Details

sample644.0ms

Algorithm

intervals

Results

464.0ms	232×	body	10240	exit
37.0ms	424×	body	80	nan
21.0ms	235×	body	80	valid
5.0ms	29×	body	160	valid

simplify299.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

297.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

Slowest

10.0ms	(sqrt (+ (exp x) 1))
7.0ms	(+ (exp x) 1)

series64.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

45.0ms	(sqrt (+ (exp x) 1))
19.0ms	(+ (exp x) 1)

simplify813.0ms

Counts

20 → 45

Calls

20 calls:

Slowest

366.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
114.0ms	(sqrt (+ (pow (exp x) 3) (pow 1 3)))
102.0ms	(sqrt (- (* (exp x) (exp x)) (* 1 1)))
66.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
20.0ms	(sqrt (* (cbrt (+ (exp x) 1)) (cbrt (+ (exp x) 1))))

prune440.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

Slowest

15.0ms	(sqrt (+ 1 (exp x)))
11.0ms	(+ 1 (exp x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

43.0ms	(sqrt (+ 1 (exp x)))
11.0ms	(+ 1 (exp x))

simplify679.0ms

Counts

19 → 46

Calls

19 calls:

Slowest

384.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
85.0ms	(sqrt (+ (pow 1 3) (pow (exp x) 3)))
63.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
18.0ms	(sqrt (- (* 1 1) (* (exp x) (exp x))))
15.0ms	(+ (exp x) 1)

prune400.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

5.7b	(- (* 1 1) (* (exp x) 1))
0.3b	(sqrt (/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
0.2b	(+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))
0.2b	(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
61×	`times-frac`
42×	`distribute-lft-out`
36×	`add-sqr-sqrt` `sqrt-prod`
33×	`add-cube-cbrt`
28×	`unpow-prod-down` `cube-prod`
11×	`add-log-exp`
10×	`associate-/l*`
7×	`cube-mult` `sum-cubes`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-+r+` `associate-/r*`
2×	`rem-sqrt-square` `sum-log` `sub-neg` `diff-log` `prod-diff` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `fma-def` `frac-2neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `fma-neg` `sqrt-div` `div-exp` `flip--`

Counts

4 → 151

Calls

4 calls:

Slowest

127.0ms	(sqrt (/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
124.0ms	(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
37.0ms	(+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))
22.0ms	(- (* 1 1) (* (exp x) 1))

series315.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(sqrt (/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
97.0ms	(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
32.0ms	(+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))
26.0ms	(- (* 1 1) (* (exp x) 1))

simplify22.2s

Counts

139 → 163

Calls

139 calls:

Slowest

544.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1 3) (pow 1 3)))
504.0ms	(- (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))
503.0ms	(/ (* (* (+ (pow (exp x) 3) (pow 1 3)) (+ (pow (exp x) 3) (pow 1 3))) (+ (pow (exp x) 3) (pow 1 3))) (* (* (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
488.0ms	(/ (cbrt (+ (pow (exp x) 3) (pow 1 3))) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
473.0ms	(/ (cbrt (+ (pow (exp x) 3) (pow 1 3))) (sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))

prune2.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

5.7b	(- 1 (exp x))
0.3b	(/ (sqrt (fma (exp (+ x x)) (exp x) 1)) (sqrt (fma (exp x) (exp x) (- 1 (exp x)))))
0.2b	(fma (exp x) (exp x) (- 1 (exp x)))
0.0b	(sqrt (fma (exp x) (exp x) (- 1 (exp x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
44×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`times-frac`
9×	`prod-diff`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `fma-udef` `div-inv` `flip--` `distribute-lft-out--`

Counts

4 → 121

Calls

4 calls:

Slowest

14.0ms	(- 1 (exp x))
12.0ms	(/ (sqrt (fma (exp (+ x x)) (exp x) 1)) (sqrt (fma (exp x) (exp x) (- 1 (exp x)))))
1.0ms	(sqrt (fma (exp x) (exp x) (- 1 (exp x))))
0.0ms	(fma (exp x) (exp x) (- 1 (exp x)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(/ (sqrt (fma (exp (+ x x)) (exp x) 1)) (sqrt (fma (exp x) (exp x) (- 1 (exp x)))))
69.0ms	(sqrt (fma (exp x) (exp x) (- 1 (exp x))))
38.0ms	(fma (exp x) (exp x) (- 1 (exp x)))
16.0ms	(- 1 (exp x))

simplify11.2s

Counts

129 → 133

Calls

129 calls:

Slowest

588.0ms	(sqrt (/ (+ (* (exp x) (exp (* 2 x))) 1) (- (+ (pow (exp x) 2) 1) (exp x))))
493.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
244.0ms	(- (+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2)))))
229.0ms	(- (+ (pow (exp x) 2) 1) (exp x))
221.0ms	(/ (* (* (sqrt (fma (exp (+ x x)) (exp x) 1)) (sqrt (fma (exp (+ x x)) (exp x) 1))) (sqrt (fma (exp (+ x x)) (exp x) 1))) (* (* (sqrt (fma (exp x) (exp x) (- 1 (exp x)))) (sqrt (fma (exp x) (exp x) (- 1 (exp x))))) (sqrt (fma (exp x) (exp x) (- 1 (exp x))))))

prune1.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample9.5s

Algorithm

intervals

Results

6.5s	6755×	body	10240	exit
1.5s	12909×	body	80	nan
961.0ms	7361×	body	80	valid
171.0ms	754×	body	160	valid