Details

sample1.4s

Algorithm

intervals

Results

765.0ms	235×	body	10240	exit
304.0ms	92×	body	2560	valid
120.0ms	84×	body	1280	valid
73.0ms	509×	body	80	nan
56.0ms	39×	body	640	valid
18.0ms	27×	body	320	valid
5.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid
0.0ms	1×	body	160	nan

simplify137.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

136.0ms

(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.5b

localize19.0ms

Local error

Found 3 expressions with local error:

58.7b	(fmod (cosh a) (* a a))
2.1b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `unpow-prod-down` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

3 → 41

Calls

3 calls:

Slowest

5.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
3.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series90.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

75.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
12.0ms	(fmod (cosh a) (* a a))
2.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify1.5s

Counts

17 → 50

Calls

17 calls:

Slowest

384.0ms	(- (+ (* 1/2 (* (pow a 2) (pow (log (fmod (cosh a) (pow a 2))) 2))) (+ (* a (log (fmod (cosh a) (pow a 2)))) 1)) (* 1/2 (* (pow a 2) (log (fmod (cosh a) (pow a 2))))))
285.0ms	(- (+ (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a))))) (+ (/ (* (log (fmod (cosh a) (pow a 2))) (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a)))))) a) (* 1/2 (/ (* (pow (log (fmod (cosh a) (pow a 2))) 2) (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a)))))) (pow a 2))))) (* 1/2 (/ (* (log (fmod (cosh a) (pow a 2))) (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a)))))) (pow a 2))))
260.0ms	(- (+ (/ (* (log (fmod (cosh a) (pow a 2))) (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a))))) a) (+ (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a)))) (* 1/2 (/ (* (pow (log (fmod (cosh a) (pow a 2))) 2) (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a))))) (pow a 2))))) (* 1/2 (/ (* (log (fmod (cosh a) (pow a 2))) (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a))))) (pow a 2))))
236.0ms	(pow (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a)))) (log1p a))
89.0ms	(pow (sqrt (fmod (cosh a) (* a a))) (log1p a))

prune588.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 58.9b

localize23.0ms

Local error

Found 4 expressions with local error:

58.7b	(fmod (cosh a) (* a a))
9.9b	(log (exp (fmod (cosh a) (* a a))))
2.1b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0b	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`log-pow`
7×	`pow1` `unpow-prod-down`
6×	`exp-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod`
1×	`acos-asin` `pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 63

Calls

4 calls:

Slowest

8.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))

series94.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

81.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
5.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
4.0ms	(log (exp (fmod (cosh a) (* a a))))
4.0ms	(fmod (cosh a) (* a a))

simplify2.2s

Counts

31 → 75

Calls

31 calls:

Slowest

442.0ms	(- (+ (* 1/2 (* (pow a 2) (pow (log (fmod (cosh a) (pow a 2))) 2))) (+ (* a (log (fmod (cosh a) (pow a 2)))) 1)) (* 1/2 (* (pow a 2) (log (fmod (cosh a) (pow a 2))))))
300.0ms	(- (+ (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a))))) (+ (/ (* (log (fmod (cosh a) (pow a 2))) (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a)))))) a) (* 1/2 (/ (* (pow (log (fmod (cosh a) (pow a 2))) 2) (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a)))))) (pow a 2))))) (* 1/2 (/ (* (log (fmod (cosh a) (pow a 2))) (exp (* -1 (* (log (fmod (cosh a) (pow a 2))) (log (/ 1 a)))))) (pow a 2))))
296.0ms	(pow (* (cbrt (log (exp (fmod (cosh a) (* a a))))) (cbrt (log (exp (fmod (cosh a) (* a a)))))) (log1p a))
264.0ms	(- (+ (/ (* (log (fmod (cosh a) (pow a 2))) (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a))))) a) (+ (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a)))) (* 1/2 (/ (* (pow (log (fmod (cosh a) (pow a 2))) 2) (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a))))) (pow a 2))))) (* 1/2 (/ (* (log (fmod (cosh a) (pow a 2))) (pow (fmod (cosh a) (pow a 2)) (- (log -1) (log (/ -1 a))))) (pow a 2))))
241.0ms	(pow (sqrt (log (exp (fmod (cosh a) (* a a))))) (log1p a))

prune818.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 58.9b

localize58.0ms

Local error

Found 4 expressions with local error:

58.7b	(fmod (cosh a) (* a a))
9.9b	(log (exp (fmod (cosh a) (* a a))))
2.1b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
1.2b	(log (exp (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `log-pow` `add-cube-cbrt`
6×	`pow1` `log-prod` `exp-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`acos-asin` `rem-log-exp`
1×	`log-div` `exp-diff`

Counts

4 → 58

Calls

4 calls:

Slowest

4.0ms	(log (exp (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
2.0ms	(log (exp (fmod (cosh a) (* a a))))
1.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))

series9.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

3.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
2.0ms	(log (exp (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(log (exp (fmod (cosh a) (* a a))))

simplify2.0s

Counts

27 → 70

Calls

27 calls:

Slowest

293.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
280.0ms	(sqrt (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))
271.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
269.0ms	(log (* (cbrt (exp (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))) (cbrt (exp (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))))))
215.0ms	(cbrt (acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))))

prune917.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 58.9b

localize69.0ms

Local error

Found 4 expressions with local error:

58.7b	(fmod (cosh a) (* a a))
58.7b	(fmod (cosh a) (* a a))
9.1b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.1b	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

Slowest

3.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series29.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

19.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
6.0ms	(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify570.0ms

Counts

22 → 64

Calls

22 calls:

Slowest

66.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))
59.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
47.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
43.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
41.0ms	(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune829.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 58.9b

regimes289.0ms

Accuracy

0% (0.2b remaining)

Error of 59.2b against oracle of 59.0b and baseline of 59.2b

bsearch5.0ms

end0.0ms

sample33.0s

Algorithm

intervals

Results

18.9s	7961×	body	10240	exit
7.1s	3115×	body	2560	valid
3.0s	2510×	body	1280	valid
2.1s	15968×	body	80	nan
907.0ms	1266×	body	640	valid
306.0ms	640×	body	320	valid
113.0ms	348×	body	160	valid
19.0ms	121×	body	80	valid
17.0ms	7×	body	5120	nan
6.0ms	8×	body	1280	nan
6.0ms	5×	body	2560	nan
5.0ms	8×	body	640	nan
3.0ms	7×	body	320	nan
3.0ms	9×	body	160	nan