Details

sample16.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify8.0ms

Calls

1 calls:

Slowest

8.0ms

(/ x (+ (* x x) 1))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize13.0ms

Local error

Found 1 expressions with local error:

16.5b

(/ x (fma x x 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-/r*`
2×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
1×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Calls

1 calls:

Slowest

1.0ms

(/ x (fma x x 1))

series53.0ms

Calls

1 calls:

Slowest

53.0ms

(/ x (fma x x 1))

simplify294.0ms

Calls

6 calls:

Slowest

102.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
87.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
85.0ms	(- (+ x (pow x 5)) (pow x 3))
8.0ms	(sqrt (fma x x 1))
7.0ms	(cbrt (fma x x 1))

prune169.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

16.4b	(sqrt (fma x x 1))
16.4b	(sqrt (fma x x 1))
0.0b	(/ x (sqrt (fma x x 1)))
0.0b	(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`times-frac` `sqrt-prod`
12×	`associate-/r*`
9×	`div-inv`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `pow1/2`
1×	`cbrt-undiv` `div-exp` `associate-/l/`

Calls

4 calls:

Slowest

10.0ms	(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
8.0ms	(sqrt (fma x x 1))
2.0ms	(sqrt (fma x x 1))
2.0ms	(/ x (sqrt (fma x x 1)))

series305.0ms

Calls

4 calls:

Slowest

88.0ms	(/ x (sqrt (fma x x 1)))
85.0ms	(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
68.0ms	(sqrt (fma x x 1))
64.0ms	(sqrt (fma x x 1))

simplify3.4s

Calls

84 calls:

Slowest

315.0ms	(/ (* (* (/ x (sqrt (fma x x 1))) (/ x (sqrt (fma x x 1)))) (/ x (sqrt (fma x x 1)))) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
195.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
189.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
156.0ms	(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
154.0ms	(- (+ (* 1/2 (pow x 2)) 1) (* 1/8 (pow x 4)))

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

16.3b	(* x (/ 1 (fma x x 1)))
0.2b	(/ 1 (fma x x 1))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
3×	`pow1` `associate-/r*` `add-exp-log`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`rec-exp` `clear-num` `frac-2neg` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Calls

2 calls:

Slowest

2.0ms	(* x (/ 1 (fma x x 1)))
1.0ms	(/ 1 (fma x x 1))

series130.0ms

Calls

2 calls:

Slowest

68.0ms	(* x (/ 1 (fma x x 1)))
62.0ms	(/ 1 (fma x x 1))

simplify532.0ms

Calls

16 calls:

Slowest

92.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
86.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
81.0ms	(- (+ x (pow x 5)) (pow x 3))
69.0ms	(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (/ 1 (pow x 4)))
63.0ms	(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (/ 1 (pow x 4)))

prune255.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

20.2b	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
0.2b	(/ (/ 1 x) x)
0.1b	(/ 1 (pow x 5))
0.1b	(/ (/ (/ 1 x) x) x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`prod-diff` `add-cube-cbrt`
15×	`div-inv`
8×	`associate-/l*`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `associate-/r*` `frac-2neg`
2×	`rec-exp` `distribute-lft-out--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `frac-sub` `pow-flip` `flip--` `inv-pow` `difference-of-squares`

Calls

4 calls:

Slowest

18.0ms	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
11.0ms	(/ (/ (/ 1 x) x) x)
6.0ms	(/ (/ 1 x) x)
2.0ms	(/ 1 (pow x 5))

series264.0ms

Calls

4 calls:

Slowest

131.0ms	(- (/ 1 (pow x 5)) (/ (/ (/ 1 x) x) x))
65.0ms	(/ 1 (pow x 5))
48.0ms	(/ (/ (/ 1 x) x) x)
20.0ms	(/ (/ 1 x) x)

simplify4.4s

Calls

63 calls:

Slowest

183.0ms	(fma (sqrt (/ 1 (pow x 5))) (sqrt (/ 1 (pow x 5))) (- (* (/ 1 x) (/ (/ 1 x) x))))
178.0ms	(fma (sqrt (/ 1 (pow x 5))) (sqrt (/ 1 (pow x 5))) (- (* (/ (/ (/ 1 x) x) x) 1)))
169.0ms	(fma (* (cbrt (/ 1 (pow x 5))) (cbrt (/ 1 (pow x 5)))) (cbrt (/ 1 (pow x 5))) (- (* (/ 1 x) (/ (/ 1 x) x))))
166.0ms	(fma (* (cbrt (/ 1 (pow x 5))) (cbrt (/ 1 (pow x 5)))) (cbrt (/ 1 (pow x 5))) (- (* (/ (/ (/ 1 x) x) x) 1)))
164.0ms	(- (* 1 x) (* (pow x 5) (/ (/ 1 x) x)))

prune986.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes64.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch112.0ms

end0.0ms

sample569.0ms

Algorithm

intervals

Results

490.0ms

8000×

body

valid