Details

sample76.0ms

Algorithm

intervals

Results

21.0ms	61×	body	1280	valid
17.0ms	253×	body	80	nan
10.0ms	37×	body	640	valid
9.0ms	131×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify21.0ms

Calls

1 calls:

Slowest

21.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize20.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
42×	`prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `hypot-def` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Calls

2 calls:

Slowest

61.0ms	(- (sqrt (+ x 1)) (sqrt x))
6.0ms	(sqrt (+ x 1))

series121.0ms

Calls

2 calls:

Slowest

93.0ms	(- (sqrt (+ x 1)) (sqrt x))
27.0ms	(sqrt (+ x 1))

simplify5.7s

Calls

120 calls:

Slowest

207.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
191.0ms	(fma 1 (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
187.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
184.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
161.0ms	(fma (- (cbrt (sqrt x))) (* (cbrt (sqrt x)) (cbrt (sqrt x))) (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))

prune861.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 29.4b

localize27.0ms

Local error

Found 4 expressions with local error:

29.9b	(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))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `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-+` `distribute-lft-out`
1×	`fma-udef`

Calls

4 calls:

Slowest

3.0ms	(cbrt (+ x 1))
3.0ms	(cbrt (+ x 1))
3.0ms	(cbrt (+ x 1))
0.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))

series300.0ms

Calls

4 calls:

Slowest

138.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
59.0ms	(cbrt (+ x 1))
57.0ms	(cbrt (+ x 1))
45.0ms	(cbrt (+ x 1))

simplify2.1s

Calls

30 calls:

Slowest

237.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
231.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
227.0ms	(- (+ (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))))
224.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
191.0ms	(- (+ (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))))

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.2b

localize33.0ms

Local error

Found 4 expressions with local error:

29.9b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
6.9b	(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))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

5.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))
5.0ms	(cbrt (+ x 1))
2.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))
1.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))

series581.0ms

Calls

4 calls:

Slowest

241.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))
175.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
130.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))
35.0ms	(cbrt (+ x 1))

simplify1.2s

Calls

31 calls:

Slowest

217.0ms	(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)))))))
211.0ms	(- (+ (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))))
209.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
165.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))
63.0ms	(cbrt (+ (pow x 3) (pow 1 3)))

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.2b

localize69.0ms

Local error

Found 4 expressions with local error:

29.8b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))
6.9b	(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 (cbrt (+ x 1)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

9.0ms	(cbrt (cbrt (+ x 1)))
3.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))))
2.0ms	(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	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))

series644.0ms

Calls

4 calls:

Slowest

268.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x))))
162.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))))
153.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))
61.0ms	(cbrt (cbrt (+ x 1)))

simplify1.5s

Calls

34 calls:

Slowest

276.0ms	(- (+ (pow (/ 1 x) -1/9) (* 1/9 (pow (/ 1 (pow x 8)) 1/9))) (* 4/81 (pow (/ 1 (pow x 17)) 1/9)))
237.0ms	(- (+ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (* 1/9 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) x))) (* 4/81 (/ (exp (* 1/9 (- (log -1) (log (/ -1 x))))) (pow x 2))))
203.0ms	(exp (* (cbrt (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x))))) (cbrt (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (cbrt (+ x 1))))) (- (sqrt x)))))))
118.0ms	(- (+ (* 1/9 x) 1) (* 4/81 (pow x 2)))
80.0ms	(cbrt (cbrt (+ (pow x 3) (pow 1 3))))

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.2b

regimes443.0ms

Accuracy

0% (0.7b remaining)

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

bsearch3.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

843.0ms	8040×	body	80	nan
702.0ms	1752×	body	1280	valid
261.0ms	1234×	body	640	valid
228.0ms	4088×	body	80	valid
137.0ms	614×	body	320	valid
33.0ms	312×	body	160	valid