Details

Time bar (total: 31.5s)

sample140.0ms

Algorithm
intervals
Results
99.0ms257×body80valid
7.0ms4×body1280valid
5.0ms4×body640valid
1.0ms2×body160valid
1.0ms1×body320valid

simplify263.0ms

Calls
1 calls:
Slowest
263.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize59.0ms

Local error

Found 3 expressions with local error:

32.9b
(cos (- (/ (* K (+ m n)) 2) M))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

rewrite4.7s

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×pow1 unpow-prod-down associate-*r*
5×add-cbrt-cube add-exp-log
3×pow-unpow associate-*l* exp-sum insert-posit16 add-log-exp
2×cos-sum sub-neg difference-of-squares
1×cos-diff pow-to-exp pow-pow times-frac exp-diff pow-prod-down pow-exp prod-exp associate-*r/ *-commutative cbrt-unprod distribute-lft-out-- unpow2 associate--r- unswap-sqr sqr-pow
Calls
3 calls:
Slowest
4.6s
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
44.0ms
(pow (- (/ (+ m n) 2) M) 2)
21.0ms
(cos (- (/ (* K (+ m n)) 2) M))

series607.0ms

Calls
3 calls:
Slowest
414.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
124.0ms
(pow (- (/ (+ m n) 2) M) 2)
70.0ms
(cos (- (/ (* K (+ m n)) 2) M))

simplify5.5s

Calls
36 calls:
Slowest
395.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
380.0ms
(- (exp (fabs (- m n))) (+ (* l (exp (fabs (- m n)))) (* 1/4 (* (pow m 2) (exp (fabs (- m n)))))))
372.0ms
(* (exp (- (+ (* m M) (+ (* M n) (fabs (- m n)))) (+ (* 1/4 (pow m 2)) (+ (pow M 2) (+ (* 1/2 (* m n)) (+ l (* 1/4 (pow n 2)))))))) (cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)))
335.0ms
(* (exp (- (+ (* m M) (+ (* M n) (fabs (- m n)))) (+ (* 1/4 (pow m 2)) (+ (pow M 2) (+ (* 1/2 (* m n)) (+ l (* 1/4 (pow n 2)))))))) (cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)))
307.0ms
(* (sqrt (cos (- (/ (* K (+ m n)) 2) M))) (sqrt (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize63.0ms

Local error

Found 1 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2) M) 2)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×unpow-prod-down
5×*-un-lft-identity
3×pow-unpow add-cube-cbrt
2×pow1 add-exp-log difference-of-squares
1×pow-to-exp pow-pow times-frac add-cbrt-cube pow-exp insert-posit16 distribute-lft-out-- unpow2 add-log-exp sqr-pow
Calls
1 calls:
Slowest
62.0ms
(pow (- (/ (+ m n) 2) M) 2)

series106.0ms

Calls
1 calls:
Slowest
106.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify1.6s

Calls
13 calls:
Slowest
435.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
264.0ms
(pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2)
254.0ms
(pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2)
180.0ms
(- (pow M 2) (+ (* m M) (* M n)))
177.0ms
(- (pow M 2) (+ (* m M) (* M n)))

prune416.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize56.0ms

Local error

Found 4 expressions with local error:

32.9b
(cos (- (/ (* K (+ m n)) 2) M))
0.5b
(log (exp (cos (- (/ (* K (+ m n)) 2) M))))
0.1b
(exp (cos (- (/ (* K (+ m n)) 2) M)))
0.0b
(pow (- (/ (+ m n) 2) M) 2)

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
9×add-cube-cbrt
6×pow1 cos-sum exp-prod unpow-prod-down
5×add-exp-log add-log-exp
4×log-prod add-cbrt-cube exp-diff log-pow insert-posit16
3×cos-diff pow-unpow sub-neg
2×log-div exp-sum difference-of-squares
1×pow-to-exp pow-pow times-frac rem-log-exp pow-exp distribute-lft-out-- unpow2 sqr-pow rem-exp-log
Calls
4 calls:
Slowest
42.0ms
(log (exp (cos (- (/ (* K (+ m n)) 2) M))))
35.0ms
(pow (- (/ (+ m n) 2) M) 2)
31.0ms
(cos (- (/ (* K (+ m n)) 2) M))
30.0ms
(exp (cos (- (/ (* K (+ m n)) 2) M)))

series444.0ms

Calls
4 calls:
Slowest
123.0ms
(pow (- (/ (+ m n) 2) M) 2)
116.0ms
(exp (cos (- (/ (* K (+ m n)) 2) M)))
102.0ms
(cos (- (/ (* K (+ m n)) 2) M))
102.0ms
(log (exp (cos (- (/ (* K (+ m n)) 2) M))))

simplify5.0s

Calls
42 calls:
Slowest
384.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
244.0ms
(log (exp (* (cos (/ (* K (+ m n)) 2)) (cos (- M)))))
241.0ms
(log (exp (* (cos (/ (* K (+ m n)) 2)) (cos M))))
236.0ms
(log (exp (* (cos (/ (* K (+ m n)) 2)) (cos (- M)))))
231.0ms
(- (pow M 2) (+ (* m M) (* M n)))

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

localize114.0ms

Local error

Found 4 expressions with local error:

32.9b
(cos (- (/ (* K (+ m n)) 2) M))
32.7b
(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
0.5b
(log (exp (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))))
0.1b
(exp (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×exp-prod
5×pow1 add-log-exp
4×add-cbrt-cube add-exp-log log-pow insert-posit16
3×log-prod
2×cos-sum
1×cos-diff sub-neg rem-log-exp remove-posit16 rem-exp-log
Calls
4 calls:
Slowest
27.0ms
(cos (- (/ (* K (+ m n)) 2) M))
7.0ms
(exp (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M)))))
2.0ms
(log (exp (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))))
0.0ms
(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))

series367.0ms

Calls
4 calls:
Slowest
129.0ms
(exp (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M)))))
93.0ms
(cos (- (/ (* K (+ m n)) 2) M))
81.0ms
(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
63.0ms
(log (exp (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))))

simplify2.6s

Calls
27 calls:
Slowest
200.0ms
(exp (* (cbrt (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))) (cbrt (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M)))))))
186.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
152.0ms
(log (sqrt (exp (posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M)))))))
150.0ms
(exp (cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)))
144.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune1.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

regimes491.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch3.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.9s8098×body80valid
195.0ms119×body1280valid
189.0ms159×body640valid
116.0ms101×body320valid
28.0ms60×body160valid
8.0ms5×body2560valid