Details

sample107.0ms

Algorithm

intervals

Results

63.0ms	66×	body	10240	exit
23.0ms	269×	body	80	valid
3.0ms	7×	body	640	valid
3.0ms	3×	body	1280	valid
2.0ms	5×	body	320	valid
2.0ms	8×	body	160	valid

simplify40.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

40.0ms

(- (log (+ 1 (exp x))) (* x y))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(log1p (exp x))
0.0b	(- (log1p (exp x)) (* y x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-neg` `prod-diff`
2×	`pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 34

Calls

2 calls:

Slowest

10.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series146.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

73.0ms	(- (log1p (exp x)) (* y x))
72.0ms	(log1p (exp x))

simplify647.0ms

Counts

17 → 40

Calls

17 calls:

Slowest

121.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
93.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
87.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))
80.0ms	(/ (exp (log1p (exp x))) (exp (* y x)))
45.0ms	(/ (+ 1 (exp x)) (exp (* y x)))

prune429.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(sqrt (log1p (exp x)))
0.7b	(sqrt (log1p (exp x)))
0.5b	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))
0.3b	(log1p (exp x))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

Slowest

1.0ms	(sqrt (log1p (exp x)))
1.0ms	(sqrt (log1p (exp x)))
0.0ms	(log1p (exp x))
0.0ms	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))
106.0ms	(sqrt (log1p (exp x)))
91.0ms	(sqrt (log1p (exp x)))
82.0ms	(log1p (exp x))

simplify1.2s

Counts

23 → 67

Calls

23 calls:

Slowest

462.0ms	(- (+ (* 1/16 (* (sqrt (/ 1 (log 2))) (pow x 2))) (+ (* 1/4 (* (sqrt (/ 1 (log 2))) x)) (sqrt (log 2)))) (* 1/32 (* (sqrt (/ 1 (pow (log 2) 3))) (pow x 2))))
364.0ms	(- (+ (* 1/16 (* (sqrt (/ 1 (log 2))) (pow x 2))) (+ (* 1/4 (* (sqrt (/ 1 (log 2))) x)) (sqrt (log 2)))) (* 1/32 (* (sqrt (/ 1 (pow (log 2) 3))) (pow x 2))))
89.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
89.0ms	(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
42.0ms	(- (log (+ (exp x) 1)) (* x y))

prune779.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

1.1b	(cbrt (- (log1p (exp x)) (* y x)))
1.1b	(cbrt (- (log1p (exp x)) (* y x)))
1.1b	(cbrt (- (log1p (exp x)) (* y x)))
0.7b	(* (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))) (cbrt (- (log1p (exp x)) (* y x))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
23×	`pow1`
14×	`associate-*l/`
13×	`cbrt-prod`
12×	`pow1/3`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-exp-log` `pow-prod-up` `add-cube-cbrt`
8×	`associate-*r/`
6×	`pow-plus` `associate-r`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2` `unswap-sqr`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 112

Calls

4 calls:

Slowest

65.0ms	(* (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))) (cbrt (- (log1p (exp x)) (* y x))))
2.0ms	(cbrt (- (log1p (exp x)) (* y x)))
2.0ms	(cbrt (- (log1p (exp x)) (* y x)))
2.0ms	(cbrt (- (log1p (exp x)) (* y x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

395.0ms	(cbrt (- (log1p (exp x)) (* y x)))
383.0ms	(cbrt (- (log1p (exp x)) (* y x)))
341.0ms	(cbrt (- (log1p (exp x)) (* y x)))
71.0ms	(* (* (cbrt (- (log1p (exp x)) (* y x))) (cbrt (- (log1p (exp x)) (* y x)))) (cbrt (- (log1p (exp x)) (* y x))))

simplify16.9s

Counts

104 → 124

Calls

104 calls:

Slowest

557.0ms	(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
541.0ms	(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
541.0ms	(* (* (cbrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (cbrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))) (cbrt (+ (log1p (exp x)) (* y x))))
526.0ms	(cbrt (- (* (log1p (exp x)) (log1p (exp x))) (* (* y x) (* y x))))
489.0ms	(- (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y)))))) (+ (* 1/9 (/ (* (pow (log (+ (exp x) 1)) 2) (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))))) (* (pow x 2) (pow y 2)))) (* 1/3 (/ (* (log (+ (exp x) 1)) (exp (* 1/3 (- (log -1) (+ (log (/ -1 x)) (log (/ -1 y))))))) (* x y)))))

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (fma 1/8 x 1/2) x (log 2))
0.0b	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

2 → 33

Calls

2 calls:

Slowest

6.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
0.0ms	(fma (fma 1/8 x 1/2) x (log 2))

series131.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

82.0ms	(- (fma (fma 1/8 x 1/2) x (log 2)) (* y x))
49.0ms	(fma (fma 1/8 x 1/2) x (log 2))

simplify1.6s

Counts

16 → 39

Calls

16 calls:

Slowest

305.0ms	(/ (exp (fma (fma 1/8 x 1/2) x (log 2))) (exp (* y x)))
215.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
210.0ms	(- (+ (* 1/2 x) (* 1/8 (pow x 2))) (* x y))
159.0ms	(fma 1 (fma (fma 1/8 x 1/2) x (log 2)) (- (* x y)))
152.0ms	(fma (* (cbrt (fma (fma 1/8 x 1/2) x (log 2))) (cbrt (fma (fma 1/8 x 1/2) x (log 2)))) (cbrt (fma (fma 1/8 x 1/2) x (log 2))) (- (* x y)))

prune495.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes127.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch4.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.6s	2265×	body	10240	exit
916.0ms	8369×	body	80	valid
152.0ms	273×	body	640	valid
128.0ms	132×	body	1280	valid
86.0ms	170×	body	320	valid
25.0ms	120×	body	160	valid