Details

Time bar (total: 1.0m)

sample1.6s

Algorithm
intervals
Results
884.0ms245×body10240exit
340.0ms97×body2560valid
140.0ms79×body1280valid
84.0ms580×body80nan
43.0ms48×body640valid
13.0ms18×body320valid
5.0ms12×body160valid
1.0ms1×body2560nan
1.0ms1×body640nan
0.0ms2×body80valid

simplify144.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
144.0ms
(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize22.0ms

Local error

Found 3 expressions with local error:

59.0b
(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))

rewrite7.0ms

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
3.0ms
(pow (fmod (cosh a) (* a a)) (log1p a))
2.0ms
(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
1.0ms
(fmod (cosh a) (* a a))

series105.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
88.0ms
(pow (fmod (cosh a) (* a a)) (log1p a))
12.0ms
(fmod (cosh a) (* a a))
4.0ms
(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify1.8s

Counts
17 → 50
Calls
17 calls:
Slowest
450.0ms
(- (+ (* 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))))))
313.0ms
(pow (* (cbrt (fmod (cosh a) (* a a))) (cbrt (fmod (cosh a) (* a a)))) (log1p a))
282.0ms
(- (+ (/ (* (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))))
270.0ms
(- (+ (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))))
122.0ms
(pow (sqrt (fmod (cosh a) (* a a))) (log1p a))

prune569.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 59.3b

localize24.0ms

Local error

Found 4 expressions with local error:

59.0b
(fmod (cosh a) (* a a))
13.4b
(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))

rewrite9.0ms

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
4.0ms
(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))

series83.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
71.0ms
(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
(fmod (cosh a) (* a a))
4.0ms
(log (exp (fmod (cosh a) (* a a))))

simplify2.8s

Counts
31 → 75
Calls
31 calls:
Slowest
862.0ms
(- (+ (* 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))))))
293.0ms
(- (+ (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))))
291.0ms
(pow (* (cbrt (log (exp (fmod (cosh a) (* a a))))) (cbrt (log (exp (fmod (cosh a) (* a a)))))) (log1p a))
283.0ms
(pow (sqrt (log (exp (fmod (cosh a) (* a a))))) (log1p a))
246.0ms
(- (+ (/ (* (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))))

prune773.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 59.3b

localize33.0ms

Local error

Found 4 expressions with local error:

59.0b
(fmod (cosh a) (* a a))
59.0b
(fmod (cosh a) (* a a))
12.2b
(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)))

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

series25.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
17.0ms
(log (exp (sqrt (fmod (cosh a) (* a a)))))
5.0ms
(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))

simplify597.0ms

Counts
22 → 64
Calls
22 calls:
Slowest
56.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
49.0ms
(sqrt (sqrt (fmod (cosh a) (* a a))))
49.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
46.0ms
(sqrt (cbrt (fmod (cosh a) (* a a))))
43.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune996.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 59.3b

localize74.0ms

Local error

Found 4 expressions with local error:

59.0b
(fmod (cosh a) (* a a))
59.0b
(fmod (cosh a) (* a a))
12.2b
(log (exp (sqrt (fmod (cosh a) (* a a)))))
1.0b
(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
50×*-un-lft-identity
48×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
7×log-pow
6×exp-prod add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv
3×log-prod sqrt-prod
2×difference-of-squares
1×asin-acos sub-neg flip3-- diff-log rem-log-exp flip-- distribute-lft-out-- associate--r-
Counts
4 → 112
Calls
4 calls:
Slowest
12.0ms
(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
3.0ms
(log (exp (sqrt (fmod (cosh a) (* a a)))))
0.0ms
(fmod (cosh a) (* a a))
0.0ms
(fmod (cosh a) (* a a))

series60.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
38.0ms
(- (/ PI 2) (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))
18.0ms
(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.0ms
(fmod (cosh a) (* a a))
2.0ms
(fmod (cosh a) (* a a))

simplify20.1s

Counts
118 → 124
Calls
118 calls:
Slowest
462.0ms
(fma (* (cbrt (/ PI 2)) (cbrt (/ PI 2))) (cbrt (/ PI 2)) (- (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))))))
459.0ms
(fma (/ (* (cbrt PI) (cbrt PI)) (* (cbrt 2) (cbrt 2))) (/ (cbrt PI) (cbrt 2)) (- (* (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))))))
449.0ms
(fma (sqrt (/ PI 2)) (sqrt (/ PI 2)) (- (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (* (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (cbrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))))))
396.0ms
(fma (- (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (* (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))) (sqrt (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))))))
378.0ms
(fma (/ (* (cbrt PI) (cbrt PI)) (* (cbrt 2) (cbrt 2))) (/ (cbrt PI) (cbrt 2)) (- (* (asin (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a))) 1)))

prune964.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 59.3b

regimes291.0ms

Accuracy

0% (0.1b remaining)

Error of 59.2b against oracle of 59.1b and baseline of 59.2b

bsearch4.0ms

end0.0ms

sample30.5s

Algorithm
intervals
Results
17.1s7651×body10240exit
6.3s3226×body2560valid
3.1s2476×body1280valid
1.9s16013×body80nan
1.1s1248×body640valid
311.0ms597×body320valid
117.0ms330×body160valid
35.0ms7×body5120nan
19.0ms123×body80valid
11.0ms9×body2560nan
5.0ms9×body640nan
4.0ms5×body1280nan
2.0ms6×body320nan
1.0ms6×body160nan