Details

sample136.0ms

Algorithm

intervals

Results

54.0ms	59×	body	1280	valid
36.0ms	61×	body	640	valid
18.0ms	25×	body	2560	valid
10.0ms	29×	body	320	valid
6.0ms	66×	body	80	valid
4.0ms	16×	body	160	valid

simplify27.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

27.0ms

(log (+ x (sqrt (+ (* x x) 1))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.7b

localize9.0ms

Local error

Found 3 expressions with local error:

3.0b	(log (+ x (hypot 1 x)))
0.7b	(+ x (hypot 1 x))
0.0b	(hypot 1 x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

Slowest

5.0ms	(+ x (hypot 1 x))
4.0ms	(log (+ x (hypot 1 x)))
0.0ms	(hypot 1 x)

series346.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

181.0ms	(log (+ x (hypot 1 x)))
87.0ms	(+ x (hypot 1 x))
78.0ms	(hypot 1 x)

simplify2.7s

Counts

20 → 56

Calls

20 calls:

Slowest

611.0ms	(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
357.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
332.0ms	(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
225.0ms	(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
224.0ms	(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))

prune560.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

11.3b	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b	(* x -1/6)
0.0b	(fma 3/40 (pow x 5) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

Slowest

6.0ms	(* x -1/6)
1.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms	(fma 3/40 (pow x 5) x)

series305.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

190.0ms	(fma 3/40 (pow x 5) x)
82.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
32.0ms	(* x -1/6)

simplify1.0s

Counts

18 → 52

Calls

18 calls:

Slowest

184.0ms	(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
164.0ms	(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
163.0ms	(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
149.0ms	(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
112.0ms	(+ x (* 3/40 (pow x 5)))

prune474.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

14.3b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))
3.0b	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`pow1/3`
1×	`rem-log-exp` `log-pow` `fma-udef`

Counts

4 → 54

Calls

4 calls:

Slowest

1.0ms	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

series917.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

292.0ms	(cbrt x)
272.0ms	(cbrt x)
180.0ms	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
173.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

simplify1.8s

Counts

22 → 66

Calls

22 calls:

Slowest

394.0ms	(- (+ (* 1/2 (/ (pow x 2) (+ x 1))) (log (+ x 1))) (+ (* 1/8 (/ (pow x 4) (+ x 1))) (* 1/8 (/ (pow x 4) (pow (+ x 1) 2)))))
382.0ms	(- (+ x (+ (* 1/2 (pow x 2)) 1)) (* 1/8 (pow x 4)))
295.0ms	(- (* 1/2 (/ 1 (pow x 2))) (+ (log (/ -1 x)) 3/2))
174.0ms	(* (pow (* x -1) 1/3) (cbrt -1))
152.0ms	(* (pow (* x -1) 1/3) (cbrt -1))

prune524.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

3.0b	(log (+ x (hypot 1 x)))
3.0b	(log (+ x (hypot 1 x)))
3.0b	(log (+ x (hypot 1 x)))
0.7b	(+ x (hypot 1 x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

Slowest

8.0ms	(+ x (hypot 1 x))
4.0ms	(log (+ x (hypot 1 x)))
3.0ms	(log (+ x (hypot 1 x)))
3.0ms	(log (+ x (hypot 1 x)))

series630.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

191.0ms	(log (+ x (hypot 1 x)))
173.0ms	(log (+ x (hypot 1 x)))
170.0ms	(log (+ x (hypot 1 x)))
96.0ms	(+ x (hypot 1 x))

simplify3.7s

Counts

37 → 84

Calls

37 calls:

Slowest

321.0ms	(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
306.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
299.0ms	(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
277.0ms	(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
233.0ms	(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune744.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.3b

bsearch163.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.1s	2280×	body	1280	valid
1.0s	851×	body	2560	valid
894.0ms	1532×	body	640	valid
301.0ms	809×	body	320	valid
245.0ms	2112×	body	80	valid
92.0ms	416×	body	160	valid