Details

sample152.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
16.0ms	263×	body	80	nan

simplify30.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

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)))

rewrite55.0ms

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×	`insert-posit16` `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 → 103

Calls

3 calls:

Slowest

33.0ms	(/ (- 1 x) (+ 1 x))
18.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

series108.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

62.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
39.0ms	(/ (- 1 x) (+ 1 x))
6.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.5s

Counts

106 → 112

Calls

106 calls:

Slowest

426.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
266.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
216.0ms	(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
209.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
142.0ms	(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune937.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

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×	`insert-posit16` `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 → 103

Calls

3 calls:

Slowest

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

series123.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

74.0ms	(sqrt (/ (- 1 x) (+ x 1)))
45.0ms	(/ (- 1 x) (+ x 1))
4.0ms	(atan (sqrt (/ (- 1 x) (+ x 1))))

simplify3.5s

Counts

106 → 112

Calls

106 calls:

Slowest

394.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ x 1) (+ x 1)) (+ x 1)))
280.0ms	(- (+ (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)))))
201.0ms	(sqrt (/ (- 1 x) (+ (pow x 3) (pow 1 3))))
114.0ms	(sqrt (/ (- 1 x) (- (* x x) (* 1 1))))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 122

Calls

3 calls:

Slowest

34.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
14.0ms	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
9.0ms	(sqrt (+ 1 x))

series101.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

56.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
40.0ms	(sqrt (+ 1 x))
4.0ms	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.0s

Counts

165 → 131

Calls

165 calls:

Slowest

267.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
247.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
196.0ms	(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
114.0ms	(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
80.0ms	(- (+ (* 1/2 (pow x 2)) 1) x)

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.0b	(* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))
0.0b	(atan (/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))))
0.0b	(/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x))))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
22×	`add-sqr-sqrt` `pow1`
18×	`sqrt-prod`
16×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
13×	`add-cube-cbrt`
12×	`flip3-+` `flip-+`
10×	`associate-l`
8×	`frac-times` `associate-r` `associate-/r/`
6×	`times-frac` `pow-prod-down` `associate-/l*`
5×	`prod-exp` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
4×	`associate-l/` `associate-r/` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `sqrt-unprod` `div-exp` `*-commutative` `distribute-lft-out` `associate-/l/`
1×	`pow2` `sqrt-undiv` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `flip3--` `cube-unmult` `pow-sqr` `div-inv` `flip--`

Counts

4 → 113

Calls

4 calls:

Slowest

74.0ms	(* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))
29.0ms	(/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x))))))
13.0ms	(* x (* x x))
9.0ms	(atan (/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

119.0ms	(/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x))))))
57.0ms	(* x (* x x))
47.0ms	(* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))
8.0ms	(atan (/ (sqrt (- 1 (* x (* x x)))) (* (sqrt (+ 1 x)) (sqrt (+ (* 1 1) (+ (* x x) (* 1 x)))))))

simplify13.2s

Counts

99 → 125

Calls

99 calls:

Slowest

507.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
488.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
454.0ms	(* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x))))
432.0ms	(+ 1 (* 2 1))
421.0ms	(* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x))))

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch7.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	8123×	body	80	nan
1.0s	8000×	body	80	valid