Details

sample52.0ms

Algorithm

intervals

Results

24.0ms	69×	body	640	valid
9.0ms	132×	body	80	valid
5.0ms	27×	body	320	valid
4.0ms	12×	body	1280	valid
2.0ms	16×	body	160	valid

simplify179.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize28.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

743×	`*-un-lft-identity`
715×	`times-frac`
544×	`add-sqr-sqrt`
494×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
99×	`distribute-lft-out`
72×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
22×	`distribute-lft-out--`
20×	`difference-of-squares`
18×	`fma-neg`
13×	`fma-def`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `1-exp` `frac-sub` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 648

Calls

4 calls:

Slowest

174.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
40.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
14.0ms	(/ 1 (+ x 1))
13.0ms	(/ 1 (- x 1))

series171.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

107.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
26.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
20.0ms	(/ 1 (- x 1))
18.0ms	(/ 1 (+ x 1))

simplify1.4s

Counts: 660 → 660

prune6.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))
0.0b	(fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2)))
0.0b	(/ 1 (- x 1))
0.0b	(/ 1 (+ x 1))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
33×	`times-frac`
26×	`add-cube-cbrt`
12×	`add-exp-log`
11×	`associate-/r*`
9×	`distribute-lft-out` `add-log-exp`
8×	`add-cbrt-cube` `difference-of-squares`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`sum-log` `fma-def` `div-inv`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `fma-udef` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l+` `associate-+r+` `flip3--` `flip--`

Counts

4 → 126

Calls

4 calls:

Slowest

47.0ms	(+ (fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))
8.0ms	(/ 1 (- x 1))
8.0ms	(/ 1 (+ x 1))
0.0ms	(fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(+ (fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))
37.0ms	(fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2)))
15.0ms	(/ 1 (+ x 1))
15.0ms	(/ 1 (- x 1))

simplify1.6s

Counts: 138 → 138

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

31.6b	(fma (- x (* 2 (+ x 1))) (- x 1) (* (+ x 1) x))
0.0b	(* (* (+ x 1) x) (- x 1))
0.0b	(- x (* 2 (+ x 1)))
0.0b	(* (+ x 1) x)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
21×	`prod-diff` `add-cube-cbrt`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`associate-r` `associate-*l/`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`sub-neg` `fma-neg`
2×	`associate-r/` `-commutative` `associate--r+` `difference-of-squares`
1×	`diff-log` `difference-of-sqr-1` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

Slowest

32.0ms	(* (* (+ x 1) x) (- x 1))
18.0ms	(* (+ x 1) x)
5.0ms	(- x (* 2 (+ x 1)))
0.0ms	(fma (- x (* 2 (+ x 1))) (- x 1) (* (+ x 1) x))

series413.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

209.0ms	(fma (- x (* 2 (+ x 1))) (- x 1) (* (+ x 1) x))
123.0ms	(* (* (+ x 1) x) (- x 1))
42.0ms	(* (+ x 1) x)
39.0ms	(- x (* 2 (+ x 1)))

simplify2.0s

Counts: 125 → 125

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (pow x 5))
0.2b	(/ 2 (pow x 7))
0.1b	(/ 2 (* x (* x x)))
0.0b	(* x (* x x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
18×	`pow1`
15×	`associate-/r*`
9×	`div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

Slowest

25.0ms	(/ 2 (* x (* x x)))
14.0ms	(* x (* x x))
5.0ms	(/ 2 (pow x 5))
5.0ms	(/ 2 (pow x 7))

series331.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(/ 2 (pow x 7))
98.0ms	(/ 2 (pow x 5))
64.0ms	(/ 2 (* x (* x x)))
52.0ms	(* x (* x x))

simplify3.0s

Counts: 161 → 161

prune1.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes48.0ms

Accuracy

98.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.8b

bsearch175.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

840.0ms	1859×	body	640	valid
407.0ms	4169×	body	80	valid
376.0ms	946×	body	320	valid
272.0ms	567×	body	1280	valid
81.0ms	459×	body	160	valid