Details

Time bar (total: 23.3s)

sample219.0ms

Algorithm
intervals
Results
94.0ms47×body2560valid
66.0ms83×body1280valid
27.0ms55×body640valid
12.0ms41×body320valid
3.0ms11×body160valid
2.0ms19×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1117
2147
3167
done167

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.3b
(- 1.0 (cos x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
20.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(- 1.0 (cos x))

series65.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(/ (- 1.0 (cos x)) (sin x))
20.0ms
(- 1.0 (cos x))

simplify1.2s

Counts
74 → 74
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0134964
1309834
21215733
done5001692

prune237.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.0b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.3b
(- 1.0 (cos x))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
23.0ms
(/ (- 1.0 (cos x)) (sin x))
32.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
28.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
8.0ms
(- 1.0 (cos x))

series237.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (- 1.0 (cos x)) (sin x))
64.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
71.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
31.0ms
(- 1.0 (cos x))

simplify1.3s

Counts
144 → 144
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01951743
13921512
214071374
done50001335

prune538.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (fma 1.0 1.0 (* (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))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
111×add-sqr-sqrt
97×*-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 log1p-expm1-u
3×pow-unpow fma-def associate-*r* associate-*l*
2×fma-udef
1×difference-cubes +-commutative distribute-rgt-in pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in flip3-+ diff-log pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 256
Calls
4 calls:
15.0ms
(* (sin x) (fma 1.0 1.0 (* (cos x) (+ (cos x) 1.0))))
4.0ms
(pow (cos x) 3)
7.0ms
(+ (cos x) 1.0)
53.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series259.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (sin x) (fma 1.0 1.0 (* (cos x) (+ (cos x) 1.0))))
45.0ms
(pow (cos x) 3)
16.0ms
(+ (cos x) 1.0)
72.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify4.2s

Counts
268 → 268
Iterations

Useful iterations: done (4.2s)

IterNodesCost
02997686
17804522
241093400
done50003398

prune651.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

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))))

rewrite249.0ms

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)
15.0ms
(+ (cos x) 1.0)
44.0ms
(- (pow 1.0 3) (pow (cos x) 3))
128.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series182.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (cos x) 3)
15.0ms
(+ (cos x) 1.0)
62.0ms
(- (pow 1.0 3) (pow (cos x) 3))
69.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify3.6s

Counts
432 → 432
Iterations

Useful iterations: done (3.6s)

IterNodesCost
047814646
19017797
237545274
done50005273

prune635.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

regimes284.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.6b

bsearch132.0ms

Steps
ItersRangePoint
9
5.2366538615162886e-09
1.4124627081995123
0.02393964535351435
8
-0.03117879455470207
-1.716801800522696e-06
-0.022947908688991478

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03761
14061
done4061

end0.0ms

sample8.9s

Algorithm
intervals
Results
4.0s1607×body2560valid
3.2s2739×body1280valid
802.0ms1869×body640valid
339.0ms936×body320valid
105.0ms374×body80valid
100.0ms472×body160valid
13.0ms3×body5120valid