Details

sample498.0ms

Algorithm

intervals

Results

291.0ms	110×	body	2560	valid
133.0ms	73×	body	1280	valid
27.0ms	32×	body	640	valid
15.0ms	26×	body	320	valid
11.0ms	256×	pre	80	true
6.0ms	14×	body	160	valid
0.0ms	1×	body	80	valid

simplify31.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

31.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize40.0ms

Local error

Found 2 expressions with local error:

4.6b	(- (/ 1 x) (/ 1 (tan x)))
0.0b	(/ 1 (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
208×	`add-cube-cbrt`
182×	`prod-diff`
33×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 262

Calls

2 calls:

Slowest

23.0ms	(- (/ 1 x) (/ 1 (tan x)))
12.0ms	(/ 1 (tan x))

series143.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

106.0ms	(- (/ 1 x) (/ 1 (tan x)))
38.0ms	(/ 1 (tan x))

simplify50.0s

Counts

440 → 268

Calls

440 calls:

Slowest

541.0ms	(fma (/ (sqrt 1) (* (cbrt x) (cbrt x))) (/ (sqrt 1) (cbrt x)) (- (* (cos x) (/ 1 (sin x)))))
459.0ms	(fma (/ (sqrt 1) (sqrt x)) (/ (sqrt 1) (sqrt x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
452.0ms	(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))
411.0ms	(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))
406.0ms	(fma (- (/ (cbrt 1) (cbrt (tan x)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune1.7s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 3 expressions with local error:

0.3b	(* x (fma x (* 1/45 x) 1/3))
0.3b	(* 1/45 x)
0.0b	(fma x (* 1/45 x) 1/3)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

3 → 55

Calls

3 calls:

Slowest

11.0ms	(* x (fma x (* 1/45 x) 1/3))
10.0ms	(* 1/45 x)
0.0ms	(fma x (* 1/45 x) 1/3)

series242.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

147.0ms	(* x (fma x (* 1/45 x) 1/3))
67.0ms	(fma x (* 1/45 x) 1/3)
28.0ms	(* 1/45 x)

simplify1.7s

Counts

30 → 64

Calls

30 calls:

Slowest

766.0ms	(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
204.0ms	(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
180.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))
134.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))
133.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune564.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (log (exp (fma x (* 1/45 x) 1/3))))
0.3b	(* 1/45 x)
0.0b	(log (exp (fma x (* 1/45 x) 1/3)))
0.0b	(fma x (* 1/45 x) 1/3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`log-prod`
10×	`pow1` `associate-r`
8×	`add-cbrt-cube` `add-exp-log` `log-pow`
6×	`exp-prod` `associate-l`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-log-exp`

Counts

4 → 84

Calls

4 calls:

Slowest

10.0ms	(* x (log (exp (fma x (* 1/45 x) 1/3))))
9.0ms	(log (exp (fma x (* 1/45 x) 1/3)))
5.0ms	(* 1/45 x)
0.0ms	(fma x (* 1/45 x) 1/3)

series289.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

135.0ms	(* x (log (exp (fma x (* 1/45 x) 1/3))))
73.0ms	(log (exp (fma x (* 1/45 x) 1/3)))
64.0ms	(fma x (* 1/45 x) 1/3)
18.0ms	(* 1/45 x)

simplify3.6s

Counts

50 → 96

Calls

50 calls:

Slowest

893.0ms	(* (* (* x x) x) (* (* (log (exp (fma x (* 1/45 x) 1/3))) (log (exp (fma x (* 1/45 x) 1/3)))) (log (exp (fma x (* 1/45 x) 1/3)))))
207.0ms	(log (exp (* x (* 1/45 x))))
157.0ms	(* (log (exp (fma x (* 1/45 x) 1/3))) x)
142.0ms	(log (exp (* (cbrt (fma x (* 1/45 x) 1/3)) (cbrt (fma x (* 1/45 x) 1/3)))))
129.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
0.4b	(* x (sqrt (fma x (* 1/45 x) 1/3)))
0.3b	(* 1/45 x)
0.3b	(* 1/45 x)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`associate-r`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
7×	`sqrt-prod`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

Slowest

23.0ms	(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
7.0ms	(* x (sqrt (fma x (* 1/45 x) 1/3)))
5.0ms	(* 1/45 x)
5.0ms	(* 1/45 x)

series309.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(* x (sqrt (fma x (* 1/45 x) 1/3)))
108.0ms	(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
29.0ms	(* 1/45 x)
16.0ms	(* 1/45 x)

simplify2.5s

Counts

57 → 103

Calls

57 calls:

Slowest

276.0ms	(* (* (* x x) x) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))))
209.0ms	(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
181.0ms	(* (* (* (* x x) x) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))) (* (* (sqrt (fma x (* 1/45 x) 1/3)) (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3))))
175.0ms	(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
161.0ms	(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes88.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample15.0s

Algorithm

intervals

Results

8.6s	3230×	body	2560	valid
3.7s	2550×	body	1280	valid
1.3s	1199×	body	640	valid
745.0ms	672×	body	320	valid
284.0ms	8000×	pre	80	true
162.0ms	310×	body	160	valid
6.0ms	39×	body	80	valid