Details

sample470.0ms

Algorithm

intervals

Results

282.0ms	96×	body	2560	valid
115.0ms	90×	body	1280	valid
31.0ms	37×	body	640	valid
13.0ms	21×	body	320	valid
11.0ms	256×	pre	80	true
3.0ms	7×	body	160	valid
1.0ms	5×	body	80	valid

simplify32.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

32.0ms

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

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.2b

localize15.0ms

Local error

Found 2 expressions with local error:

2.3b	(- (/ 1 x) (/ 1 (tan x)))
0.0b	(/ 1 (tan x))

rewrite36.0ms

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

series160.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

121.0ms	(- (/ 1 x) (/ 1 (tan x)))
40.0ms	(/ 1 (tan x))

simplify51.1s

Counts

440 → 268

Calls

440 calls:

Slowest

600.0ms	(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (- (* (/ 1 (cbrt (tan x))) (/ 1 (* (cbrt (tan x)) (cbrt (tan x)))))))
495.0ms	(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))))))
460.0ms	(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))))))
445.0ms	(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))))))
444.0ms	(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))))))

prune1.8s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (fma x (* 1/45 x) 1/3))
0.2b	(* 1/45 x)
0.0b	(fma x (* 1/45 x) 1/3)
0.0b	(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`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

4 → 66

Calls

4 calls:

Slowest

8.0ms	(* 1/45 x)
6.0ms	(* x (fma x (* 1/45 x) 1/3))
0.0ms	(fma x (* 1/45 x) 1/3)
0.0ms	(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(* x (fma x (* 1/45 x) 1/3))
89.0ms	(fma (pow x 5) 2/945 (* x (fma x (* 1/45 x) 1/3)))
73.0ms	(fma x (* 1/45 x) 1/3)
29.0ms	(* 1/45 x)

simplify3.0s

Counts

33 → 78

Calls

33 calls:

Slowest

863.0ms	(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
339.0ms	(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
333.0ms	(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
318.0ms	(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
186.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune799.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (log (exp (fma x (* 1/45 x) 1/3))))
0.2b	(* 1/45 x)
0.0b	(log (exp (fma x (* 1/45 x) 1/3)))
0.0b	(fma x (* 1/45 x) 1/3)

rewrite39.0ms

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

19.0ms	(* x (log (exp (fma x (* 1/45 x) 1/3))))
16.0ms	(* 1/45 x)
3.0ms	(log (exp (fma x (* 1/45 x) 1/3)))
0.0ms	(fma x (* 1/45 x) 1/3)

series311.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(* x (log (exp (fma x (* 1/45 x) 1/3))))
72.0ms	(log (exp (fma x (* 1/45 x) 1/3)))
60.0ms	(fma x (* 1/45 x) 1/3)
29.0ms	(* 1/45 x)

simplify4.1s

Counts

50 → 96

Calls

50 calls:

Slowest

907.0ms	(* (* (* 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)))))
223.0ms	(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
207.0ms	(log (exp (* x (* 1/45 x))))
203.0ms	(* x (log (exp (fma x (* 1/45 x) 1/3))))
163.0ms	(* (sqrt x) (sqrt (log (exp (fma x (* 1/45 x) 1/3)))))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

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)))
0.2b	(* 1/45 x)
0.2b	(* 1/45 x)

rewrite59.0ms

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

28.0ms	(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
12.0ms	(* x (sqrt (fma x (* 1/45 x) 1/3)))
9.0ms	(* 1/45 x)
9.0ms	(* 1/45 x)

series328.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(* x (sqrt (fma x (* 1/45 x) 1/3)))
111.0ms	(* (* x (sqrt (fma x (* 1/45 x) 1/3))) (sqrt (fma x (* 1/45 x) 1/3)))
19.0ms	(* 1/45 x)
16.0ms	(* 1/45 x)

simplify3.1s

Counts

57 → 103

Calls

57 calls:

Slowest

289.0ms	(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
279.0ms	(* (* (* 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))))
247.0ms	(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
220.0ms	(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
206.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes87.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample17.1s

Algorithm

intervals

Results

9.9s	3287×	body	2560	valid
4.5s	2513×	body	1280	valid
1.1s	1236×	body	640	valid
693.0ms	294×	body	160	valid
433.0ms	627×	body	320	valid
327.0ms	8000×	pre	80	true
8.0ms	43×	body	80	valid