Details

sample783.0ms

Algorithm

intervals

Results

276.0ms	98×	body	1280	valid
238.0ms	55×	body	2560	valid
126.0ms	54×	body	640	valid
22.0ms	28×	body	320	valid
6.0ms	9×	body	160	valid
3.0ms	12×	body	80	valid

simplify27.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

26.0ms

(/ (- x (sin x)) (- x (tan x)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.6b	(- x (tan x))
0.6b	(- x (sin x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

Slowest

19.0ms	(- x (tan x))
19.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (sin x))

series268.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

135.0ms	(/ (- x (sin x)) (- x (tan x)))
81.0ms	(- x (tan x))
52.0ms	(- x (sin x))

simplify5.9s

Counts

122 → 122

Calls

122 calls:

Slowest

472.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
457.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
444.0ms	(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
287.0ms	(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
243.0ms	(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune985.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

17.1b	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.1b	(* (* x x) (* x x))
0.0b	(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 88

Calls

3 calls:

Slowest

23.0ms	(* (* x x) (* x x))
0.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)

series231.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

137.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
51.0ms	(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
43.0ms	(* (* x x) (* x x))

simplify2.6s

Counts

76 → 97

Calls

76 calls:

Slowest

360.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
321.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
306.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
275.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
160.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune826.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(- x (tan x))
0.6b	(- x (sin x))
0.5b	(expm1 (/ (- x (sin x)) (- x (tan x))))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`associate-/r` `log1p-expm1-u` `associate-/l`
4×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv` `expm1-udef`

Counts

4 → 125

Calls

4 calls:

Slowest

19.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (sin x))
10.0ms	(- x (tan x))
0.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(expm1 (/ (- x (sin x)) (- x (tan x))))
112.0ms	(/ (- x (sin x)) (- x (tan x)))
76.0ms	(- x (tan x))
49.0ms	(- x (sin x))

simplify7.8s

Counts

126 → 137

Calls

126 calls:

Slowest

750.0ms	(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
619.0ms	(- (+ (* 1/2 (/ (* (pow (sin x) 2) E) (pow x 2))) (+ (/ (* (sin x) E) (* (cos x) x)) (+ E (* 3/2 (/ (* (pow (sin x) 2) E) (* (pow (cos x) 2) (pow x 2))))))) (+ (* 2 (/ (* (pow (sin x) 2) E) (* (cos x) (pow x 2)))) (+ (/ (* (sin x) E) x) 1)))
565.0ms	(- (+ (* 1/2 (/ (* (pow (sin x) 2) E) (pow x 2))) (+ (/ (* (sin x) E) (* (cos x) x)) (+ E (* 3/2 (/ (* (pow (sin x) 2) E) (* (pow (cos x) 2) (pow x 2))))))) (+ (* 2 (/ (* (pow (sin x) 2) E) (* (cos x) (pow x 2)))) (+ (/ (* (sin x) E) x) 1)))
474.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
428.0ms	(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))

prune1.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch190.0ms

end0.0ms

sample16.9s

Algorithm

intervals

Results

6.7s	1624×	body	2560	valid
5.6s	2726×	body	1280	valid
2.5s	1919×	body	640	valid
1.5s	930×	body	320	valid
251.0ms	457×	body	160	valid
93.0ms	344×	body	80	valid