Details

sample128.0ms

Algorithm

intervals

Results

36.0ms	256×	body	80	valid
28.0ms	257×	body	80	nan

simplify86.0ms

Calls

1 calls:

Slowest

86.0ms

(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1 x) (+ 1 x))
0.0b	(sqrt (/ (- 1 x) (+ 1 x)))
0.0b	(atan (sqrt (/ (- 1 x) (+ 1 x))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`*-un-lft-identity` `add-cube-cbrt`
15×	`sqrt-prod`
5×	`add-cbrt-cube` `add-exp-log`
4×	`associate-/r/`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Calls

3 calls:

Slowest

10.0ms	(/ (- 1 x) (+ 1 x))
4.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
2.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

series130.0ms

Calls

3 calls:

Slowest

63.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
62.0ms	(/ (- 1 x) (+ 1 x))
4.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify2.6s

Calls

57 calls:

Slowest

503.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
275.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
252.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
134.0ms	(- (+ (* 2 (pow x 2)) 1) (* 2 x))
133.0ms	(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune942.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1 x) (+ 1 x))
0.0b	(expm1 (log1p (/ (- 1 x) (+ 1 x))))
0.0b	(log1p (/ (- 1 x) (+ 1 x)))
0.0b	(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u`
4×	`pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `flip3-+` `flip3--` `pow1/2` `div-sub` `div-exp` `log1p-expm1` `flip-+` `div-inv` `flip--` `expm1-udef`

Calls

4 calls:

Slowest

7.0ms	(/ (- 1 x) (+ 1 x))
2.0ms	(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
1.0ms	(log1p (/ (- 1 x) (+ 1 x)))
1.0ms	(expm1 (log1p (/ (- 1 x) (+ 1 x))))

series357.0ms

Calls

4 calls:

Slowest

144.0ms	(sqrt (expm1 (log1p (/ (- 1 x) (+ 1 x)))))
114.0ms	(expm1 (log1p (/ (- 1 x) (+ 1 x))))
72.0ms	(log1p (/ (- 1 x) (+ 1 x)))
27.0ms	(/ (- 1 x) (+ 1 x))

simplify3.6s

Calls

48 calls:

Slowest

429.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
375.0ms	(- (+ (exp (+ (log -2) (log (/ -1 x)))) (/ (exp (+ (log -2) (log (/ -1 x)))) (pow x 2))) (+ (/ (exp (+ (log -2) (log (/ -1 x)))) x) 1))
361.0ms	(- (+ (/ (exp (+ (log 2) (log (/ 1 x)))) (pow x 2)) (exp (+ (log 2) (log (/ 1 x))))) (+ (/ (exp (+ (log 2) (log (/ 1 x)))) x) 1))
323.0ms	(- (+ (log 2) (+ (log (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))) (/ 1 x))
222.0ms	(- (+ (* 1/2 (* (/ (exp (+ (log -2) (log (/ -1 x)))) (pow x 2)) (sqrt (/ 1 (- (exp (+ (log -2) (log (/ -1 x)))) 1))))) (sqrt (- (exp (+ (log -2) (log (/ -1 x)))) 1))) (+ (* 1/8 (* (/ (pow (exp (+ (log -2) (log (/ -1 x)))) 2) (pow x 2)) (sqrt (/ 1 (pow (- (exp (+ (log -2) (log (/ -1 x)))) 1) 3))))) (* 1/2 (* (/ (exp (+ (log -2) (log (/ -1 x)))) x) (sqrt (/ 1 (- (exp (+ (log -2) (log (/ -1 x)))) 1)))))))

prune915.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
0.0b	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
0.0b	(sqrt (- 1 x))
0.0b	(sqrt (+ 1 x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-prod`
36×	`add-sqr-sqrt` `times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip3--` `pow1/2` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Calls

4 calls:

Slowest

11.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
7.0ms	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
2.0ms	(sqrt (- 1 x))
1.0ms	(sqrt (+ 1 x))

series127.0ms

Calls

4 calls:

Slowest

61.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
38.0ms	(sqrt (- 1 x))
24.0ms	(sqrt (+ 1 x))
4.0ms	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify3.4s

Calls

114 calls:

Slowest

270.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
255.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
211.0ms	(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
195.0ms	(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
182.0ms	(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ 1 x)) (sqrt (+ 1 x)))
0.0b	(/ (sqrt (- 1 (* x x))) (* (sqrt (+ 1 x)) (sqrt (+ 1 x))))
0.0b	(sqrt (- 1 (* x x)))
0.0b	(atan (/ (sqrt (- 1 (* x x))) (* (sqrt (+ 1 x)) (sqrt (+ 1 x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`sqrt-div`
15×	`sqrt-prod`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
8×	`frac-times` `associate-/r/`
6×	`times-frac` `associate-r` `associate-l` `associate-/l*`
5×	`pow1/2`
4×	`expm1-log1p-u` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `sqrt-unprod` `div-exp` `pow-prod-down` `prod-exp` `pow-prod-up` `cbrt-unprod` `flip--` `associate-/l/`
1×	`pow2` `rem-sqrt-square` `sqrt-undiv` `clear-num` `associate-/r` `rem-square-sqrt` `frac-2neg` `pow-plus` `-commutative` `div-inv`

Calls

4 calls:

Slowest

19.0ms	(* (sqrt (+ 1 x)) (sqrt (+ 1 x)))
9.0ms	(/ (sqrt (- 1 (* x x))) (* (sqrt (+ 1 x)) (sqrt (+ 1 x))))
4.0ms	(atan (/ (sqrt (- 1 (* x x))) (* (sqrt (+ 1 x)) (sqrt (+ 1 x)))))
1.0ms	(sqrt (- 1 (* x x)))

series167.0ms

Calls

4 calls:

Slowest

70.0ms	(sqrt (- 1 (* x x)))
68.0ms	(/ (sqrt (- 1 (* x x))) (* (sqrt (+ 1 x)) (sqrt (+ 1 x))))
24.0ms	(* (sqrt (+ 1 x)) (sqrt (+ 1 x)))
5.0ms	(atan (/ (sqrt (- 1 (* x x))) (* (sqrt (+ 1 x)) (sqrt (+ 1 x)))))

simplify5.5s

Calls

84 calls:

Slowest

640.0ms	(* (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
360.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
345.0ms	(- (/ (sqrt -1) x) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (+ (sqrt -1) (/ (sqrt -1) (pow x 2)))))
341.0ms	(- (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (+ (sqrt -1) (/ (sqrt -1) (pow x 2)))) (/ (sqrt -1) x))
298.0ms	(/ (- 1 (* x x)) (* (+ 1 x) (+ 1 x)))

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

943.0ms	8000×	body	80	valid
803.0ms	8010×	body	80	nan