Details

Time bar (total: 4.3s)

sample60.0ms

Algorithm
intervals
Results
23.0ms45×body2560valid
10.0ms37×body1280valid
9.0ms51×body640valid
5.0ms37×body320valid
4.0ms71×body80valid
2.0ms15×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: 31.5b

localize6.0ms

Local error

Found 2 expressions with local error:

1.4b
(- 1.0 (cos x))
13.9b
(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

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))

series63.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
46.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune131.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.4b
(- 1.0 (cos x))

rewrite39.0ms

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:
22.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
9.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series109.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
41.0ms
(/ (- 1.0 (cos x)) x)
22.0ms
(- 1.0 (cos x))

simplify72.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0582999
12640823
25001787

prune248.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.1b
(/ (- 1.0 (cos x)) x)
1.4b
(- 1.0 (cos x))

rewrite42.0ms

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-*l*
17×add-cbrt-cube
13×associate-*r*
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 un-div-inv *-commutative
Counts
3 → 133
Calls
3 calls:
25.0ms
(* (/ (- 1.0 (cos x)) x) (/ 1 x))
9.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series107.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* (/ (- 1.0 (cos x)) x) (/ 1 x))
47.0ms
(/ (- 1.0 (cos x)) x)
19.0ms
(- 1.0 (cos x))

simplify69.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05981004
12536831
25001809

prune262.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

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)))
1.2b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite100.0ms

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:
59.0ms
(/ (- (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))

series322.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(/ (- (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)
52.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify132.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
07663804
129492790
250012733

prune391.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.0b

bsearch64.0ms

Steps
ItersRangePoint
8
0.003211336228265424
0.8894813891870064
0.03412323894191713
8
-1.3862719480695398
-4.2961337728369966e-05
-0.026274439846840626

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03110
13110

end0.0ms

sample2.0s

Algorithm
intervals
Results
891.0ms1653×body2560valid
370.0ms1236×body1280valid
292.0ms1491×body640valid
124.0ms877×body320valid
109.0ms2278×body80valid
51.0ms465×body160valid