Details

sample483.0ms

Algorithm

intervals

Results

201.0ms	220×	body	10240	exit
72.0ms	410×	body	80	nan
27.0ms	240×	body	80	valid
4.0ms	17×	body	160	valid

simplify179.0ms

Calls

1 calls:

Slowest

178.0ms

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

5.0ms	(+ (exp x) 1)
4.0ms	(sqrt (+ (exp x) 1))

series50.0ms

Calls

2 calls:

Slowest

33.0ms	(sqrt (+ (exp x) 1))
17.0ms	(+ (exp x) 1)

simplify507.0ms

Calls

12 calls:

Slowest

246.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
68.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
61.0ms	(sqrt (- (* (exp x) (exp x)) (* 1 1)))
42.0ms	(sqrt (+ (pow (exp x) 3) (pow 1 3)))
20.0ms	(sqrt (* (cbrt (+ (exp x) 1)) (cbrt (+ (exp x) 1))))

prune195.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1))))
0.0b	(sqrt (sqrt (+ (exp x) 1)))
0.0b	(sqrt (sqrt (+ (exp x) 1)))
0.0b	(+ (exp x) 1)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

38×	`sqrt-prod`
32×	`sqrt-div`
18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `flip3-+` `associate-r` `associate-l` `flip-+`
6×	`add-cbrt-cube` `pow1/2` `add-exp-log`
4×	`frac-times` `rem-sqrt-square` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-prod-up`
1×	`pow2` `+-commutative` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

22.0ms	(* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1))))
5.0ms	(sqrt (sqrt (+ (exp x) 1)))
4.0ms	(sqrt (sqrt (+ (exp x) 1)))
3.0ms	(+ (exp x) 1)

series309.0ms

Calls

4 calls:

Slowest

131.0ms	(sqrt (sqrt (+ (exp x) 1)))
130.0ms	(sqrt (sqrt (+ (exp x) 1)))
31.0ms	(* (sqrt (sqrt (+ (exp x) 1))) (sqrt (sqrt (+ (exp x) 1))))
17.0ms	(+ (exp x) 1)

simplify2.7s

Calls

72 calls:

Slowest

229.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
225.0ms	(+ (* 1/8 (* x (pow 2 1/4))) (+ (* 5/128 (* (pow x 2) (pow 2 1/4))) (pow 2 1/4)))
210.0ms	(+ (* 1/8 (* x (pow 2 1/4))) (+ (* 5/128 (* (pow x 2) (pow 2 1/4))) (pow 2 1/4)))
140.0ms	(* (sqrt (sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))) (sqrt (sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))))
132.0ms	(* (sqrt (sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))) (sqrt (sqrt (- (exp x) 1))))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (+ (exp x) 1))
0.1b	(cbrt (+ (exp x) 1))
0.1b	(* (fabs (cbrt (+ (exp x) 1))) (sqrt (cbrt (+ (exp x) 1))))
0.0b	(+ (exp x) 1)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `associate-r`
6×	`pow1` `cbrt-div` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
4×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
3×	`associate-l`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

9.0ms	(* (fabs (cbrt (+ (exp x) 1))) (sqrt (cbrt (+ (exp x) 1))))
3.0ms	(+ (exp x) 1)
2.0ms	(cbrt (+ (exp x) 1))
2.0ms	(cbrt (+ (exp x) 1))

series355.0ms

Calls

4 calls:

Slowest

141.0ms	(* (fabs (cbrt (+ (exp x) 1))) (sqrt (cbrt (+ (exp x) 1))))
107.0ms	(cbrt (+ (exp x) 1))
99.0ms	(cbrt (+ (exp x) 1))
9.0ms	(+ (exp x) 1)

simplify1.5s

Calls

38 calls:

Slowest

201.0ms	(+ (* 1/12 (* (* x (fabs (pow (+ (exp x) 1) 1/3))) (pow 2 1/6))) (+ (* 7/288 (* (* (pow x 2) (fabs (pow (+ (exp x) 1) 1/3))) (pow 2 1/6))) (* (fabs (pow (+ (exp x) 1) 1/3)) (pow 2 1/6))))
171.0ms	(+ (* 1/18 (* (pow x 2) (pow 2 1/3))) (+ (* 1/6 (* x (pow 2 1/3))) (pow 2 1/3)))
155.0ms	(sqrt (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
152.0ms	(+ (* 1/18 (* (pow x 2) (pow 2 1/3))) (+ (* 1/6 (* x (pow 2 1/3))) (pow 2 1/3)))
134.0ms	(* (* (* (fabs (cbrt (+ (exp x) 1))) (fabs (cbrt (+ (exp x) 1)))) (fabs (cbrt (+ (exp x) 1)))) (* (* (sqrt (cbrt (+ (exp x) 1))) (sqrt (cbrt (+ (exp x) 1)))) (sqrt (cbrt (+ (exp x) 1)))))

prune839.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample9.9s

Algorithm

intervals

Results

7.0s	6796×	body	10240	exit
1.4s	12663×	body	80	nan
907.0ms	7423×	body	80	valid
157.0ms	708×	body	160	valid