Details

Time bar (total: 4.1s)

sample50.0ms

Algorithm
intervals
Results
22.0ms51×body2560valid
10.0ms45×body1280valid
5.0ms36×body640valid
3.0ms86×body80valid
2.0ms22×body320valid
1.0ms16×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b
(- 1.0 (cos x))
15.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite14.0ms

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:
3.0ms
(- 1.0 (cos x))
10.0ms
(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
48.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify31.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0279446
11006326
25001317

prune131.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

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)
1.7b
(- 1.0 (cos x))

rewrite38.0ms

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:
21.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
9.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series104.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
45.0ms
(/ (- 1.0 (cos x)) x)
18.0ms
(- 1.0 (cos x))

simplify74.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0582999
12640823
25001787

prune255.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
1.7b
(- 1.0 (cos x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
110×add-sqr-sqrt *-un-lft-identity
76×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
9×prod-diff
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u fma-neg div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 165
Calls
3 calls:
11.0ms
(/ (/ (- 1.0 (cos x)) x) x)
9.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series106.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(/ (/ (- 1.0 (cos x)) x) x)
41.0ms
(/ (- 1.0 (cos x)) x)
18.0ms
(- 1.0 (cos x))

simplify58.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05921453
122121292
250011283

prune314.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.3b
(pow (cos x) 3)
0.4b
(fma (cos x) (cos x) (* 1.0 (cos x)))
1.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
156×add-sqr-sqrt
144×prod-diff
114×unpow-prod-down *-un-lft-identity cube-prod
84×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
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×difference-cubes pow-unpow
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub pow-exp prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv rem-cube-cbrt
Counts
4 → 297
Calls
4 calls:
58.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
1.0ms
(pow (cos x) 3)
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series325.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
28.0ms
(pow (cos x) 3)
51.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
51.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify130.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
07663804
129492790
250012733

prune386.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes63.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.6b

bsearch73.0ms

Steps
ItersRangePoint
10
4.127477794865454e-14
0.2287861600326909
0.029885297278870192
7
-0.03925098124715615
-0.001787912586083248
-0.03546967480400207

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03724
13724

end0.0ms

sample1.7s

Algorithm
intervals
Results
709.0ms1562×body2560valid
338.0ms1405×body640valid
289.0ms1318×body1280valid
105.0ms918×body320valid
71.0ms2340×body80valid
32.0ms457×body160valid