Details

Time bar (total: 4.7s)

sample56.0ms

Algorithm
intervals
Results
26.0ms56×body2560valid
10.0ms44×body1280valid
6.0ms42×body640valid
3.0ms29×body320valid
2.0ms65×body80valid
1.0ms20×body160valid

simplify8.0ms

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: 30.6b

localize7.0ms

Local error

Found 2 expressions with local error:

1.6b
(- 1.0 (cos x))
17.6b
(/ (- 1.0 (cos x)) (* x x))

rewrite18.0ms

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:
4.0ms
(- 1.0 (cos x))
12.0ms
(/ (- 1.0 (cos x)) (* x x))

series61.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
43.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune139.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) x)
0.3b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.6b
(- 1.0 (cos x))

rewrite29.0ms

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:
6.0ms
(/ (- 1.0 (cos x)) x)
14.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms
(- 1.0 (cos x))

series110.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(/ (- 1.0 (cos x)) x)
42.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
22.0ms
(- 1.0 (cos x))

simplify71.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0582999
12640823
25001787

prune249.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 x) (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) x))
0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
1.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
527×add-sqr-sqrt
486×times-frac
362×*-un-lft-identity
257×add-cube-cbrt
241×associate-*r*
198×unpow-prod-down cube-prod
160×difference-of-squares
144×prod-diff
106×sqr-pow
50×distribute-lft-out--
44×add-exp-log
26×cube-mult unpow3 add-cbrt-cube
18×div-exp
13×associate-*l*
12×fma-neg prod-exp
10×difference-cubes
9×cbrt-undiv unswap-sqr
8×add-log-exp
7×pow1
6×cbrt-unprod
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp pow-unpow fma-def 1-exp
1×+-commutative frac-times pow-to-exp sub-neg flip3-- pow-pow flip3-+ diff-log associate-*r/ pow-prod-down associate-*l/ pow-exp sum-log *-commutative flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 529
Calls
4 calls:
95.0ms
(* (/ 1 x) (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) x))
2.0ms
(pow (cos x) 3)
4.0ms
(+ 1.0 (cos x))
19.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series239.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (/ 1 x) (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) x))
27.0ms
(pow (cos x) 3)
9.0ms
(+ 1.0 (cos x))
55.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify108.0ms

Algorithm
egg-herbie
Counts
541 → 541
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
021017426
150026365

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
1.0b
(log (exp (pow (cos x) 3)))
1.5b
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
192×prod-diff
170×log-pow
156×exp-prod
119×add-sqr-sqrt
117×*-un-lft-identity
112×add-cube-cbrt
94×unpow-prod-down cube-prod
32×sqr-pow
31×cube-mult unpow3
19×pow1
12×fma-neg
7×add-log-exp
6×log-prod
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×pow-unpow fma-def associate--r+
2×distribute-lft-out--
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 295
Calls
4 calls:
3.0ms
(pow (cos x) 3)
4.0ms
(+ 1.0 (cos x))
4.0ms
(log (exp (pow (cos x) 3)))
20.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series121.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
34.0ms
(log (exp (pow (cos x) 3)))
48.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify115.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06534257
120712171
250022159

prune342.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes79.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch88.0ms

Steps
ItersRangePoint
10
1.4316099847845607e-10
21.660028671588154
0.03040407886584754
9
-8.718619127186496
-1.4100946153605287e-08
-0.035460081688607266

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05139
15339
25339

end0.0ms

sample1.6s

Algorithm
intervals
Results
759.0ms1581×body2560valid
289.0ms1257×body1280valid
208.0ms1468×body640valid
99.0ms916×body320valid
71.0ms2298×body80valid
34.0ms480×body160valid