Details

sample485.0ms

Algorithm

intervals

Results

305.0ms	117×	body	2560	valid
80.0ms	63×	body	1280	valid
38.0ms	19×	body	320	valid
34.0ms	44×	body	640	valid
10.0ms	256×	pre	80	true
4.0ms	12×	body	160	valid
0.0ms	1×	body	80	valid

simplify21.0ms

Calls

1 calls:

Slowest

21.0ms

(- (/ 1 x) (/ 1 (tan x)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize10.0ms

Local error

Found 2 expressions with local error:

2.9b	(- (/ 1 x) (/ 1 (tan x)))
0.0b	(/ 1 (tan x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

6.0ms	(- (/ 1 x) (/ 1 (tan x)))
1.0ms	(/ 1 (tan x))

series147.0ms

Calls

2 calls:

Slowest

116.0ms	(- (/ 1 x) (/ 1 (tan x)))
30.0ms	(/ 1 (tan x))

simplify3.1s

Calls

62 calls:

Slowest

364.0ms	(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
128.0ms	(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
126.0ms	(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))
114.0ms	(fma (* (cbrt (/ 1 x)) (cbrt (/ 1 x))) (cbrt (/ 1 x)) (- (* (cos x) (/ 1 (sin x)))))
112.0ms	(fma (- (cos x)) (/ 1 (sin x)) (* (cos x) (/ 1 (sin x))))

prune543.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 1 expressions with local error:

0.3b	(* (fma 1/45 (* x x) 1/3) x)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-l`
2×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
1×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

1 calls:

Slowest

3.0ms

(* (fma 1/45 (* x x) 1/3) x)

series118.0ms

Calls

1 calls:

Slowest

118.0ms

(* (fma 1/45 (* x x) 1/3) x)

simplify237.0ms

Calls

5 calls:

Slowest

75.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))
67.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))
52.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))
26.0ms	(sqrt (fma 1/45 (* x x) 1/3))
16.0ms	(* (cbrt (fma 1/45 (* x x) 1/3)) (cbrt (fma 1/45 (* x x) 1/3)))

prune180.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (fma 1/45 (* x x) 1/3)) x)
0.4b	(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-l`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`

Calls

2 calls:

Slowest

15.0ms	(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
6.0ms	(* (sqrt (fma 1/45 (* x x) 1/3)) x)

series271.0ms

Calls

2 calls:

Slowest

156.0ms	(* (sqrt (fma 1/45 (* x x) 1/3)) x)
114.0ms	(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))

simplify1.8s

Calls

19 calls:

Slowest

505.0ms	(* (* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))) (* (* (* (sqrt (fma 1/45 (* x x) 1/3)) x) (* (sqrt (fma 1/45 (* x x) 1/3)) x)) (* (sqrt (fma 1/45 (* x x) 1/3)) x)))
311.0ms	(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
306.0ms	(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
242.0ms	(- (+ (* x (sqrt 1/3)) (* 1/90 (/ (pow x 3) (sqrt 1/3)))) (* 1/16200 (/ (pow x 5) (pow (sqrt 1/3) 3))))
61.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune492.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.4b

(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))

0.3b

(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))

0.1b

(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-l`
21×	`sqrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-r`

Calls

3 calls:

Slowest

58.0ms

(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))

12.0ms

(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))

4.0ms

(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)

series580.0ms

Calls

3 calls:

Slowest

249.0ms

(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)

187.0ms

(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))

144.0ms

(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))

simplify3.5s

Calls

40 calls:

Slowest

363.0ms	(- (+ (* x (pow 1/3 1/4)) (* 1/60 (* (pow x 3) (pow 1/3 1/4)))) (* 1/2400 (* (pow x 5) (pow 1/3 1/4))))
311.0ms	(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
303.0ms	(- (+ (* x (sqrt 1/3)) (* 1/90 (/ (pow x 3) (sqrt 1/3)))) (* 1/16200 (/ (pow x 5) (pow (sqrt 1/3) 3))))
292.0ms	(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
280.0ms	(* (* (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (* (* (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample17.0s

Algorithm

intervals

Results

10.4s	3339×	body	2560	valid
4.3s	2487×	body	1280	valid
1.1s	1202×	body	640	valid
452.0ms	8000×	pre	80	true
398.0ms	633×	body	320	valid
164.0ms	310×	body	160	valid
6.0ms	29×	body	80	valid