Details

Time bar (total: 13.5s)

sample133.0ms

Algorithm
intervals
Results
65.0ms50×body2560valid
41.0ms94×body1280valid
12.0ms58×body640valid
3.0ms22×body320valid
2.0ms20×body160valid
1.0ms12×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
1117
2147
3167
done167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
3.4b
(- 1.0 (cos x))

rewrite14.0ms

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:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series60.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
18.0ms
(- 1.0 (cos x))

simplify3.1s

Counts
74 → 74
Iterations

Useful iterations: 3 (500.0ms)

IterNodesCost
0134964
1302831
2898731
34757692
done5000692

prune179.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
0.2b
(exp (/ (- 1.0 (cos x)) (sin x)))
2.2b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.4b
(- 1.0 (cos x))

rewrite43.0ms

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:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
11.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms
(- 1.0 (cos x))

series129.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (- 1.0 (cos x)) (sin x))
43.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms
(- 1.0 (cos x))

simplify496.0ms

Counts
144 → 144
Iterations

Useful iterations: done (492.0ms)

IterNodesCost
01951743
13781509
210381372
done50001360

prune342.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sin x))
0.1b
(/ (cos x) (sin x))
3.6b
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
271×times-frac
222×add-sqr-sqrt
218×*-un-lft-identity
210×add-cube-cbrt
169×prod-diff
31×div-inv
13×fma-neg
7×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
5×add-log-exp
4×distribute-lft-out-- difference-of-squares
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 265
Calls
3 calls:
2.0ms
(/ 1.0 (sin x))
3.0ms
(/ (cos x) (sin x))
28.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series122.0ms

Counts
3 → 9
Calls
3 calls:
21.0ms
(/ 1.0 (sin x))
18.0ms
(/ (cos x) (sin x))
83.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify1.0s

Counts
274 → 274
Iterations

Useful iterations: done (1.0s)

IterNodesCost
037110874
18149603
222286890
done50006799

prune476.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
3.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
144×prod-diff
117×*-un-lft-identity
114×unpow-prod-down cube-prod
85×add-cube-cbrt
50×sqr-pow
48×difference-of-squares
26×cube-mult unpow3
25×times-frac associate-/l*
15×distribute-lft-out--
12×fma-neg
10×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×difference-cubes pow-unpow fma-def
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×+-commutative pow-to-exp sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub pow-exp prod-exp clear-num associate-/r* sum-log cbrt-unprod flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 304
Calls
4 calls:
57.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
23.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series246.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
27.0ms
(pow (cos x) 3)
9.0ms
(+ 1.0 (cos x))
50.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify2.1s

Counts
316 → 316
Iterations

Useful iterations: 2 (373.0ms)

IterNodesCost
03429345
18175855
230684730
done50004730

prune424.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes119.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch78.0ms

Steps
ItersRangePoint
9
6.379368274952145e-05
25.411711264148785
0.02572971521680811
10
-155084744.97222546
-0.0009113054925467739
-0.020168669770568547

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13755
done3755

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.1s1649×body2560valid
1.1s2670×body1280valid
427.0ms1833×body640valid
162.0ms952×body320valid
52.0ms494×body160valid
29.0ms6×body5120valid
25.0ms396×body80valid