Details

Time bar (total: 21.8s)

sample77.0ms

Algorithm
intervals
Results
31.0ms47×body2560valid
13.0ms40×body1280valid
10.0ms45×body640valid
7.0ms41×body320valid
4.0ms72×body80valid
2.0ms11×body160valid

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1138
2218
3268
4288
done288

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize17.0ms

Local error

Found 2 expressions with local error:

1.3b
(- 1.0 (cos x))
15.7b
(/ (- 1.0 (cos x)) (* x x))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
16.0ms
(- 1.0 (cos x))
42.0ms
(/ (- 1.0 (cos x)) (* x x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(- 1.0 (cos x))
79.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts
64 → 64
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0116808
1301681
21709566
done5001553

prune204.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.3b
(- 1.0 (cos x))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
54×*-un-lft-identity
46×times-frac
36×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp prod-diff
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×expm1-log1p-u fma-neg associate-/r* log1p-expm1-u div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 132
Calls
3 calls:
45.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
25.0ms
(/ (- 1.0 (cos x)) x)
7.0ms
(- 1.0 (cos x))

series172.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
64.0ms
(/ (- 1.0 (cos x)) x)
43.0ms
(- 1.0 (cos x))

simplify3.4s

Counts
141 → 141
Iterations

Useful iterations: done (3.4s)

IterNodesCost
02191855
16171600
238671382
done50001365

prune403.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ (cos x) 1.0))
0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.1b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
111×add-sqr-sqrt
99×*-un-lft-identity
90×unpow-prod-down cube-prod
85×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×fma-neg
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×pow-unpow fma-def associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod rem-cube-cbrt unswap-sqr
Counts
4 → 259
Calls
4 calls:
50.0ms
(* (cos x) (+ (cos x) 1.0))
7.0ms
(pow (cos x) 3)
14.0ms
(+ (cos x) 1.0)
60.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series173.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (cos x) (+ (cos x) 1.0))
48.0ms
(pow (cos x) 3)
17.0ms
(+ (cos x) 1.0)
56.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify6.4s

Counts
271 → 271
Iterations

Useful iterations: done (6.4s)

IterNodesCost
02767533
17324394
244563246
done50003245

prune513.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.1b
(- (pow 1.0 3) (pow (cos x) 3))
1.2b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
288×prod-diff
205×add-sqr-sqrt
179×*-un-lft-identity
174×unpow-prod-down cube-prod
157×add-cube-cbrt
149×log-prod
146×exp-sum
66×sqr-pow
50×cube-mult unpow3
32×difference-of-squares
26×log-pow
25×exp-prod
12×fma-neg
10×distribute-lft-out--
8×add-log-exp
6×pow1
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def
2×difference-cubes sub-neg
1×+-commutative pow-to-exp log-div flip3-- pow-pow flip3-+ exp-diff diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 420
Calls
4 calls:
7.0ms
(pow (cos x) 3)
9.0ms
(+ (cos x) 1.0)
32.0ms
(- (pow 1.0 3) (pow (cos x) 3))
108.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series185.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (cos x) 3)
11.0ms
(+ (cos x) 1.0)
77.0ms
(- (pow 1.0 3) (pow (cos x) 3))
61.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify3.4s

Counts
432 → 432
Iterations

Useful iterations: done (3.4s)

IterNodesCost
047814646
19017797
237545274
done50005273

prune658.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes109.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.1b

bsearch94.0ms

Steps
ItersRangePoint
9
5.2366538615162886e-09
1.4124627081995123
0.03201386298905525
7
-3.309911606533295
-0.03117879455470207
-0.033546375590763663

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03173
14047
done4047

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.1s1611×body2560valid
542.0ms1257×body1280valid
502.0ms1464×body640valid
246.0ms2255×body80valid
190.0ms937×body320valid
102.0ms476×body160valid