Details

sample74.0ms

Algorithm

intervals

Results

19.0ms	288×	body	80	nan
18.0ms	54×	body	1280	valid
9.0ms	136×	body	80	valid
9.0ms	35×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify11.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

11.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize35.0ms

Local error

Found 2 expressions with local error:

3.0b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite72.0ms

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--`

Counts

2 → 92

Calls

2 calls:

Slowest

60.0ms	(- (sqrt (+ x 1)) (sqrt x))
9.0ms	(sqrt (+ x 1))

series117.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

78.0ms	(- (sqrt (+ x 1)) (sqrt x))
40.0ms	(sqrt (+ x 1))

simplify5.7s

Counts

120 → 98

Calls

120 calls:

Slowest

210.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
201.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
189.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (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))))))
179.0ms	(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune873.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 28.5b

localize44.0ms

Local error

Found 4 expressions with local error:

29.3b	(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))

rewrite18.0ms

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`

Counts

4 → 62

Calls

4 calls:

Slowest

8.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))
3.0ms	(cbrt (+ x 1))
1.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
60.0ms	(cbrt (+ x 1))
53.0ms	(cbrt (+ x 1))
38.0ms	(cbrt (+ x 1))

simplify2.2s

Counts

30 → 74

Calls

30 calls:

Slowest

284.0ms	(- (+ (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))))
242.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
218.0ms	(- (+ (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))))
208.0ms	(- (+ (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))))
204.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))

prune868.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 28.3b

localize55.0ms

Local error

Found 4 expressions with local error:

29.3b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
5.5b	(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`
4×	`cbrt-prod` `expm1-log1p-u` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`cbrt-div` `log-pow`
1×	`flip3-+` `pow1/3` `rem-log-exp` `flip-+` `fma-udef` `distribute-lft-out` `rem-exp-log`

Counts

4 → 61

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)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

312.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))
168.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
149.0ms	(exp (log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))
42.0ms	(cbrt (+ x 1))

simplify1.2s

Counts

30 → 73

Calls

30 calls:

Slowest

243.0ms	(- (+ (* 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	(- (+ (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	(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)))))))
120.0ms	(- (+ (* 1/3 x) 1) (* 1/9 (pow x 2)))
70.0ms	(cbrt (+ (pow x 3) (pow 1 3)))

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.3b

localize66.0ms

Local error

Found 4 expressions with local error:

29.3b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
29.3b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
29.3b	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
5.5b	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `fma-udef`
1×	`rem-log-exp` `log-pow`

Counts

4 → 48

Calls

4 calls:

Slowest

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

series756.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

284.0ms	(log (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x))))
174.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
160.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
138.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))

simplify160.0ms

Counts

16 → 60

Calls

16 calls:

Slowest

51.0ms	(log (sqrt (fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))))
47.0ms	(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (sqrt x)))
44.0ms	(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))))))
3.0ms	(log 1)
0.0ms	(- (+ (log (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0)) (* 1/2 (/ (* (exp (* 1/6 (- (log -1) (log (/ -1 x))))) (exp (* 1/3 (- (log -1) (log (/ -1 x)))))) (* x (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0))))) (+ (* +nan.0 (/ (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) (* (pow x 2) (pow (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0) 2)))) (- (+ (* 1/8 (/ (* (pow (exp (* 1/3 (- (log -1) (log (/ -1 x))))) 2) (pow (exp (* 1/6 (- (log -1) (log (/ -1 x))))) 2)) (* (pow x 2) (pow (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0) 2)))) (* 1/8 (/ (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) (* (pow x 2) (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0))))) (+ (* +nan.0 (/ 1 (* (pow x 2) (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0)))) (- (+ (* +nan.0 (/ 1 (* x (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0)))) (- (* +nan.0 (/ 1 (* (pow x 2) (pow (- (* (exp (* 1/3 (- (log -1) (log (/ -1 x))))) (exp (* 1/6 (- (log -1) (log (/ -1 x)))))) +nan.0) 2)))))))))))

prune934.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 28.3b

regimes132.0ms

Accuracy

0% (0.9b remaining)

Error of 29.6b against oracle of 28.7b and baseline of 29.6b

bsearch7.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

882.0ms	8044×	body	80	nan
584.0ms	1716×	body	1280	valid
341.0ms	1267×	body	640	valid
338.0ms	4114×	body	80	valid
96.0ms	586×	body	320	valid
34.0ms	317×	body	160	valid