Details

sample85.0ms

Algorithm

intervals

Results

28.0ms	246×	body	80	nan
18.0ms	52×	body	1280	valid
11.0ms	42×	body	640	valid
9.0ms	126×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	13×	body	160	valid

simplify20.0ms

Calls

1 calls:

Slowest

20.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize20.0ms

Local error

Found 2 expressions with local error:

3.4b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
16×	`sqrt-prod`
6×	`fma-neg`
4×	`add-log-exp`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--` `distribute-lft-out--`

Calls

2 calls:

Slowest

15.0ms	(- (sqrt (+ x 1)) (sqrt x))
1.0ms	(sqrt (+ x 1))

series42.0ms

Calls

2 calls:

Slowest

32.0ms	(- (sqrt (+ x 1)) (sqrt x))
10.0ms	(sqrt (+ x 1))

simplify1.9s

Calls

59 calls:

Slowest

158.0ms	(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
73.0ms	(fma 1 (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
71.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
64.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (sqrt (sqrt x)) (sqrt (sqrt x)))))
64.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (sqrt x) 1)))

prune549.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 30.2b

localize15.0ms

Local error

Found 4 expressions with local error:

30.8b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`fma-udef`

Calls

4 calls:

Slowest

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

series254.0ms

Calls

4 calls:

Slowest

126.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
45.0ms	(cbrt (+ x 1))
44.0ms	(cbrt (+ x 1))
38.0ms	(cbrt (+ x 1))

simplify2.2s

Calls

27 calls:

Slowest

391.0ms	(- (+ (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))))
351.0ms	(- (+ (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 (* 1/3 (- (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))))
157.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))
154.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))

prune875.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 30.0b

localize14.0ms

Local error

Found 4 expressions with local error:

30.8b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
6.3b	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))
0.6b	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))
0.3b	(cbrt (+ x 1))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `exp-sum`
2×	`cbrt-div` `log-pow`
1×	`flip3-+` `pow1/3` `rem-log-exp` `flip-+` `fma-udef` `rem-exp-log`

Calls

4 calls:

Slowest

5.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))
2.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))
2.0ms	(cbrt (+ x 1))
0.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))

series415.0ms

Calls

4 calls:

Slowest

151.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))
132.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
100.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))
32.0ms	(cbrt (+ x 1))

simplify1.1s

Calls

29 calls:

Slowest

333.0ms	(- (+ (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))))
152.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))
135.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
61.0ms	(exp (* (cbrt (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))) (cbrt (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))))
56.0ms	(log (* (cbrt (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))) (cbrt (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))))

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.0b

localize24.0ms

Local error

Found 4 expressions with local error:

30.8b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))
6.3b	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x))))
0.6b	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))))
0.3b	(cbrt (+ x 1))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `exp-sum`
2×	`cbrt-div` `log-pow`
1×	`flip3-+` `pow1/3` `rem-log-exp` `flip-+` `fma-udef` `rem-exp-log`

Calls

4 calls:

Slowest

2.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))))
1.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x))))
1.0ms	(cbrt (+ x 1))
0.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))

series398.0ms

Calls

4 calls:

Slowest

163.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x))))
113.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))))
90.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))
31.0ms	(cbrt (+ x 1))

simplify1.1s

Calls

29 calls:

Slowest

327.0ms	(- (+ (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))))
122.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))
120.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
72.0ms	(log (* (cbrt (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))) (cbrt (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x))))))
64.0ms	(exp (sqrt (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x))))))

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.0b

regimes335.0ms

Accuracy

0% (0.8b remaining)

Error of 29.8b against oracle of 29.1b and baseline of 29.8b

bsearch2.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

995.0ms	7996×	body	80	nan
485.0ms	1717×	body	1280	valid
342.0ms	1248×	body	640	valid
322.0ms	4095×	body	80	valid
98.0ms	601×	body	320	valid
36.0ms	339×	body	160	valid