fma-udef` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

12.0ms	(+ 1 (/ i n))
0.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
18.0ms	(pow (+ 1 (/ i n)) n)
9.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ 1 (/ i n))
343.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
298.0ms	(pow (+ 1 (/ i n)) n)
454.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

simplify4.7s

Counts

135 → 135

Iterations

Iter	Nodes
3	5325
2	1715
1	571
0	241

prune880.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 100 i (* (* i i) (+ 50 (* i 50/3))))
0.2b	(* (* i i) (+ 50 (* i 50/3)))
0.5b	(* i 50/3)
14.7b	(/ (fma 100 i (* (* i i) (+ 50 (* i 50/3)))) (/ i n))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
52×	`add-sqr-sqrt`
49×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
11×	`pow1`
6×	`associate-r`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`associate-r/` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-/r/` `flip-+` `fma-udef`

Counts

4 → 131

Calls

4 calls:

0.0ms	(fma 100 i (* (* i i) (+ 50 (* i 50/3))))
22.0ms	(* (* i i) (+ 50 (* i 50/3)))
11.0ms	(* i 50/3)
12.0ms	(/ (fma 100 i (* (* i i) (+ 50 (* i 50/3)))) (/ i n))

series293.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma 100 i (* (* i i) (+ 50 (* i 50/3))))
124.0ms	(* (* i i) (+ 50 (* i 50/3)))
25.0ms	(* i 50/3)
92.0ms	(/ (fma 100 i (* (* i i) (+ 50 (* i 50/3)))) (/ i n))

simplify1.3s

Counts

143 → 143

Iterations

Iter	Nodes
2	2047
1	619
0	243

prune622.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* n (+ (* 50 i) 100))
4.5b	(fma (* (* i i) n) 50/3 (* n (+ (* 50 i) 100)))
6.6b	(* (* i i) n)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `fma-udef`

Counts

3 → 58

Calls

3 calls:

19.0ms	(* n (+ (* 50 i) 100))
0.0ms	(fma (* (* i i) n) 50/3 (* n (+ (* 50 i) 100)))
15.0ms	(* (* i i) n)

series121.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* n (+ (* 50 i) 100))
37.0ms	(fma (* (* i i) n) 50/3 (* n (+ (* 50 i) 100)))
23.0ms	(* (* i i) n)

simplify1.3s

Counts

67 → 67

Iterations

Iter	Nodes
3	3461
2	905
1	280
0	99

prune316.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

6.2b	(/ (* i (+ 100 (* (fma 50/3 i 50) i))) (* (cbrt (/ i n)) (cbrt (/ i n))))
13.0b	(cbrt (/ i n))
13.0b	(cbrt (/ i n))
13.0b	(cbrt (/ i n))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
28×	`times-frac`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`add-exp-log`
12×	`add-cbrt-cube`
7×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `associate-*r/` `associate-/r/`
2×	`associate-/l/`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `flip3-+` `associate-l/` `flip-+` `associate-/l*`

Counts

4 → 104

Calls

4 calls:

15.0ms	(/ (* i (+ 100 (* (fma 50/3 i 50) i))) (* (cbrt (/ i n)) (cbrt (/ i n))))
1.0ms	(cbrt (/ i n))
1.0ms	(cbrt (/ i n))
1.0ms	(cbrt (/ i n))

series338.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* i (+ 100 (* (fma 50/3 i 50) i))) (* (cbrt (/ i n)) (cbrt (/ i n))))
66.0ms	(cbrt (/ i n))
72.0ms	(cbrt (/ i n))
88.0ms	(cbrt (/ i n))

simplify2.6s

Counts

116 → 116

Iterations

Iter	Nodes
3	7997
2	1552
1	452
0	178

prune455.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 5.2b

regimes245.0ms

Accuracy

63% (10.3b remaining)

Error of 16.2b against oracle of 5.9b and baseline of 33.8b

bsearch346.0ms

Steps

Iters	Range		Point
11	2.9348777329819658e-12	3.1891227468784625e+20	4.5457902375689345
9	-1.9696345359431407e-07	-4.750217372511675e-17	-2.7755718047646672e-12

simplify5.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.3s	2440×	body	1280	valid
2.8s	957×	body	2560	valid
964.0ms	1643×	body	640	valid
354.0ms	877×	body	320	valid
314.0ms	3092×	body	80	valid
254.0ms	2249×	body	80	nan
101.0ms	445×	body	160	valid
28.0ms	6×	body	5120	valid