Details

Time bar (total: 3.2m)

sample116.0ms

Algorithm
intervals
Results
79.0ms272×body80valid
4.0ms5×body320valid
3.0ms2×body1280valid
1.0ms1×body640valid

simplify332.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
332.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize95.0ms

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

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
204×add-sqr-sqrt
173×*-un-lft-identity
160×prod-diff
83×add-cube-cbrt
78×unpow-prod-down
68×distribute-rgt-neg-in
66×distribute-lft-neg-in
53×difference-of-squares
45×distribute-lft-out--
26×fma-neg
23×cos-sum
22×times-frac
14×add-log-exp
13×unpow2 sqr-pow
11×associate--r+
7×pow1 add-exp-log
6×neg-mul-1 add-cbrt-cube diff-log
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u
3×pow-unpow sub-neg associate-*l* div-inv
2×neg-log associate-*r/
1×associate--l- neg-sub0 distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ flip3-- pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ flip-- distribute-lft-out associate--r- unswap-sqr
Counts
4 → 276
Calls
4 calls:
Slowest
915.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
37.0ms
(cos (- (/ (* K (+ m n)) 2) M))
34.0ms
(pow (- (/ (+ m n) 2) M) 2)
13.0ms
(* K (+ m n))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
123.0ms
(pow (- (/ (+ m n) 2) M) 2)
91.0ms
(cos (- (/ (* K (+ m n)) 2) M))
29.0ms
(* K (+ m n))

simplify1.3m

Counts
366 → 288
Calls
366 calls:
Slowest
678.0ms
(fma (- (/ (+ m n) 2) M) (- (- (/ (+ m n) 2) M)) (- (* (- l (fabs (- m n))) 1)))
637.0ms
(fma (- (- l (fabs (- m n)))) 1 (* (- l (fabs (- m n))) 1))
636.0ms
(- (pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2))
583.0ms
(fma (pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2) (- (pow (cbrt (- (/ (+ m n) 2) M)) 2)) (- (* (- l (fabs (- m n))) 1)))
580.0ms
(fma (pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2) (- (pow (- (sqrt (/ (+ m n) 2)) (sqrt M)) 2)) (- (* (- (sqrt l) (sqrt (fabs (- m n)))) (+ (sqrt l) (sqrt (fabs (- m n)))))))

prune5.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize38.0ms

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
(- l (fabs (- m n)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
195×add-sqr-sqrt
164×*-un-lft-identity
148×prod-diff
78×unpow-prod-down
74×add-cube-cbrt
68×distribute-rgt-neg-in
66×distribute-lft-neg-in
54×difference-of-squares
46×distribute-lft-out--
29×fma-neg
15×add-log-exp
13×times-frac unpow2 sqr-pow
11×associate--r+
7×diff-log
6×neg-mul-1
4×pow1 add-exp-log
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 → 245
Calls
3 calls:
Slowest
979.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
58.0ms
(pow (- (/ (+ m n) 2) M) 2)
10.0ms
(- l (fabs (- m n)))

series365.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
238.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
99.0ms
(pow (- (/ (+ m n) 2) M) 2)
28.0ms
(- l (fabs (- m n)))

simplify1.3m

Counts
348 → 254
Calls
348 calls:
Slowest
745.0ms
(fma (* (cbrt (- (pow (- (/ (+ m n) 2) M) 2))) (cbrt (- (pow (- (/ (+ m n) 2) M) 2)))) (cbrt (- (pow (- (/ (+ m n) 2) M) 2))) (- (* (sqrt (- l (fabs (- m n)))) (sqrt (- l (fabs (- m n)))))))
735.0ms
(fma (* (cbrt (pow (- (/ (+ m n) 2) M) 2)) (cbrt (pow (- (/ (+ m n) 2) M) 2))) (- (cbrt (pow (- (/ (+ m n) 2) M) 2))) (- (* (- l (fabs (- m n))) 1)))
729.0ms
(fma (- (* (cbrt (pow (- (/ (+ m n) 2) M) 2)) (cbrt (pow (- (/ (+ m n) 2) M) 2)))) (cbrt (pow (- (/ (+ m n) 2) M) 2)) (- (* (- l (fabs (- m n))) 1)))
595.0ms
(- (pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2))
569.0ms
(fma (pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2) (- (pow (cbrt (- (/ (+ m n) 2) M)) 2)) (- (* (- l (fabs (- m n))) 1)))

prune4.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize145.0ms

Local error

Found 4 expressions with local error:

34.3b
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
34.2b
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
16.2b
(cbrt (/ (* K (+ m n)) 2))
16.2b
(cbrt (/ (* K (+ m n)) 2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×times-frac
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-div pow1/3 fma-udef div-inv
1×cos-sum sin-sum
Counts
4 → 60
Calls
4 calls:
Slowest
17.0ms
(cbrt (/ (* K (+ m n)) 2))
8.0ms
(cbrt (/ (* K (+ m n)) 2))
5.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
4.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
693.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
664.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
258.0ms
(cbrt (/ (* K (+ m n)) 2))
227.0ms
(cbrt (/ (* K (+ m n)) 2))

simplify5.0s

Counts
30 → 72
Calls
30 calls:
Slowest
860.0ms
(* (cbrt 1/2) (exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K))))))
510.0ms
(* (cbrt 1/2) (exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K))))))
409.0ms
(* (cbrt 1/2) (exp (* 1/3 (+ (log K) (log n)))))
404.0ms
(- (sin (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) (* (cos (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) M))
363.0ms
(* (cbrt 1/2) (exp (* 1/3 (+ (log K) (log n)))))

prune2.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize155.0ms

Local error

Found 4 expressions with local error:

34.3b
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
34.3b
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
34.3b
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
34.2b
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))

rewrite20.0ms

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
3×cos-sum
1×sin-sum
Counts
4 → 44
Calls
4 calls:
Slowest
5.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
5.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
5.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
4.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))

series2.9s

Counts
4 → 12
Calls
4 calls:
Slowest
810.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
729.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
700.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
670.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))

simplify3.2s

Counts
16 → 56
Calls
16 calls:
Slowest
357.0ms
(- (sin (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) (* (cos (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) M))
333.0ms
(+ (cos (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) (* (sin (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) M))
332.0ms
(+ (cos (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) (* (sin (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) M))
258.0ms
(+ (cos (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) (* (sin (* 1/2 (* (exp (* 1/3 (+ (* 2 (log K)) (* 2 (log n))))) (exp (* 1/3 (+ (log K) (log n))))))) M))
212.0ms
(cos (- (* 1/2 (* (exp (* -1/3 (+ (log (/ 1 m)) (log (/ 1 K))))) (exp (* -1/3 (+ (* 2 (log (/ 1 m))) (* 2 (log (/ 1 K)))))))) M))

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes399.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch5.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.7s8056×body80valid
246.0ms173×body640valid
246.0ms133×body1280valid
76.0ms103×body320valid
26.0ms59×body160valid
4.0ms2×body2560valid