Details

Time bar (total: 4.0m)

sample107.0ms

Algorithm
intervals
Results
63.0ms256×body80valid
6.0ms6×body640valid
4.0ms6×body320valid
4.0ms2×body1280valid

simplify280.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
280.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize70.0ms

Local error

Found 4 expressions with local error:

36.6b
(cos (- (/ (* K (+ m n)) 2) M))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b
(- (/ (* K (+ m n)) 2) M)

rewrite948.0ms

Algorithm
rewrite-expression-head
Rules
217×add-sqr-sqrt
186×*-un-lft-identity
181×prod-diff
96×add-cube-cbrt
78×unpow-prod-down
68×distribute-rgt-neg-in
66×distribute-lft-neg-in
54×difference-of-squares
46×distribute-lft-out--
34×times-frac
33×fma-neg
23×cos-sum
16×add-log-exp
13×unpow2 sqr-pow
11×associate--r+
7×diff-log div-inv
6×neg-mul-1
5×pow1 add-exp-log
4×expm1-log1p-u sub-neg add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-unpow
2×flip3-- neg-log flip--
1×associate--l- neg-sub0 cos-diff pow-to-exp pow-pow pow-exp associate--r-
Counts
4 → 295
Calls
4 calls:
Slowest
852.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
46.0ms
(pow (- (/ (+ m n) 2) M) 2)
22.0ms
(cos (- (/ (* K (+ m n)) 2) M))
22.0ms
(- (/ (* K (+ m n)) 2) M)

series495.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
230.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
109.0ms
(pow (- (/ (+ m n) 2) M) 2)
81.0ms
(- (/ (* K (+ m n)) 2) M)
75.0ms
(cos (- (/ (* K (+ m n)) 2) M))

simplify1.8m

Counts
494 → 307
Calls
494 calls:
Slowest
797.0ms
(fma (- (* (cbrt (pow (- (/ (+ m n) 2) M) 2)) (cbrt (pow (- (/ (+ m n) 2) M) 2)))) (cbrt (pow (- (/ (+ m n) 2) M) 2)) (- (* (cbrt (- l (fabs (- m n)))) (* (cbrt (- l (fabs (- m n)))) (cbrt (- l (fabs (- m n))))))))
760.0ms
(fma (- (/ (+ m n) 2) M) (- (- (/ (+ m n) 2) M)) (- (* (- l (fabs (- m n))) 1)))
722.0ms
(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)))
652.0ms
(- (* (- (pow (- (/ (+ m n) 2) M) 2)) (- (pow (- (/ (+ m n) 2) M) 2))) (* (- l (fabs (- m n))) (- l (fabs (- m n)))))
644.0ms
(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)))

prune5.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize44.0ms

Local error

Found 2 expressions with local error:

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

rewrite970.0ms

Algorithm
rewrite-expression-head
Rules
185×add-sqr-sqrt
154×*-un-lft-identity
139×prod-diff
78×unpow-prod-down
68×distribute-rgt-neg-in
66×distribute-lft-neg-in add-cube-cbrt
53×difference-of-squares
45×distribute-lft-out--
26×fma-neg
13×times-frac unpow2 sqr-pow
12×add-log-exp
11×associate--r+
6×neg-mul-1 diff-log
3×pow1 pow-unpow add-exp-log
2×expm1-log1p-u sub-neg add-cbrt-cube neg-log insert-posit16 log1p-expm1-u
1×associate--l- neg-sub0 pow-to-exp pow-pow flip3-- pow-exp flip-- associate--r-
Counts
2 → 216
Calls
2 calls:
Slowest
923.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
40.0ms
(pow (- (/ (+ m n) 2) M) 2)

series348.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
235.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
113.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify1.5m

Counts
361 → 222
Calls
361 calls:
Slowest
768.0ms
(fma (sqrt (pow (- (/ (+ m n) 2) M) 2)) (- (sqrt (pow (- (/ (+ m n) 2) M) 2))) (- (* (cbrt (- l (fabs (- m n)))) (* (cbrt (- l (fabs (- m n)))) (cbrt (- l (fabs (- m n))))))))
748.0ms
(fma (- (sqrt (pow (- (/ (+ m n) 2) M) 2))) (sqrt (pow (- (/ (+ m n) 2) M) 2)) (- (* (- l (fabs (- m n))) 1)))
675.0ms
(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)))))))
631.0ms
(log1p (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
619.0ms
(expm1 (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))

prune3.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize82.0ms

Local error

Found 4 expressions with local error:

36.4b
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M)))
0.4b
(/ (+ m n) (sqrt 2))
0.4b
(/ K (sqrt 2))
0.2b
(fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
42×times-frac
36×add-sqr-sqrt add-cube-cbrt
27×sqrt-prod
12×associate-/r*
8×add-cbrt-cube add-exp-log
7×distribute-lft-out associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv associate-/l/
1×cos-sum flip3-+ flip-+
Counts
4 → 115
Calls
4 calls:
Slowest
16.0ms
(/ (+ m n) (sqrt 2))
5.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M)))
5.0ms
(/ K (sqrt 2))
0.0ms
(fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
665.0ms
(fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M))
277.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M)))
126.0ms
(/ (+ m n) (sqrt 2))
82.0ms
(/ K (sqrt 2))

simplify6.6s

Counts
172 → 127
Calls
172 calls:
Slowest
320.0ms
(/ (* (* (+ m n) (+ m n)) (+ m n)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
307.0ms
(* (* (/ (+ m n) (sqrt 2)) (/ (+ m n) (sqrt 2))) (/ (+ m n) (sqrt 2)))
268.0ms
(* (sqrt 2) (+ (* m m) (- (* n n) (* m n))))
238.0ms
(- (+ (/ (* K n) (pow (sqrt 2) 2)) (/ (* m K) (pow (sqrt 2) 2))) M)
237.0ms
(- (+ (/ (* K n) (pow (sqrt 2) 2)) (/ (* m K) (pow (sqrt 2) 2))) M)

prune2.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize132.0ms

Local error

Found 4 expressions with local error:

36.6b
(cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M)))
1.0b
(/ 1 (fabs (cbrt 2)))
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
8×add-exp-log
6×cbrt-prod add-cbrt-cube
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×pow1/3 div-exp
1×cbrt-undiv rec-exp cos-sum clear-num frac-2neg 1-exp fma-udef div-inv pow-flip inv-pow
Counts
4 → 73
Calls
4 calls:
Slowest
8.0ms
(/ 1 (fabs (cbrt 2)))
6.0ms
(cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M)))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)

series717.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
716.0ms
(cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M)))
0.0ms
(/ 1 (fabs (cbrt 2)))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify8.7s

Counts
93 → 79
Calls
93 calls:
Slowest
583.0ms
(sqrt (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M))))
561.0ms
(log1p (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M))))
557.0ms
(* (* (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M))) (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M)))) (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M))))
550.0ms
(* (cbrt (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M)))) (cbrt (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M)))))
549.0ms
(log (cos (fma (* (/ 1 (fabs (cbrt 2))) (/ K (sqrt (cbrt 2)))) (/ (+ m n) (sqrt 2)) (- M))))

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes574.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.7s8109×body80valid
270.0ms158×body640valid
159.0ms109×body1280valid
120.0ms110×body320valid
25.0ms54×body160valid
5.0ms4×body2560valid