Details

sample181.0ms

Algorithm

intervals

Results

37.0ms	256×	body	80	valid
29.0ms	263×	body	80	nan

simplify61.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

61.0ms

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
49×	`times-frac`
30×	`sqrt-prod`
26×	`add-cube-cbrt`
18×	`difference-of-squares`
13×	`distribute-lft-out`
9×	`distribute-lft-out--`
6×	`associate-/l*`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

3 → 109

Calls

3 calls:

Slowest

32.0ms	(/ (- 1 x) (+ 1 x))
10.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

series107.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

58.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
45.0ms	(/ (- 1 x) (+ 1 x))
4.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.8s

Counts

106 → 118

Calls

106 calls:

Slowest

393.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
288.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
259.0ms	(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
246.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
123.0ms	(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b	(expm1 (/ (- 1 x) (+ 1 x)))
0.0b	(/ (- 1 x) (+ 1 x))
0.0b	(sqrt (log1p (expm1 (/ (- 1 x) (+ 1 x)))))
0.0b	(atan (sqrt (log1p (expm1 (/ (- 1 x) (+ 1 x))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
24×	`times-frac`
17×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`distribute-lft-out`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `log1p-expm1-u` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `expm1-log1p` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `div-sub` `div-exp` `flip-+` `div-inv` `flip--` `expm1-udef`

Counts

4 → 92

Calls

4 calls:

Slowest

17.0ms	(/ (- 1 x) (+ 1 x))
1.0ms	(sqrt (log1p (expm1 (/ (- 1 x) (+ 1 x)))))
1.0ms	(atan (sqrt (log1p (expm1 (/ (- 1 x) (+ 1 x))))))
1.0ms	(expm1 (/ (- 1 x) (+ 1 x)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(sqrt (log1p (expm1 (/ (- 1 x) (+ 1 x)))))
86.0ms	(expm1 (/ (- 1 x) (+ 1 x)))
28.0ms	(/ (- 1 x) (+ 1 x))
4.0ms	(atan (sqrt (log1p (expm1 (/ (- 1 x) (+ 1 x))))))

simplify4.5s

Counts

81 → 104

Calls

81 calls:

Slowest

505.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
460.0ms	(/ (- 1 x) (cbrt (+ 1 x)))
426.0ms	(- (+ (* 4 (* (pow x 2) E)) E) (+ 1 (* 2 (* x E))))
270.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
267.0ms	(- (+ (exp -1) (* 2 (/ (exp -1) x))) (+ (* 2/3 (/ (exp -1) (pow x 3))) 1))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
49×	`times-frac`
30×	`sqrt-prod`
27×	`add-cube-cbrt`
18×	`difference-of-squares`
13×	`distribute-lft-out`
9×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--` `expm1-udef`

Counts

4 → 121

Calls

4 calls:

Slowest

33.0ms	(/ (- 1 x) (+ 1 x))
20.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms	(atan (expm1 (log1p (sqrt (/ (- 1 x) (+ 1 x))))))
0.0ms	(expm1 (log1p (sqrt (/ (- 1 x) (+ 1 x)))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

230.0ms	(expm1 (log1p (sqrt (/ (- 1 x) (+ 1 x)))))
52.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
38.0ms	(/ (- 1 x) (+ 1 x))
4.0ms	(atan (expm1 (log1p (sqrt (/ (- 1 x) (+ 1 x))))))

simplify4.6s

Counts

110 → 133

Calls

110 calls:

Slowest

435.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
323.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
314.0ms	(- (+ (/ 1 (* x (sqrt -1))) (+ (sqrt -1) (* 1/4 (/ (sqrt -1) (pow x 2))))) (* 1/2 (/ 1 (* (pow x 2) (pow (+ (sqrt -1) 1) 2)))))
291.0ms	(- (+ (/ 1 (* x (sqrt -1))) (+ (sqrt -1) (* 1/4 (/ (sqrt -1) (pow x 2))))) (* 1/2 (/ 1 (* (pow x 2) (pow (+ (sqrt -1) 1) 2)))))
260.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

92×	`sqrt-prod`
88×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
63×	`times-frac`
41×	`add-cube-cbrt`
16×	`difference-of-squares`
11×	`distribute-lft-out`
9×	`associate-/l*`
8×	`distribute-lft-out--`
7×	`associate-/r*`
6×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `associate-/r/` `flip-+` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `expm1-log1p` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-exp` `hypot-1-def` `div-inv` `flip--` `expm1-udef`

Counts

4 → 143

Calls

4 calls:

Slowest

22.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
9.0ms	(sqrt (+ 1 x))
1.0ms	(atan (expm1 (log1p (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))))
0.0ms	(expm1 (log1p (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

213.0ms	(expm1 (log1p (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))))
51.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
34.0ms	(sqrt (+ 1 x))
3.0ms	(atan (expm1 (log1p (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))))

simplify4.5s

Counts

170 → 155

Calls

170 calls:

Slowest

289.0ms	(- (+ (/ 1 (* x (sqrt -1))) (+ (sqrt -1) (* 1/4 (/ (sqrt -1) (pow x 2))))) (* 1/2 (/ 1 (* (pow x 2) (pow (+ (sqrt -1) 1) 2)))))
254.0ms	(- (+ (/ 1 (* x (sqrt -1))) (+ (sqrt -1) (* 1/4 (/ (sqrt -1) (pow x 2))))) (* 1/2 (/ 1 (* (pow x 2) (pow (+ (sqrt -1) 1) 2)))))
234.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
229.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
225.0ms	(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))

prune1.8s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

959.0ms	8000×	body	80	valid
822.0ms	8123×	body	80	nan