Details

sample29.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize15.0ms

Local error

Found 1 expressions with local error:

14.6b

(/ x (fma x x 1))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 30

Calls

1 calls:

Slowest

10.0ms

(/ x (fma x x 1))

series72.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

72.0ms

(/ x (fma x x 1))

simplify1.6s

Counts

28 → 33

Calls

28 calls:

Slowest

536.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
283.0ms	(- (+ x (pow x 5)) (pow x 3))
230.0ms	(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
147.0ms	(/ (* (* x x) x) (* (* (fma x x 1) (fma x x 1)) (fma x x 1)))
51.0ms	(/ (* (cbrt x) (cbrt x)) (* (cbrt (fma x x 1)) (cbrt (fma x x 1))))

prune284.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

14.5b	(sqrt (fma x x 1))
14.5b	(sqrt (fma x x 1))
0.0b	(/ x (sqrt (fma x x 1)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 74

Calls

3 calls:

Slowest

8.0ms	(/ x (sqrt (fma x x 1)))
1.0ms	(sqrt (fma x x 1))
1.0ms	(sqrt (fma x x 1))

series230.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

121.0ms	(/ x (sqrt (fma x x 1)))
56.0ms	(sqrt (fma x x 1))
53.0ms	(sqrt (fma x x 1))

simplify3.2s

Counts

65 → 83

Calls

65 calls:

Slowest

456.0ms	(/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
345.0ms	(- (+ x (* 3/8 (pow x 5))) (* 1/2 (pow x 3)))
235.0ms	(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
220.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
197.0ms	(- (* 1/2 (/ 1 (pow x 2))) (+ (* 3/8 (/ 1 (pow x 4))) 1))

prune793.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 1 expressions with local error:

13.9b

(fma x (- 1 (* x x)) (pow x 5))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

Slowest

1.0ms

(fma x (- 1 (* x x)) (pow x 5))

series72.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

72.0ms

(fma x (- 1 (* x x)) (pow x 5))

simplify849.0ms

Counts

3 → 14

Calls

3 calls:

Slowest

292.0ms	(- (+ x (pow x 5)) (pow x 3))
280.0ms	(- (+ x (pow x 5)) (pow x 3))
275.0ms	(- (+ x (pow x 5)) (pow x 3))

prune127.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

18.7b	(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
0.1b	(/ 1 (* (* x x) x))
0.1b	(* (* x x) x)
0.1b	(/ 1 (pow x 5))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
102×	`times-frac`
70×	`add-sqr-sqrt` `prod-diff`
67×	`add-cube-cbrt`
64×	`distribute-lft-out`
57×	`div-inv`
43×	`pow1`
39×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`pow-flip`
12×	`unpow-prod-down` `pow-plus` `div-exp` `prod-exp` `pow-prod-up`
10×	`fma-neg` `distribute-lft-out--`
9×	`add-log-exp`
8×	`associate-/r*`
6×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod` `associate-/l*`
4×	`pow2` `expm1-log1p-u` `cbrt-undiv` `pow-sqr` `insert-posit16` `log1p-expm1-u` `sqr-pow`
3×	`pow-to-exp` `associate-r` `pow-exp` `frac-sub`
2×	`clear-num` `frac-2neg` `diff-log` `pow3` `inv-pow`
1×	`sum-log` `sub-neg` `flip3-+` `flip3--` `associate-l` `frac-add` `associate--l+` `*-commutative` `flip-+` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 243

Calls

4 calls:

Slowest

178.0ms	(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
27.0ms	(/ 1 (* (* x x) x))
20.0ms	(* (* x x) x)
11.0ms	(/ 1 (pow x 5))

series160.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

52.0ms	(/ 1 (pow x 5))
37.0ms	(/ 1 (* (* x x) x))
36.0ms	(- (+ (/ 1 x) (/ 1 (pow x 5))) (/ 1 (* (* x x) x)))
35.0ms	(* (* x x) x)

simplify49.6s

Counts

280 → 255

Calls

280 calls:

Slowest

1.0s	(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
1.0s	(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
687.0ms	(fma 1 (+ (/ 1 x) (/ 1 (pow x 5))) (- (* (/ (sqrt 1) x) (/ (sqrt 1) (* x x)))))
581.0ms	(* (+ (* (/ 1 x) (/ 1 x)) (- (* (/ 1 (pow x 5)) (/ 1 (pow x 5))) (* (/ 1 x) (/ 1 (pow x 5))))) (* (* x x) x))
520.0ms	(/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt x) (cbrt x)) 5))

prune2.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch92.0ms

end1.0ms

sample647.0ms

Algorithm

intervals

Results

555.0ms

8000×

body

valid