Details

Time bar (total: 3.8m)

sample112.0ms

Algorithm
intervals
Results
75.0ms258×body80valid
5.0ms5×body320valid
4.0ms3×body640valid
3.0ms2×body1280valid
1.0ms2×body160valid

simplify292.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize71.0ms

Local error

Found 4 expressions with local error:

34.9b
(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))))

rewrite1.1s

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
1.0s
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
44.0ms
(pow (- (/ (+ m n) 2) M) 2)
28.0ms
(cos (- (/ (* K (+ m n)) 2) M))
16.0ms
(* K (+ m n))

series718.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
499.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
105.0ms
(pow (- (/ (+ m n) 2) M) 2)
85.0ms
(cos (- (/ (* K (+ m n)) 2) M))
28.0ms
(* K (+ m n))

simplify1.4m

Counts
366 → 288
Calls
366 calls:
Slowest
709.0ms
(fma (pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2) (- (pow (- (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)) (- (* (- l (fabs (- m n))) 1)))
639.0ms
(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))))))))
628.0ms
(- (pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2))
572.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
560.0ms
(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)))

prune5.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.7b

localize62.0ms

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)))

rewrite1.0s

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
935.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
63.0ms
(pow (- (/ (+ m n) 2) M) 2)
10.0ms
(- l (fabs (- m n)))

series312.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
209.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
89.0ms
(pow (- (/ (+ m n) 2) M) 2)
13.0ms
(- l (fabs (- m n)))

simplify1.3m

Counts
348 → 254
Calls
348 calls:
Slowest
793.0ms
(fma (pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2) (- (pow (- (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)) (- (* (- l (fabs (- m n))) 1)))
740.0ms
(fma (- (pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)) (pow (- (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2) (- (* (- l (fabs (- m n))) 1)))
598.0ms
(fma (pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2) (- (pow (- (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)) (- (* (- (sqrt l) (sqrt (fabs (- m n)))) (+ (sqrt l) (sqrt (fabs (- m n)))))))
592.0ms
(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)))))))
584.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

prune4.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

localize98.0ms

Local error

Found 4 expressions with local error:

19.2b
(posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
0.0b
(- l (fabs (- m n)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
76×add-sqr-sqrt
68×prod-diff
47×add-cube-cbrt
20×distribute-rgt-neg-in
18×distribute-lft-neg-in distribute-lft-out--
16×add-log-exp
14×difference-of-squares
13×fma-neg
11×associate--r+
7×diff-log
6×neg-mul-1 unpow-prod-down
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-unpow sub-neg
2×flip3-- neg-log flip--
1×associate--l- neg-sub0 pow-to-exp pow-pow times-frac pow-exp remove-posit16 unpow2 associate--r- sqr-pow
Counts
4 → 160
Calls
4 calls:
Slowest
64.0ms
(pow (- (/ (+ m n) 2) M) 2)
40.0ms
(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
10.0ms
(- l (fabs (- m n)))
1.0ms
(posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
254.0ms
(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
124.0ms
(pow (- (/ (+ m n) 2) M) 2)
96.0ms
(posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))
14.0ms
(- l (fabs (- m n)))

simplify33.7s

Counts
176 → 172
Calls
176 calls:
Slowest
660.0ms
(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
573.0ms
(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
561.0ms
(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
557.0ms
(- (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2)))) (- l (fabs (- m n))))
540.0ms
(* (cbrt (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2))))) (cbrt (- (posit16->real (real->posit16 (pow (- (/ (+ m n) 2) M) 2))))))

prune4.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.7b

localize136.0ms

Local error

Found 4 expressions with local error:

35.3b
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
35.3b
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
15.0b
(cbrt (/ (* K (+ m n)) 2))
15.0b
(cbrt (/ (* K (+ m n)) 2))

rewrite14.0ms

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
4.0ms
(cbrt (/ (* K (+ m n)) 2))
4.0ms
(cbrt (/ (* K (+ m n)) 2))
3.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
2.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
733.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
677.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2)) (cbrt (/ (* K (+ m n)) 2))) (cbrt (/ (* K (+ m n)) 2)) (- (* M 1))))
264.0ms
(cbrt (/ (* K (+ m n)) 2))
215.0ms
(cbrt (/ (* K (+ m n)) 2))

simplify4.4s

Counts
30 → 72
Calls
30 calls:
Slowest
442.0ms
(* (cbrt 1/2) (exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K))))))
409.0ms
(* (cbrt 1/2) (exp (* 1/3 (+ (log K) (log n)))))
394.0ms
(* (cbrt 1/2) (exp (* 1/3 (+ (log K) (log n)))))
378.0ms
(* (cbrt 1/2) (exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K))))))
373.0ms
(+ (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))

prune2.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.7b

regimes559.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.7s8090×body80valid
151.0ms114×body1280valid
149.0ms152×body640valid
75.0ms100×body320valid
28.0ms57×body160valid
2.0ms1×body2560valid