Details

sample536.0ms

Algorithm

intervals

Results

348.0ms	119×	body	2560	valid
116.0ms	77×	body	1280	valid
29.0ms	32×	body	640	valid
12.0ms	19×	body	320	valid
12.0ms	256×	pre	80	true
5.0ms	9×	body	160	valid

simplify46.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

46.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize21.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (/ 1 x) (/ 1 (tan x)))
0.0b	(/ 1 (tan x))

rewrite61.0ms

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

37.0ms	(- (/ 1 x) (/ 1 (tan x)))
12.0ms	(/ 1 (tan x))

series129.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

93.0ms	(- (/ 1 x) (/ 1 (tan x)))
36.0ms	(/ 1 (tan x))

simplify49.0s

Counts

440 → 268

Calls

440 calls:

Slowest

722.0ms	(fma (- (/ (sqrt 1) (cbrt (tan x)))) (/ (sqrt 1) (* (cbrt (tan x)) (cbrt (tan x)))) (* (/ (sqrt 1) (cbrt (tan x))) (/ (sqrt 1) (* (cbrt (tan x)) (cbrt (tan x))))))
461.0ms	(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))))))
404.0ms	(fma (* (cbrt (/ 1 x)) (cbrt (/ 1 x))) (cbrt (/ 1 x)) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
403.0ms	(fma 1 (/ 1 x) (- (* (/ (cbrt 1) (cbrt (tan x))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (tan x)) (cbrt (tan x)))))))
399.0ms	(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

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)

rewrite12.0ms

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

6.0ms	(* x (fma x (* 1/45 x) 1/3))
5.0ms	(* 1/45 x)
0.0ms	(fma x (* 1/45 x) 1/3)

series218.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

118.0ms	(* x (fma x (* 1/45 x) 1/3))
77.0ms	(fma x (* 1/45 x) 1/3)
23.0ms	(* 1/45 x)

simplify1.7s

Counts

30 → 64

Calls

30 calls:

Slowest

724.0ms	(* (* (* x x) x) (* (* (fma x (* 1/45 x) 1/3) (fma x (* 1/45 x) 1/3)) (fma x (* 1/45 x) 1/3)))
161.0ms	(* (* (* 1/45 1/45) 1/45) (* (* x x) x))
148.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))
135.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))
135.0ms	(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune619.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* x (fma x (* 1/45 x) 1/3)))
0.6b	(cbrt (* x (fma x (* 1/45 x) 1/3)))
0.6b	(cbrt (* x (fma x (* 1/45 x) 1/3)))
0.5b	(* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt (* x (fma x (* 1/45 x) 1/3))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

Slowest

16.0ms	(* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt (* x (fma x (* 1/45 x) 1/3))))
3.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))
3.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))
3.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

243.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))
239.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))
226.0ms	(* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt (* x (fma x (* 1/45 x) 1/3))))
177.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))

simplify5.6s

Counts

45 → 82

Calls

45 calls:

Slowest

497.0ms	(- (+ (* 2/45 (* (pow x 2) (exp (* 1/3 (+ (log 1/9) (* 2 (log x))))))) (exp (* 1/3 (+ (log 1/9) (* 2 (log x)))))) (* 1/2025 (* (pow x 4) (exp (* 1/3 (+ (log 1/9) (* 2 (log x))))))))
396.0ms	(- (+ (exp (* 1/3 (- (log 1/45) (* 3 (log (/ 1 x)))))) (* 5 (/ (exp (* 1/3 (- (log 1/45) (* 3 (log (/ 1 x)))))) (pow x 2)))) (* 25 (/ (exp (* 1/3 (- (log 1/45) (* 3 (log (/ 1 x)))))) (pow x 4))))
381.0ms	(- (+ (exp (* 1/3 (+ (log 1/3) (log x)))) (* 1/45 (* (pow x 2) (exp (* 1/3 (+ (log 1/3) (log x))))))) (* 1/2025 (* (pow x 4) (exp (* 1/3 (+ (log 1/3) (log x)))))))
367.0ms	(- (+ (exp (* 1/3 (- (log 1/2025) (* 6 (log (/ 1 x)))))) (* 10 (/ (exp (* 1/3 (- (log 1/2025) (* 6 (log (/ 1 x)))))) (pow x 2)))) (* 25 (/ (exp (* 1/3 (- (log 1/2025) (* 6 (log (/ 1 x)))))) (pow x 4))))
360.0ms	(- (+ (exp (* 1/3 (+ (log 1/3) (log x)))) (* 1/45 (* (pow x 2) (exp (* 1/3 (+ (log 1/3) (log x))))))) (* 1/2025 (* (pow x 4) (exp (* 1/3 (+ (log 1/3) (log x)))))))

prune937.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.6b	(cbrt (* x (fma x (* 1/45 x) 1/3)))
0.6b	(cbrt (* x (fma x (* 1/45 x) 1/3)))
0.4b	(* (* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt x)) (cbrt (fma x (* 1/45 x) 1/3)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1/3` `associate-r`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`associate-l` `*-commutative`

Counts

4 → 63

Calls

4 calls:

Slowest

53.0ms	(* (* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt x)) (cbrt (fma x (* 1/45 x) 1/3)))
6.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))
6.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))
2.0ms	(cbrt x)

series876.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

275.0ms	(cbrt x)
226.0ms	(* (* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt x)) (cbrt (fma x (* 1/45 x) 1/3)))
192.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))
182.0ms	(cbrt (* x (fma x (* 1/45 x) 1/3)))

simplify4.7s

Counts

31 → 75

Calls

31 calls:

Slowest

814.0ms	(* (* (* (* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt x)) (* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt x))) (* (cbrt (* x (fma x (* 1/45 x) 1/3))) (cbrt x))) (fma x (* 1/45 x) 1/3))
403.0ms	(- (+ (* 2/45 (* (pow x 2) (exp (* 1/3 (+ (log 1/9) (* 2 (log x))))))) (exp (* 1/3 (+ (log 1/9) (* 2 (log x)))))) (* 1/2025 (* (pow x 4) (exp (* 1/3 (+ (log 1/9) (* 2 (log x))))))))
372.0ms	(- (+ (exp (* 1/3 (+ (log 1/3) (log x)))) (* 1/45 (* (pow x 2) (exp (* 1/3 (+ (log 1/3) (log x))))))) (* 1/2025 (* (pow x 4) (exp (* 1/3 (+ (log 1/3) (log x)))))))
365.0ms	(- (+ (exp (* 1/3 (+ (log 1/3) (log x)))) (* 1/45 (* (pow x 2) (exp (* 1/3 (+ (log 1/3) (log x))))))) (* 1/2025 (* (pow x 4) (exp (* 1/3 (+ (log 1/3) (log x)))))))
330.0ms	(- (+ (exp (* 1/3 (- (log 1/45) (* 3 (log (/ 1 x)))))) (* 5 (/ (exp (* 1/3 (- (log 1/45) (* 3 (log (/ 1 x)))))) (pow x 2)))) (* 25 (/ (exp (* 1/3 (- (log 1/45) (* 3 (log (/ 1 x)))))) (pow x 4))))

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes90.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample17.3s

Algorithm

intervals

Results

10.8s	3211×	body	2560	valid
3.9s	2509×	body	1280	valid
1.3s	1299×	body	640	valid
445.0ms	612×	body	320	valid
440.0ms	8000×	pre	80	true
133.0ms	320×	body	160	valid
10.0ms	49×	body	80	valid