Details

sample140.0ms

Algorithm

intervals

Results

81.0ms	96×	body	1280	valid
25.0ms	48×	body	640	valid
14.0ms	22×	body	2560	valid
6.0ms	21×	body	320	valid
5.0ms	61×	body	80	valid
1.0ms	8×	body	160	valid

simplify11.0ms

Calls

1 calls:

Slowest

11.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.0b

localize18.0ms

Local error

Found 2 expressions with local error:

1.8b	(log (+ x (hypot 1 x)))
0.1b	(+ x (hypot 1 x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

8.0ms	(+ x (hypot 1 x))
7.0ms	(log (+ x (hypot 1 x)))

series270.0ms

Calls

2 calls:

Slowest

195.0ms	(log (+ x (hypot 1 x)))
75.0ms	(+ x (hypot 1 x))

simplify1.7s

Calls

17 calls:

Slowest

319.0ms	(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
316.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
215.0ms	(log (- (* x x) (* (hypot 1 x) (hypot 1 x))))
213.0ms	(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
176.0ms	(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))

prune415.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 3 expressions with local error:

15.5b	(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)

rewrite12.0ms

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`

Calls

3 calls:

Slowest

10.0ms	(* 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)

series312.0ms

Calls

3 calls:

Slowest

187.0ms	(fma 3/40 (pow x 5) x)
100.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
25.0ms	(* x -1/6)

simplify1.0s

Calls

18 calls:

Slowest

187.0ms	(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
168.0ms	(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
164.0ms	(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
145.0ms	(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
124.0ms	(+ x (* 3/40 (pow x 5)))

prune528.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

31.1b	(log (expm1 (log1p (+ x (hypot 1 x)))))
1.4b	(expm1 (log1p (+ x (hypot 1 x))))
0.1b	(+ x (hypot 1 x))
0.0b	(log1p (+ x (hypot 1 x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

4.0ms	(+ x (hypot 1 x))
1.0ms	(log (expm1 (log1p (+ x (hypot 1 x)))))
0.0ms	(log1p (+ x (hypot 1 x)))
0.0ms	(expm1 (log1p (+ x (hypot 1 x))))

series666.0ms

Calls

4 calls:

Slowest

322.0ms	(log (expm1 (log1p (+ x (hypot 1 x)))))
159.0ms	(expm1 (log1p (+ x (hypot 1 x))))
103.0ms	(log1p (+ x (hypot 1 x)))
82.0ms	(+ x (hypot 1 x))

simplify2.7s

Calls

21 calls:

Slowest

347.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
341.0ms	(- (+ (* 1/2 (/ (exp (- (log 2) (log (/ 1 x)))) (* (- (exp (- (log 2) (log (/ 1 x)))) 1) x))) (+ (log (- (exp (- (log 2) (log (/ 1 x)))) 1)) (* 1/4 (/ (exp (- (log 2) (log (/ 1 x)))) (* (- (exp (- (log 2) (log (/ 1 x)))) 1) (pow x 2)))))) (* 1/8 (/ (pow (exp (- (log 2) (log (/ 1 x)))) 2) (* (pow (- (exp (- (log 2) (log (/ 1 x)))) 1) 2) (pow x 2)))))
309.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
254.0ms	(- (* 1/12 (/ 1 (pow x 3))) (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
254.0ms	(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))

prune661.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

31.1b	(log (expm1 (log (+ 1 (+ x (hypot 1 x))))))
1.4b	(expm1 (log (+ 1 (+ x (hypot 1 x)))))
0.1b	(+ x (hypot 1 x))
0.0b	(log (+ 1 (+ x (hypot 1 x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

17.0ms	(log (+ 1 (+ x (hypot 1 x))))
9.0ms	(+ x (hypot 1 x))
2.0ms	(log (expm1 (log (+ 1 (+ x (hypot 1 x))))))
1.0ms	(expm1 (log (+ 1 (+ x (hypot 1 x)))))

series643.0ms

Calls

4 calls:

Slowest

322.0ms	(log (expm1 (log (+ 1 (+ x (hypot 1 x))))))
164.0ms	(expm1 (log (+ 1 (+ x (hypot 1 x)))))
91.0ms	(log (+ 1 (+ x (hypot 1 x))))
67.0ms	(+ x (hypot 1 x))

simplify3.2s

Calls

30 calls:

Slowest

333.0ms	(log (- (* 1 1) (* (+ x (hypot 1 x)) (+ x (hypot 1 x)))))
325.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
318.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
296.0ms	(- (+ (* 1/2 (/ (exp (- (log 2) (log (/ 1 x)))) (* (- (exp (- (log 2) (log (/ 1 x)))) 1) x))) (+ (log (- (exp (- (log 2) (log (/ 1 x)))) 1)) (* 1/4 (/ (exp (- (log 2) (log (/ 1 x)))) (* (- (exp (- (log 2) (log (/ 1 x)))) 1) (pow x 2)))))) (* 1/8 (/ (pow (exp (- (log 2) (log (/ 1 x)))) 2) (* (pow (- (exp (- (log 2) (log (/ 1 x)))) 1) 2) (pow x 2)))))
285.0ms	(- (+ (log 2) (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 x)))) (log (/ 1 x)))

prune804.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.1b

bsearch115.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.1s	2336×	body	1280	valid
900.0ms	1558×	body	640	valid
535.0ms	769×	body	2560	valid
530.0ms	415×	body	160	valid
298.0ms	800×	body	320	valid
254.0ms	2122×	body	80	valid