Details

sample349.0ms

Algorithm

intervals

Results

139.0ms	212×	body	10240	exit
86.0ms	372×	body	80	nan
19.0ms	238×	body	80	valid
4.0ms	22×	body	160	valid

simplify505.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

504.0ms

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

prune10.0ms

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))

rewrite32.0ms

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

15.0ms	(sqrt (+ (exp x) 1))
14.0ms	(+ (exp x) 1)

series61.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

33.0ms	(sqrt (+ (exp x) 1))
27.0ms	(+ (exp x) 1)

simplify831.0ms

Counts

20 → 45

Calls

20 calls:

Slowest

355.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
152.0ms	(sqrt (+ (pow (exp x) 3) (pow 1 3)))
58.0ms	(sqrt (- (* (exp x) (exp x)) (* 1 1)))
53.0ms	(sqrt (sqrt (+ (exp x) 1)))
47.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))

prune428.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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

8.0ms	(sqrt (+ (exp x) 1))
7.0ms	(+ (exp x) 1)

series60.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

50.0ms	(sqrt (+ (exp x) 1))
10.0ms	(+ (exp x) 1)

simplify792.0ms

Counts

20 → 45

Calls

20 calls:

Slowest

409.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
109.0ms	(sqrt (+ (pow (exp x) 3) (pow 1 3)))
73.0ms	(sqrt (- (* (exp x) (exp x)) (* 1 1)))
70.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
15.0ms	(sqrt (+ (exp x) 1))

prune325.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (+ (exp x) 1))
0.1b	(expm1 (log1p (+ (exp x) 1)))
0.0b	(+ (exp x) 1)
0.0b	(sqrt (expm1 (log1p (+ (exp x) 1))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

Slowest

8.0ms	(+ (exp x) 1)
1.0ms	(sqrt (expm1 (log1p (+ (exp x) 1))))
1.0ms	(log1p (+ (exp x) 1))
0.0ms	(expm1 (log1p (+ (exp x) 1)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(expm1 (log1p (+ (exp x) 1)))
138.0ms	(sqrt (expm1 (log1p (+ (exp x) 1))))
95.0ms	(log1p (+ (exp x) 1))
9.0ms	(+ (exp x) 1)

simplify827.0ms

Counts

23 → 70

Calls

23 calls:

Slowest

386.0ms	(- (+ (sqrt 2) (+ (* 1/4 (/ (pow x 2) (sqrt 2))) (* 1/2 (/ x (sqrt 2))))) (* 1/8 (/ (pow x 2) (pow (sqrt 2) 3))))
98.0ms	(+ (* 1/3 x) (+ (log 3) (* 1/9 (pow x 2))))
76.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
65.0ms	(+ x (+ (* 1/2 (pow x 2)) 2))
27.0ms	(sqrt (* (cbrt (expm1 (log1p (+ (exp x) 1)))) (cbrt (expm1 (log1p (+ (exp x) 1))))))

prune698.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

5.5b	(- (* 1 1) (* (exp x) 1))
0.3b	(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
0.1b	(pow (exp x) 3)
0.0b	(* (exp x) (exp x))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
30×	`times-frac`
24×	`distribute-lft-out`
21×	`exp-prod`
19×	`unpow-prod-down` `cube-prod`
12×	`pow1`
10×	`associate-/l*`
9×	`add-cbrt-cube`
6×	`add-exp-log` `add-log-exp`
5×	`cube-mult`
4×	`expm1-log1p-u` `pow-pow` `pow-prod-down` `pow-sqr` `sum-cubes` `pow-prod-up` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r` `swap-sqr` `associate-r` `associate-l*`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`pow2` `pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 146

Calls

4 calls:

Slowest

167.0ms	(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
29.0ms	(- (* 1 1) (* (exp x) 1))
27.0ms	(* (exp x) (exp x))
7.0ms	(pow (exp x) 3)

series173.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

96.0ms	(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1))))
30.0ms	(pow (exp x) 3)
25.0ms	(- (* 1 1) (* (exp x) 1))
22.0ms	(* (exp x) (exp x))

simplify16.3s

Counts

144 → 158

Calls

144 calls:

Slowest

807.0ms	(/ (cbrt (+ (pow (exp x) 3) (pow 1 3))) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
533.0ms	(/ (sqrt (+ (pow (exp x) 3) (pow 1 3))) (sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
496.0ms	(/ (* (* (+ (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)))))
476.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1 3) (pow 1 3)))
432.0ms	(/ (sqrt (+ (pow (exp x) 3) (pow 1 3))) (cbrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))

prune1.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.7s	6700×	body	10240	exit
2.2s	12876×	body	80	nan
874.0ms	7372×	body	80	valid
233.0ms	737×	body	160	valid