Details

Time bar (total: 4.8m)

sample115.0ms

Algorithm
intervals
Results
77.0ms258×body80valid
10.0ms7×body1280valid
4.0ms5×body320valid
4.0ms5×body640valid
1.0ms2×body160valid

simplify314.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
314.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize53.0ms

Local error

Found 4 expressions with local error:

34.1b
(cos (- (/ (* K (+ m n)) 2) M))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
356×add-sqr-sqrt
303×*-un-lft-identity
290×prod-diff
138×unpow-prod-down
133×exp-sum add-cube-cbrt
125×distribute-rgt-neg-in
121×distribute-lft-neg-in
100×difference-of-squares
87×distribute-lft-out--
32×times-frac
26×fma-neg
25×add-log-exp
23×cos-sum unpow2 sqr-pow
12×diff-log
11×neg-mul-1 associate--r+
8×exp-prod
5×pow1 add-exp-log rem-exp-log
4×expm1-log1p-u sub-neg add-cbrt-cube neg-log insert-posit16 log1p-expm1-u
3×pow-unpow div-inv
2×associate--r-
1×associate--l- neg-sub0 cos-diff pow-to-exp pow-pow flip3-- exp-diff pow-exp flip--
Counts
4 → 407
Calls
4 calls:
Slowest
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.0s
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
52.0ms
(cos (- (/ (* K (+ m n)) 2) M))
32.0ms
(pow (- (/ (+ m n) 2) M) 2)

series502.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
117.0ms
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
99.0ms
(pow (- (/ (+ m n) 2) M) 2)
89.0ms
(cos (- (/ (* K (+ m n)) 2) M))

simplify2.1m

Counts
498 → 419
Calls
498 calls:
Slowest
811.0ms
(fma (sqrt (- (pow (- (/ (+ m n) 2) M) 2))) (sqrt (- (pow (- (/ (+ m n) 2) M) 2))) (- (* (- l (fabs (- m n))) 1)))
728.0ms
(exp (fma (- 1) (pow (- (/ (+ m n) 2) M) 2) (- (* (- (sqrt l) (sqrt (fabs (- m n)))) (+ (sqrt l) (sqrt (fabs (- m n))))))))
641.0ms
(fma (- (- l (fabs (- m n)))) 1 (* (- l (fabs (- m n))) 1))
626.0ms
(exp (fma (- (pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)) (pow (- (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2) (- (* (cbrt (- l (fabs (- m n)))) (* (cbrt (- l (fabs (- m n)))) (cbrt (- l (fabs (- m n)))))))))
609.0ms
(exp (fma (- (/ (+ m n) 2) M) (- (- (/ (+ m n) 2) M)) (- (* (- l (fabs (- m n))) 1))))

prune8.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.8b

localize69.0ms

Local error

Found 3 expressions with local error:

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

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
342×add-sqr-sqrt
289×*-un-lft-identity
269×prod-diff
138×unpow-prod-down
133×exp-sum
125×distribute-rgt-neg-in
121×distribute-lft-neg-in
119×add-cube-cbrt
100×difference-of-squares
87×distribute-lft-out--
26×fma-neg
24×add-log-exp
23×times-frac unpow2 sqr-pow
12×diff-log
11×neg-mul-1 associate--r+
8×exp-prod
5×rem-exp-log
4×pow1 neg-log add-exp-log
3×expm1-log1p-u pow-unpow sub-neg add-cbrt-cube insert-posit16 log1p-expm1-u
2×associate--r-
1×associate--l- neg-sub0 pow-to-exp pow-pow flip3-- exp-diff pow-exp flip--
Counts
3 → 373
Calls
3 calls:
Slowest
1.4s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
846.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
43.0ms
(pow (- (/ (+ m n) 2) M) 2)

series471.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
231.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
146.0ms
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
94.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify2.0m

Counts
471 → 382
Calls
471 calls:
Slowest
653.0ms
(exp (fma (- (pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2)) (pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2) (- (* (- l (fabs (- m n))) 1))))
651.0ms
(fma (pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2) (- (pow (cbrt (- (/ (+ m n) 2) M)) 2)) (- (* (cbrt (- l (fabs (- m n)))) (* (cbrt (- l (fabs (- m n)))) (cbrt (- l (fabs (- m n))))))))
632.0ms
(exp (fma -1 (pow (- (/ (+ m n) 2) M) 2) (- (* (- l (fabs (- m n))) 1))))
628.0ms
(fma (- (cbrt (- l (fabs (- m n))))) (* (cbrt (- l (fabs (- m n)))) (cbrt (- l (fabs (- m n))))) (* (cbrt (- l (fabs (- m n)))) (* (cbrt (- l (fabs (- m n)))) (cbrt (- l (fabs (- m n)))))))
618.0ms
(fma (- (pow (sqrt (- (/ (+ m n) 2) M)) 2)) (pow (sqrt (- (/ (+ m n) 2) M)) 2) (- (* (sqrt (- l (fabs (- m n)))) (sqrt (- l (fabs (- m n)))))))

prune6.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize153.0ms

Local error

Found 4 expressions with local error:

60.3b
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
60.3b
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
40.8b
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
40.8b
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))

rewrite11.0ms

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 fma-udef insert-posit16 log1p-expm1-u add-log-exp
1×cos-sum sin-sum
Counts
4 → 44
Calls
4 calls:
Slowest
5.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
5.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
1.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
0.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
871.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
788.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
359.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
347.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))

simplify1.0s

Counts
14 → 56
Calls
14 calls:
Slowest
254.0ms
(- (+ (/ (* K n) (pow (sqrt 2) 2)) (/ (* m K) (pow (sqrt 2) 2))) M)
189.0ms
(* (sin (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))) (cos (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
142.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M)))
121.0ms
(* (cos (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))) (cos (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
119.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (* -1 M)))

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize186.0ms

Local error

Found 4 expressions with local error:

60.3b
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
60.3b
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
40.8b
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
40.8b
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))

rewrite11.0ms

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 fma-udef insert-posit16 log1p-expm1-u add-log-exp
1×cos-sum sin-sum
Counts
4 → 44
Calls
4 calls:
Slowest
4.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
4.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
1.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
0.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
868.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
808.0ms
(fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))
317.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
281.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M))))))

simplify1.1s

Counts
14 → 56
Calls
14 calls:
Slowest
287.0ms
(- (+ (/ (* K n) (pow (sqrt 2) 2)) (/ (* m K) (pow (sqrt 2) 2))) M)
162.0ms
(* (sin (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))) (cos (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
154.0ms
(* (cos (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))) (cos (- (* (cbrt M) (* (cbrt M) (cbrt M))))))
142.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (* -1 M)))
128.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (* -1 M)))

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.8b

regimes737.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.0s8083×body80valid
208.0ms159×body640valid
204.0ms117×body1280valid
84.0ms106×body320valid
43.0ms3×body2560valid
30.0ms59×body160valid