Details

sample371.0ms

Algorithm

intervals

Results

170.0ms	171×	body	10240	exit
44.0ms	386×	body	80	nan
31.0ms	243×	body	80	valid
5.0ms	18×	body	160	valid

simplify277.0ms

Calls

1 calls:

Slowest

277.0ms

(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp x) 1)
0.0b	(sqrt (+ (exp x) 1))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

9.0ms	(+ (exp x) 1)
7.0ms	(sqrt (+ (exp x) 1))

series53.0ms

Calls

2 calls:

Slowest

27.0ms	(+ (exp x) 1)
26.0ms	(sqrt (+ (exp x) 1))

simplify512.0ms

Calls

14 calls:

Slowest

232.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
73.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
69.0ms	(sqrt (- (* (exp x) (exp x)) (* 1 1)))
43.0ms	(sqrt (+ (pow (exp x) 3) (pow 1 3)))
17.0ms	(sqrt (* (cbrt (+ (exp x) 1)) (cbrt (+ (exp x) 1))))

prune739.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (exp x))
0.3b	(sqrt (exp x))
0.0b	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))
0.0b	(fma (sqrt (exp x)) (sqrt (exp x)) 1)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow1/2`
1×	`fma-udef`

Calls

4 calls:

Slowest

2.0ms	(sqrt (exp x))
2.0ms	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))
2.0ms	(sqrt (exp x))
0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1)

series162.0ms

Calls

4 calls:

Slowest

68.0ms	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))
54.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) 1)
21.0ms	(sqrt (exp x))
18.0ms	(sqrt (exp x))

simplify710.0ms

Calls

24 calls:

Slowest

240.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
119.0ms	(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
94.0ms	(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
68.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
32.0ms	(sqrt (* (cbrt (fma (sqrt (exp x)) (sqrt (exp x)) 1)) (cbrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))))

prune642.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (exp x))
0.3b	(sqrt (exp x))
0.0b	(log1p (sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1)))
0.0b	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`expm1-log1p-u`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow1/2`
1×	`log1p-udef` `log1p-expm1`

Calls

4 calls:

Slowest

1.0ms	(sqrt (exp x))
1.0ms	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))
1.0ms	(sqrt (exp x))
0.0ms	(log1p (sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1)))

series222.0ms

Calls

4 calls:

Slowest

134.0ms	(log1p (sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1)))
55.0ms	(sqrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))
19.0ms	(sqrt (exp x))
14.0ms	(sqrt (exp x))

simplify997.0ms

Calls

25 calls:

Slowest

352.0ms	(- (+ (* 1/4 (/ (pow x 2) (* (sqrt 2) (+ (sqrt 2) 1)))) (+ (log (+ (sqrt 2) 1)) (* 1/2 (/ x (* (+ (sqrt 2) 1) (sqrt 2)))))) (+ (* 1/8 (/ (pow x 2) (* (pow (sqrt 2) 3) (+ (sqrt 2) 1)))) (* 1/8 (/ (pow x 2) (* (pow (+ (sqrt 2) 1) 2) (pow (sqrt 2) 2))))))
240.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
87.0ms	(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
87.0ms	(+ (* 1/2 x) (+ (* 1/8 (pow x 2)) 1))
35.0ms	(sqrt (* (cbrt (fma (sqrt (exp x)) (sqrt (exp x)) 1)) (cbrt (fma (sqrt (exp x)) (sqrt (exp x)) 1))))

prune775.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (exp x))
0.5b	(cbrt (exp x))
0.5b	(cbrt (exp x))
0.1b	(* (cbrt (exp x)) (cbrt (exp x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
7×	`pow1/3`
6×	`associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

12.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
1.0ms	(cbrt (exp x))
1.0ms	(cbrt (exp x))
1.0ms	(cbrt (exp x))

series542.0ms

Calls

4 calls:

Slowest

157.0ms	(cbrt (exp x))
132.0ms	(cbrt (exp x))
127.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
125.0ms	(cbrt (exp x))

simplify579.0ms

Calls

41 calls:

Slowest

109.0ms	(+ (* 2/3 x) (+ (* 2/9 (pow x 2)) 1))
87.0ms	(+ (* 1/3 x) (+ (* 1/18 (pow x 2)) 1))
82.0ms	(+ (* 1/3 x) (+ (* 1/18 (pow x 2)) 1))
79.0ms	(+ (* 1/3 x) (+ (* 1/18 (pow x 2)) 1))
18.0ms	(pow (pow (exp x) 2) 1/3)

prune841.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample8.8s

Algorithm

intervals

Results

5.9s	6530×	body	10240	exit
1.4s	12485×	body	80	nan
1.1s	7436×	body	80	valid
150.0ms	708×	body	160	valid