Details

sample1.6s

Algorithm

intervals

Results

856.0ms	251×	body	10240	exit
333.0ms	112×	body	2560	valid
122.0ms	80×	body	1280	valid
121.0ms	527×	body	80	nan
27.0ms	31×	body	640	valid
13.0ms	19×	body	320	valid
4.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid
1.0ms	2×	body	160	nan

simplify50.0ms

Calls

1 calls:

Slowest

49.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.3b

localize42.0ms

Local error

Found 3 expressions with local error:

59.9b	(fmod (cosh a) (* a a))
2.0b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))

rewrite6.0ms

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`

Calls

3 calls:

Slowest

2.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
1.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms	(fmod (cosh a) (* a a))

series80.0ms

Calls

3 calls:

Slowest

64.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
11.0ms	(fmod (cosh a) (* a a))
4.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify1.2s

Calls

17 calls:

Slowest

386.0ms	(- (+ (* 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))))))
318.0ms	(- (+ (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))))
206.0ms	(- (+ (/ (* (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))))
55.0ms	(* (log (fmod (cosh a) (* a a))) (log1p a))
53.0ms	(pow (sqrt (fmod (cosh a) (* a a))) (log1p a))

prune554.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.2b

localize22.0ms

Local error

Found 4 expressions with local error:

59.9b	(fmod (cosh a) (* a a))
10.6b	(log (exp (fmod (cosh a) (* a a))))
2.0b	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0b	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))

rewrite17.0ms

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`

Calls

4 calls:

Slowest

6.0ms	(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))))
0.0ms	(fmod (cosh a) (* a a))

series64.0ms

Calls

4 calls:

Slowest

51.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
5.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
3.0ms	(log (exp (fmod (cosh a) (* a a))))
3.0ms	(fmod (cosh a) (* a a))

simplify1.5s

Calls

31 calls:

Slowest

436.0ms	(- (+ (* 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))))))
297.0ms	(- (+ (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))))
182.0ms	(- (+ (/ (* (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))))
61.0ms	(pow (* (cbrt (log (exp (fmod (cosh a) (* a a))))) (cbrt (log (exp (fmod (cosh a) (* a a)))))) (log1p a))
53.0ms	(pow (sqrt (log (exp (fmod (cosh a) (* a a))))) (log1p a))

prune821.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.2b

localize28.0ms

Local error

Found 4 expressions with local error:

59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))
10.0b	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

6.0ms	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series156.0ms

Calls

4 calls:

Slowest

147.0ms	(log (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify379.0ms

Calls

18 calls:

Slowest

70.0ms	(log (* (cbrt (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a)))))) (cbrt (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a))))))))
39.0ms	(log (sqrt (exp (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a)))))))
36.0ms	(pow (pow (fmod (cosh a) (pow a 2)) 2) 1/3)
35.0ms	(cbrt (fmod (cosh a) (* a a)))
33.0ms	(cbrt (fmod (cosh a) (* a a)))

prune868.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.2b

localize49.0ms

Local error

Found 4 expressions with local error:

59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))
59.9b	(fmod (cosh a) (* a a))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

4 calls:

Slowest

0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))
0.0ms	(fmod (cosh a) (* a a))

series14.0ms

Calls

4 calls:

Slowest

4.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(fmod (cosh a) (* a a))

simplify126.0ms

Calls

12 calls:

Slowest

15.0ms	(fmod (cosh a) (pow a 2))
11.0ms	(fmod (cosh a) (pow a 2))
11.0ms	(fmod (cosh a) (pow a 2))
11.0ms	(fmod (cosh a) (pow a 2))
11.0ms	(fmod (cosh a) (pow a 2))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 59.2b

regimes362.0ms

Accuracy

0% (0.2b remaining)

Error of 59.6b against oracle of 59.3b and baseline of 59.6b

bsearch4.0ms

end0.0ms

sample32.5s

Algorithm

intervals

Results

18.8s	7926×	body	10240	exit
7.0s	3224×	body	2560	valid
3.0s	2554×	body	1280	valid
1.9s	16167×	body	80	nan
869.0ms	1217×	body	640	valid
300.0ms	629×	body	320	valid
106.0ms	277×	body	160	valid
18.0ms	7×	body	5120	nan
16.0ms	99×	body	80	valid
9.0ms	7×	body	2560	nan
7.0ms	8×	body	1280	nan
4.0ms	8×	body	160	nan
4.0ms	9×	body	320	nan
3.0ms	6×	body	640	nan