Details

sample76.0ms

Algorithm

intervals

Results

43.0ms	391×	body	80	valid
14.0ms	145×	body	80	nan

simplify946.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	655
4	215
3	97
2	52
1	26
0	12

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (pow k m) a)
2.3b	(/ (* (pow k m) a) (fma (+ k 10) k 1))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
12×	`add-sqr-sqrt`
9×	`add-cbrt-cube`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`associate-/r` `times-frac` `associate-r*` `unswap-sqr`
2×	`expm1-log1p-u` `pow-to-exp` `pow1` `cbrt-undiv` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`clear-num` `frac-2neg` `-commutative` `div-inv` `associate-/l`

Counts

2 → 54

Calls

2 calls:

9.0ms	(* (pow k m) a)
14.0ms	(/ (* (pow k m) a) (fma (+ k 10) k 1))

series265.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(* (pow k m) a)
140.0ms	(/ (* (pow k m) a) (fma (+ k 10) k 1))

simplify706.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	2001
2	1033
1	311
0	129

prune282.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 2.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (sqrt (fma (+ k 10) k 1)))
0.0b	(* (/ (pow k m) (sqrt (fma (+ k 10) k 1))) (/ a (sqrt (fma (+ k 10) k 1))))
13.1b	(sqrt (fma (+ k 10) k 1))
13.1b	(sqrt (fma (+ k 10) k 1))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-sqr-sqrt`
110×	`times-frac`
64×	`sqrt-prod`
61×	`*-un-lft-identity` `add-cube-cbrt`
46×	`associate-l`
30×	`add-exp-log`
24×	`unpow-prod-down`
22×	`associate-r`
21×	`unswap-sqr`
18×	`add-cbrt-cube`
12×	`sqr-pow`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 190

Calls

4 calls:

8.0ms	(/ a (sqrt (fma (+ k 10) k 1)))
39.0ms	(* (/ (pow k m) (sqrt (fma (+ k 10) k 1))) (/ a (sqrt (fma (+ k 10) k 1))))
2.0ms	(sqrt (fma (+ k 10) k 1))
2.0ms	(sqrt (fma (+ k 10) k 1))

series343.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ a (sqrt (fma (+ k 10) k 1)))
173.0ms	(* (/ (pow k m) (sqrt (fma (+ k 10) k 1))) (/ a (sqrt (fma (+ k 10) k 1))))
50.0ms	(sqrt (fma (+ k 10) k 1))
37.0ms	(sqrt (fma (+ k 10) k 1))

simplify676.0ms

Counts

202 → 202

Iterations

Iter	Nodes
done	2000
1	747
0	265

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (pow k m) (sqrt (fma (+ k 10) k 1)))) (/ a (sqrt (fma (+ k 10) k 1))))
13.1b	(sqrt (fma (+ k 10) k 1))
13.1b	(sqrt (fma (+ k 10) k 1))
13.1b	(sqrt (fma (+ k 10) k 1))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

127×	`add-sqr-sqrt`
123×	`sqrt-prod`
94×	`times-frac`
49×	`associate-l`
48×	`*-un-lft-identity` `add-cube-cbrt`
24×	`unpow-prod-down` `unswap-sqr`
22×	`associate-r`
12×	`sqr-pow`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`sqrt-div` `prod-exp` `cbrt-unprod` `div-inv`
1×	`frac-times` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 162

Calls

4 calls:

25.0ms	(* (sqrt (/ (pow k m) (sqrt (fma (+ k 10) k 1)))) (/ a (sqrt (fma (+ k 10) k 1))))
2.0ms	(sqrt (fma (+ k 10) k 1))
1.0ms	(sqrt (fma (+ k 10) k 1))
1.0ms	(sqrt (fma (+ k 10) k 1))

series350.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (sqrt (/ (pow k m) (sqrt (fma (+ k 10) k 1)))) (/ a (sqrt (fma (+ k 10) k 1))))
35.0ms	(sqrt (fma (+ k 10) k 1))
37.0ms	(sqrt (fma (+ k 10) k 1))
33.0ms	(sqrt (fma (+ k 10) k 1))

simplify868.0ms

Counts

174 → 174

Iterations

Iter	Nodes
done	2000
2	1526
1	594
0	255

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ (exp (- (- (* m (log k))))) (/ (* (* k k) (* k k)) a))
7.8b	(/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k)))
10.3b	(- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k))))
12.1b	(fma (/ (exp (- (- (* m (log k))))) (/ (* (* k k) (* k k)) a)) 99 (- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k)))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

96×	`distribute-neg-in`
95×	`times-frac`
65×	`add-cbrt-cube`
53×	`add-exp-log`
49×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`log-prod` `exp-sum`
26×	`prod-exp` `cbrt-unprod`
24×	`distribute-rgt-in` `distribute-lft-in`
20×	`cbrt-undiv` `div-exp`
13×	`div-inv`
10×	`associate-/l*`
8×	`associate-/r*`
6×	`add-log-exp`
5×	`prod-diff` `associate-/l/`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`exp-neg` `associate-*r/` `frac-sub`
2×	`neg-sub0` `clear-num` `frac-2neg` `exp-diff`
1×	`frac-times` `sub-neg` `flip3--` `fma-neg` `diff-log` `associate-*l/` `associate-/r/` `un-div-inv` `fma-udef` `flip--`

Counts

4 → 179

Calls

4 calls:

27.0ms	(/ (exp (- (- (* m (log k))))) (/ (* (* k k) (* k k)) a))
54.0ms	(/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k)))
30.0ms	(- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k))))
0.0ms	(fma (/ (exp (- (- (* m (log k))))) (/ (* (* k k) (* k k)) a)) 99 (- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k)))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (exp (- (- (* m (log k))))) (/ (* (* k k) (* k k)) a))
108.0ms	(/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k)))
213.0ms	(- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k))))
213.0ms	(fma (/ (exp (- (- (* m (log k))))) (/ (* (* k k) (* k k)) a)) 99 (- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (* 10 a) (exp (- (- (* m (log k)))))) (* k (* k k)))))

simplify980.0ms

Counts

191 → 191

Iterations

Iter	Nodes
done	2000
1	1248
0	463

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes98.0ms

Accuracy

99.1% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.2b

bsearch65.0ms

Steps

Iters	Range		Point
7	1.1611962541267347e+129	2.0056155501151023e+130	8.14236707063809e+129

simplify11.0ms

Iterations

Iter	Nodes
done	57
3	57
2	52
1	45
0	32

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.8s	11992×	body	80	valid
580.0ms	4229×	body	80	nan