Details

Time bar (total: 2.2m)

sample97.0ms

Algorithm
intervals
Results
58.0ms253×body80valid
6.0ms7×body640valid
3.0ms6×body160valid
3.0ms2×body1280valid
0.0ms1×body320valid

simplify313.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
313.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize78.0ms

Local error

Found 4 expressions with local error:

34.0b
(cos (- (/ (* K (+ m n)) 2) M))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(* K (+ m n))
0.0b
(- (/ (* K (+ m n)) 2) M)

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
42×*-un-lft-identity prod-diff
36×add-cube-cbrt
23×cos-sum
22×times-frac
7×pow1 fma-neg add-exp-log div-inv
6×unpow-prod-down add-cbrt-cube add-log-exp
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u
3×pow-unpow associate-*l* difference-of-squares
2×sub-neg associate-*r/ distribute-lft-out--
1×distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ flip3-- diff-log pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ flip-- distribute-lft-out unpow2 unswap-sqr sqr-pow
Counts
4 → 129
Calls
4 calls:
Slowest
71.0ms
(pow (- (/ (+ m n) 2) M) 2)
44.0ms
(cos (- (/ (* K (+ m n)) 2) M))
14.0ms
(* K (+ m n))
14.0ms
(- (/ (* K (+ m n)) 2) M)

series345.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(cos (- (/ (* K (+ m n)) 2) M))
104.0ms
(pow (- (/ (+ m n) 2) M) 2)
90.0ms
(- (/ (* K (+ m n)) 2) M)
46.0ms
(* K (+ m n))

simplify10.9s

Counts
113 → 141
Calls
113 calls:
Slowest
445.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
315.0ms
(/ (exp (/ (* K (+ m n)) 2)) (exp M))
256.0ms
(- (pow M 2) (+ (* m M) (* M n)))
229.0ms
(fma 1 (/ (* K (+ m n)) 2) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))
223.0ms
(- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize53.0ms

Local error

Found 3 expressions with local error:

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

rewrite899.0ms

Algorithm
rewrite-expression-head
Rules
239×add-sqr-sqrt
229×*-un-lft-identity
187×prod-diff
115×add-cube-cbrt
78×unpow-prod-down
68×distribute-rgt-neg-in
66×distribute-lft-neg-in
62×times-frac
55×difference-of-squares
46×distribute-lft-out--
42×fma-neg
15×add-log-exp
13×unpow2 sqr-pow
12×distribute-lft-out
11×associate--r+
7×diff-log
6×neg-mul-1
4×pow1 add-exp-log div-inv
3×expm1-log1p-u pow-unpow sub-neg add-cbrt-cube insert-posit16 log1p-expm1-u
2×flip3-- neg-log flip--
1×associate--l- neg-sub0 pow-to-exp pow-pow pow-exp associate--r-
Counts
3 → 298
Calls
3 calls:
Slowest
820.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
36.0ms
(- (/ (+ m n) 2) M)
35.0ms
(pow (- (/ (+ m n) 2) M) 2)

series320.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
179.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
98.0ms
(pow (- (/ (+ m n) 2) M) 2)
43.0ms
(- (/ (+ m n) 2) M)

simplify1.4m

Counts
441 → 307
Calls
441 calls:
Slowest
824.0ms
(fma (sqrt (- (pow (- (/ (+ m n) 2) M) 2))) (sqrt (- (pow (- (/ (+ m n) 2) M) 2))) (- (* (- l (fabs (- m n))) 1)))
617.0ms
(fma (- (- l (fabs (- m n)))) 1 (* (- l (fabs (- m n))) 1))
581.0ms
(- (pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2))
576.0ms
(fma (- 1) (pow (- (/ (+ m n) 2) M) 2) (- (* (cbrt (- l (fabs (- m n)))) (* (cbrt (- l (fabs (- m n)))) (cbrt (- l (fabs (- m n))))))))
555.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

prune4.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

localize71.0ms

Local error

Found 4 expressions with local error:

33.9b
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))
0.5b
(cbrt K)
0.5b
(cbrt K)
0.5b
(cbrt K)

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
21×prod-diff
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×cbrt-prod times-frac
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 div-inv
1×cos-diff sub-neg
Counts
4 → 76
Calls
4 calls:
Slowest
79.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))
1.0ms
(cbrt K)
1.0ms
(cbrt K)
1.0ms
(cbrt K)

series849.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
247.0ms
(cbrt K)
236.0ms
(cbrt K)
228.0ms
(cbrt K)
139.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))

simplify8.8s

Counts
45 → 88
Calls
45 calls:
Slowest
653.0ms
(* (cos (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2)) (cos (- M)))
505.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) 1) (/ (* (cbrt K) (+ m n)) 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
504.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) (sqrt 2)) (/ (* (cbrt K) (+ m n)) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
466.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) 1) (/ (* (cbrt K) (+ m n)) 2) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
443.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) 1) (/ (* (cbrt K) (+ m n)) 2) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize80.0ms

Local error

Found 4 expressions with local error:

33.9b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))
16.0b
(cbrt (* K (+ m n)))
16.0b
(cbrt (* K (+ m n)))
16.0b
(cbrt (* K (+ m n)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
21×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×cbrt-div associate-*r/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+ div-inv
1×cos-diff sub-neg
Counts
4 → 76
Calls
4 calls:
Slowest
71.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))
10.0ms
(cbrt (* K (+ m n)))
10.0ms
(cbrt (* K (+ m n)))
10.0ms
(cbrt (* K (+ m n)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(cbrt (* K (+ m n)))
150.0ms
(cbrt (* K (+ m n)))
131.0ms
(cbrt (* K (+ m n)))
104.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

simplify8.8s

Counts
45 → 88
Calls
45 calls:
Slowest
324.0ms
(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))
297.0ms
(cbrt (* K (+ (pow m 3) (pow n 3))))
295.0ms
(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))
282.0ms
(* (cos (fma 1 (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
272.0ms
(cbrt (* K (- (* m m) (* n n))))

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

regimes639.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch5.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.7s8102×body80valid
184.0ms152×body640valid
151.0ms116×body1280valid
70.0ms105×body320valid
60.0ms60×body160valid
4.0ms2×body2560valid