Details

sample76.0ms

Algorithm

intervals

Results

18.0ms	51×	body	1280	valid
18.0ms	277×	body	80	nan
14.0ms	49×	body	640	valid
9.0ms	125×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	11×	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: 31.5b

localize12.0ms

Local error

Found 1 expressions with local error:

3.2b	(- (sqrt (+ x 1)) (sqrt x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

1 → 71

Calls

1 calls:

Slowest

59.0ms

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

series65.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

65.0ms

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

simplify5.3s

Counts

107 → 74

Calls

107 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))))))
198.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
183.0ms	(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
183.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
177.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune592.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 30.8b

localize27.0ms

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)))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
16×	`*-un-lft-identity`
12×	`sqrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `sqrt-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 → 71

Calls

4 calls:

Slowest

6.0ms	(cbrt (sqrt (+ x 1)))
6.0ms	(cbrt (sqrt (+ x 1)))
6.0ms	(cbrt (sqrt (+ x 1)))
1.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

171.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (sqrt x)))
61.0ms	(cbrt (sqrt (+ x 1)))
55.0ms	(cbrt (sqrt (+ x 1)))
39.0ms	(cbrt (sqrt (+ x 1)))

simplify2.5s

Counts

39 → 83

Calls

39 calls:

Slowest

287.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
257.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
244.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
213.0ms	(- (+ (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))))
206.0ms	(- (+ (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))))

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 30.6b

localize81.0ms

Local error

Found 4 expressions with local error:

31.3b	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (- (sqrt x)))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (sqrt (+ x 1)))
0.3b	(cbrt (+ x 1))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

Slowest

7.0ms	(cbrt (sqrt (+ x 1)))
6.0ms	(cbrt (sqrt (+ x 1)))
2.0ms	(cbrt (+ x 1))
1.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (- (sqrt x)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (- (sqrt x)))
60.0ms	(cbrt (+ x 1))
42.0ms	(cbrt (sqrt (+ x 1)))
35.0ms	(cbrt (sqrt (+ x 1)))

simplify2.5s

Counts

36 → 80

Calls

36 calls:

Slowest

286.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
281.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
240.0ms	(- (+ (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))))
236.0ms	(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
222.0ms	(- (+ (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))))

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.6b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

110×	`sqrt-prod`
100×	`cbrt-prod`
70×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`sqrt-div`
26×	`add-cube-cbrt`
21×	`swap-sqr`
16×	`cbrt-div` `unswap-sqr`
13×	`associate-r` `associate-l`
11×	`pow1`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
6×	`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-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 149

Calls

4 calls:

Slowest

45.0ms	(* (cbrt (sqrt (sqrt (+ x 1)))) (cbrt (sqrt (sqrt (+ x 1)))))
4.0ms	(cbrt (sqrt (sqrt (+ x 1))))
4.0ms	(cbrt (sqrt (sqrt (+ x 1))))
1.0ms	(fma (* (cbrt (sqrt (+ x 1))) (* (cbrt (sqrt (sqrt (+ x 1)))) (cbrt (sqrt (sqrt (+ x 1)))))) (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (- (sqrt x)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

164.0ms	(fma (* (cbrt (sqrt (+ x 1))) (* (cbrt (sqrt (sqrt (+ x 1)))) (cbrt (sqrt (sqrt (+ x 1)))))) (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (- (sqrt x)))
54.0ms	(cbrt (sqrt (sqrt (+ x 1))))
43.0ms	(cbrt (sqrt (sqrt (+ x 1))))
43.0ms	(* (cbrt (sqrt (sqrt (+ x 1)))) (cbrt (sqrt (sqrt (+ x 1)))))

simplify6.2s

Counts

160 → 161

Calls

160 calls:

Slowest

303.0ms	(- (+ (* 1/12 (pow (/ 1 (pow x 11)) 1/12)) (pow (/ 1 x) -1/12)) (* 11/288 (pow (/ 1 (pow x 23)) 1/12)))
293.0ms	(- (+ (* 1/6 (pow (/ 1 (pow x 5)) 1/6)) (pow (/ 1 x) -1/6)) (* 5/72 (pow (/ 1 (pow x 11)) 1/6)))
288.0ms	(- (+ (* 1/12 (pow (/ 1 (pow x 11)) 1/12)) (pow (/ 1 x) -1/12)) (* 11/288 (pow (/ 1 (pow x 23)) 1/12)))
283.0ms	(* (cbrt (sqrt (sqrt (- (* x x) (* 1 1))))) (cbrt (sqrt (sqrt (+ (pow x 3) (pow 1 3))))))
245.0ms	(* (cbrt (sqrt (sqrt (+ (pow x 3) (pow 1 3))))) (cbrt (sqrt (sqrt (+ x 1)))))

prune3.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.5b

regimes223.0ms

Accuracy

0% (0.7b remaining)

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

bsearch8.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	1714×	body	1280	valid
557.0ms	7931×	body	80	nan
365.0ms	1263×	body	640	valid
356.0ms	4089×	body	80	valid
105.0ms	612×	body	320	valid
37.0ms	322×	body	160	valid