Details

sample2.1s

Algorithm

intervals

Results

1.1s	244×	body	10240	exit
266.0ms	90×	body	2560	valid
129.0ms	88×	body	1280	valid
102.0ms	506×	body	80	nan
74.0ms	47×	body	640	valid
12.0ms	20×	body	320	valid
4.0ms	8×	body	160	valid
1.0ms	3×	body	80	valid

simplify94.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

93.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.6b

localize23.0ms

Local error

Found 3 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
2.3b	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
0.0b	(pow (fmod (cosh a) (* a a)) (log1p a))

rewrite24.0ms

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

14.0ms	(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
5.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
1.0ms	(fmod (cosh a) (* a a))

series57.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

45.0ms	(pow (fmod (cosh a) (* a a)) (log1p a))
9.0ms	(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

358.0ms	(- (+ (* 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))))))
302.0ms	(- (+ (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))))
261.0ms	(- (+ (/ (* (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))))
206.0ms	(pow (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a)))) (log1p a))
95.0ms	(pow (sqrt (fmod (cosh a) (* a a))) (log1p a))

prune655.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.2b

localize24.0ms

Local error

Found 4 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
14.6b	(log (exp (fmod (cosh a) (* a a))))
2.3b	(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` `sqr-pow`

Counts

4 → 63

Calls

4 calls:

Slowest

12.0ms	(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))

series66.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

58.0ms	(pow (log (exp (fmod (cosh a) (* a a)))) (log1p a))
3.0ms	(fmod (cosh a) (* a a))
3.0ms	(log (exp (fmod (cosh a) (* a a))))
2.0ms	(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))

simplify2.2s

Counts

31 → 75

Calls

31 calls:

Slowest

375.0ms	(- (+ (* 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))))))
286.0ms	(- (+ (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))))
250.0ms	(pow (* (cbrt (log (exp (fmod (cosh a) (* a a))))) (cbrt (log (exp (fmod (cosh a) (* a a)))))) (log1p a))
215.0ms	(pow (sqrt (log (exp (fmod (cosh a) (* a a))))) (log1p a))
198.0ms	(- (+ (/ (* (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))))

prune865.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.2b

localize44.0ms

Local error

Found 4 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
59.4b	(fmod (cosh a) (* a a))
13.9b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.3b	(acos (* (pow (sqrt (fmod (cosh a) (* a a))) (log1p a)) (pow (log (exp (sqrt (fmod (cosh a) (* a a))))) (log1p a))))

rewrite6.0ms

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

series28.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

14.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
6.0ms	(fmod (cosh a) (* a a))
6.0ms	(acos (* (pow (sqrt (fmod (cosh a) (* a a))) (log1p a)) (pow (log (exp (sqrt (fmod (cosh a) (* a a))))) (log1p a))))
2.0ms	(fmod (cosh a) (* a a))

simplify1.5s

Counts

22 → 64

Calls

22 calls:

Slowest

394.0ms	(acos (pow (pow (sqrt (fmod (cosh a) (pow a 2))) (log1p a)) 2))
334.0ms	(acos (pow (pow (sqrt (fmod (cosh a) (pow a 2))) (log1p a)) 2))
326.0ms	(acos (pow (pow (sqrt (fmod (cosh a) (pow a 2))) (log1p a)) 2))
65.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))
45.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))

prune931.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 59.2b

localize79.0ms

Local error

Found 4 expressions with local error:

59.4b	(fmod (cosh a) (* a a))
59.4b	(fmod (cosh a) (* a a))
13.9b	(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.3b	(acos (* (pow (sqrt (fmod (cosh a) (* a a))) (log1p a)) (pow (log (exp (sqrt (fmod (cosh a) (* a a))))) (log1p a))))

rewrite7.0ms

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

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

series20.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

13.0ms	(log (exp (sqrt (fmod (cosh a) (* a a)))))
3.0ms	(acos (* (pow (sqrt (fmod (cosh a) (* a a))) (log1p a)) (pow (log (exp (sqrt (fmod (cosh a) (* a a))))) (log1p a))))
2.0ms	(fmod (cosh a) (* a a))
2.0ms	(fmod (cosh a) (* a a))

simplify1.4s

Counts

22 → 64

Calls

22 calls:

Slowest

321.0ms	(acos (pow (pow (sqrt (fmod (cosh a) (pow a 2))) (log1p a)) 2))
300.0ms	(acos (pow (pow (sqrt (fmod (cosh a) (pow a 2))) (log1p a)) 2))
279.0ms	(acos (pow (pow (sqrt (fmod (cosh a) (pow a 2))) (log1p a)) 2))
63.0ms	(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
62.0ms	(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))

prune834.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 59.2b

regimes371.0ms

Accuracy

0% (0.1b remaining)

Error of 59.3b against oracle of 59.2b and baseline of 59.3b

bsearch3.0ms

end0.0ms

sample36.1s

Algorithm

intervals

Results

21.1s	8094×	body	10240	exit
7.6s	3159×	body	2560	valid
3.3s	2525×	body	1280	valid
2.1s	16063×	body	80	nan
909.0ms	1251×	body	640	valid
422.0ms	658×	body	320	valid
101.0ms	293×	body	160	valid
38.0ms	114×	body	80	valid
22.0ms	8×	body	5120	nan
11.0ms	8×	body	2560	nan
5.0ms	9×	body	640	nan
5.0ms	6×	body	1280	nan
4.0ms	9×	body	320	nan
2.0ms	8×	body	160	nan