Details

Time bar (total: 21.8s)

sample65.0ms

Algorithm
intervals
Results
29.0ms263×body80valid
4.0ms6×body1280valid
3.0ms6×body640valid
0.0ms1×body320valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (104.0ms)

IterNodesCost
02129
15029
29529
322029
468028
5321028
done500128

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b
(- (/ (* K (+ m n)) 2.0) M)
33.7b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
208×add-sqr-sqrt
180×*-un-lft-identity
171×prod-diff
94×add-cube-cbrt
72×unpow-prod-down
62×distribute-rgt-neg-in
60×distribute-lft-neg-in
50×difference-of-squares
43×distribute-lft-out--
33×times-frac
31×fma-neg
23×cos-sum
16×add-log-exp
12×sqr-pow
11×associate--r+
7×diff-log div-inv
6×pow1 add-exp-log neg-mul-1 add-cbrt-cube
4×expm1-log1p-u sub-neg associate-*r* log1p-expm1-u
3×associate-*l*
2×flip3-- associate-*r/ neg-log flip--
1×associate--l- neg-sub0 distribute-rgt-in cos-diff distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out associate--r- unswap-sqr
Counts
4 → 281
Calls
4 calls:
29.0ms
(* K (+ m n))
1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
22.0ms
(- (/ (* K (+ m n)) 2.0) M)
44.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series497.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* K (+ m n))
282.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
85.0ms
(- (/ (* K (+ m n)) 2.0) M)
86.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.8s

Counts
293 → 293
Iterations

Useful iterations: done (1.8s)

IterNodesCost
047411880
110169351
232167598
done50007595

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize39.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
179×add-sqr-sqrt
148×*-un-lft-identity
129×prod-diff
78×unpow-prod-down
64×add-cube-cbrt
62×distribute-rgt-neg-in
60×distribute-lft-neg-in
51×difference-of-squares
43×distribute-lft-out--
24×fma-neg
13×times-frac sqr-pow
12×add-log-exp
11×associate--r+
6×neg-mul-1 diff-log
3×pow1 add-exp-log pow-unpow
2×expm1-log1p-u sub-neg neg-log add-cbrt-cube log1p-expm1-u
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow pow-exp flip-- associate--r-
Counts
2 → 201
Calls
2 calls:
105.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
1.7s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series613.0ms

Counts
2 → 6
Calls
2 calls:
322.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
291.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify2.4s

Counts
207 → 207
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02749396
16497425
220486187
done50005080

prune682.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
33.9b
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
3.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

series333.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
332.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

simplify1.8s

Counts
55 → 55
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
051459
180434
2167393
3474300
42151300
done5000300

prune439.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.5b
(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
0.6b
(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
33.7b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
42×prod-diff
40×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
23×cos-sum
21×times-frac
12×cbrt-prod
7×fma-neg div-inv
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow
2×cube-mult sub-neg unpow3 sqr-pow
1×cos-diff pow-to-exp flip3-- pow-pow pow1/3 diff-log pow-exp flip-- rem-cbrt-cube distribute-lft-out-- rem-cube-cbrt difference-of-squares
Counts
4 → 125
Calls
4 calls:
39.0ms
(- (/ (* K (+ m n)) 2.0) M)
5.0ms
(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
10.0ms
(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
71.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series562.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (/ (* K (+ m n)) 2.0) M)
100.0ms
(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
246.0ms
(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
109.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.7s

Counts
137 → 137
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02473670
15072921
217582437
done50012263

prune682.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 1.0b

regimes219.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01720
12118
22218
done2218

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.0s8123×body80valid
168.0ms145×body640valid
111.0ms124×body1280valid
50.0ms115×body320valid
19.0ms48×body160valid
2.0ms1×body2560valid