Details

sample47.0ms

Algorithm

intervals

Results

11.0ms	57×	body	1280	valid
10.0ms	257×	body	80	nan
7.0ms	40×	body	640	valid
5.0ms	125×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	15×	body	160	valid

simplify12.0ms

Calls

1 calls:

Slowest

12.0ms

(- (sqrt (+ x 1)) (sqrt x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize9.0ms

Local error

Found 1 expressions with local error:

3.8b	(- (sqrt (+ x 1)) (sqrt x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`sqrt-prod`
6×	`fma-neg`
3×	`add-log-exp`
2×	`difference-of-squares`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--`

Calls

1 calls:

Slowest

11.0ms

(- (sqrt (+ x 1)) (sqrt x))

series79.0ms

Calls

1 calls:

Slowest

79.0ms

(- (sqrt (+ x 1)) (sqrt x))

simplify1.7s

Calls

50 calls:

Slowest

71.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
70.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
60.0ms	(/ (exp (sqrt (+ x 1))) (exp (sqrt x)))
59.0ms	(fma (- (cbrt (sqrt x))) (* (cbrt (sqrt x)) (cbrt (sqrt x))) (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))
59.0ms	(fma (- (cbrt (sqrt x))) (* (cbrt (sqrt x)) (cbrt (sqrt x))) (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))

prune368.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 30.6b

localize13.0ms

Local error

Found 4 expressions with local error:

31.2b	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))
0.3b	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
16×	`cbrt-div` `sqrt-div`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`sqrt-prod`
9×	`pow1` `associate-r` `associate-l`
8×	`flip3-+` `flip-+`
6×	`pow1/3` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Calls

4 calls:

Slowest

8.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
1.0ms	(cbrt (sqrt (+ x 1)))
1.0ms	(cbrt (sqrt (+ x 1)))
0.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))

series261.0ms

Calls

4 calls:

Slowest

125.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))
57.0ms	(cbrt (sqrt (+ x 1)))
41.0ms	(cbrt (sqrt (+ x 1)))
37.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))

simplify3.6s

Calls

66 calls:

Slowest

647.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
332.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
328.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
152.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
145.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.4b

localize8.0ms

Local error

Found 4 expressions with local error:

31.5b	(fma (cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))
0.3b	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))
0.2b	(cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
13×	`flip3-+` `flip-+`
10×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `sqrt-prod`
8×	`frac-times`
7×	`cbrt-prod`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `pow1/2` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `pow-prod-down` `pow-prod-up`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Calls

4 calls:

Slowest

8.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1))))
8.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
2.0ms	(cbrt (sqrt (+ x 1)))
0.0ms	(fma (cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))

series304.0ms

Calls

4 calls:

Slowest

183.0ms	(fma (cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))
51.0ms	(cbrt (sqrt (+ x 1)))
37.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1))))
34.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))

simplify3.8s

Calls

62 calls:

Slowest

643.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
368.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
336.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
167.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))
158.0ms	(- (+ (* 1/6 x) 1) (* 5/72 (pow x 2)))

prune1.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.4b

localize14.0ms

Local error

Found 4 expressions with local error:

31.5b	(fma (cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))
0.3b	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))
0.2b	(cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
13×	`flip3-+` `flip-+`
10×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `sqrt-prod`
8×	`frac-times`
7×	`cbrt-prod`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `pow1/2` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `pow-prod-down` `pow-prod-up`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Calls

4 calls:

Slowest

12.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
4.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1))))
1.0ms	(cbrt (sqrt (+ x 1)))
1.0ms	(fma (cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))

series255.0ms

Calls

4 calls:

Slowest

132.0ms	(fma (cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))
51.0ms	(cbrt (sqrt (+ x 1)))
41.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (+ x 1))))
30.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))

simplify3.8s

Calls

62 calls:

Slowest

673.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
354.0ms	(- (+ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) x))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (pow x 2))))
352.0ms	(- (+ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (* 1/6 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) x))) (* 5/72 (/ (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (pow x 2))))
165.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))
157.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune1.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.4b

regimes275.0ms

Accuracy

0% (0.8b remaining)

Error of 29.6b against oracle of 28.8b and baseline of 29.6b

bsearch3.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

888.0ms	8028×	body	80	nan
492.0ms	1730×	body	1280	valid
276.0ms	4113×	body	80	valid
275.0ms	1239×	body	640	valid
127.0ms	628×	body	320	valid
70.0ms	290×	body	160	valid