Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	63×	body	640	valid
3.0ms	123×	body	80	valid
3.0ms	36×	body	320	valid
2.0ms	17×	body	1280	valid
1.0ms	17×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7
done	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

12.0ms	(/ 1.0 (- x 1.0))
11.0ms	(/ 1.0 (+ x 1.0))
74.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
321.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (- x 1.0))
24.0ms	(/ 1.0 (+ x 1.0))
40.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
207.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify146.0ms

Counts

630 → 630

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670
done	5001	7670

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(fma 1 (/ 1.0 (+ x 1.0)) (- (/ 2.0 x)))
3.5b	(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
27×	`times-frac`
24×	`add-cube-cbrt`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-def`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`
1×	`+-commutative` `associate-+l+` `flip3--` `sum-log` `flip--`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/ 1.0 (- x 1.0))
10.0ms	(/ 1.0 (+ x 1.0))
0.0ms	(fma 1 (/ 1.0 (+ x 1.0)) (- (/ 2.0 x)))
21.0ms	(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (- x 1.0))
24.0ms	(/ 1.0 (+ x 1.0))
48.0ms	(fma 1 (/ 1.0 (+ x 1.0)) (- (/ 2.0 x)))
212.0ms	(+ (fma 1 (/ 1.0 (+ x 1.0)) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

simplify42.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	421	694
1	1527	652
2	5001	642
done	5001	642

prune259.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3)))))
0.1b	(/ 1 (pow x 3))
0.2b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 5))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
18×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `div-inv` `inv-pow`
1×	`fma-udef`

Counts

4 → 195

Calls

4 calls:

0.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3)))))
9.0ms	(/ 1 (pow x 3))
8.0ms	(/ 1 (pow x 7))
12.0ms	(/ 1 (pow x 5))

series204.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3)))))
38.0ms	(/ 1 (pow x 3))
53.0ms	(/ 1 (pow x 7))
50.0ms	(/ 1 (pow x 5))

simplify55.0ms

Counts

207 → 207

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	440	976
1	2301	770
2	5001	765
done	5001	765

prune350.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (pow x (- 3)))))
0.2b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 5))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
21×	`add-exp-log`
14×	`associate-/r*`
12×	`div-exp`
8×	`sqr-pow`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `div-inv` `inv-pow`
1×	`fma-udef`

Counts

3 → 120

Calls

3 calls:

0.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (pow x (- 3)))))
8.0ms	(/ 1 (pow x 7))
8.0ms	(/ 1 (pow x 5))

series170.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (pow x (- 3)))))
59.0ms	(/ 1 (pow x 7))
42.0ms	(/ 1 (pow x 5))

simplify38.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	311	668
1	1343	604
2	5002	540
done	5002	540

prune247.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 9.5b

bsearch96.0ms

Steps

Iters	Range		Point
9	9.85435867085541e-08	110.15968793260775	108.28044055233757
8	-3231.0590912120524	-0.1517943218839364	-110.36399629437352

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	17
1	40	17
done	40	17

end0.0ms

sample603.0ms

Algorithm

intervals

Results

194.0ms	1881×	body	640	valid
116.0ms	4156×	body	80	valid
77.0ms	553×	body	1280	valid
74.0ms	935×	body	320	valid
24.0ms	476×	body	160	valid