Details

Time bar (total: 3.5s)

sample50.0ms

Algorithm
intervals
Results
23.0ms53×body2560valid
8.0ms36×body1280valid
6.0ms44×body640valid
3.0ms85×body80valid
2.0ms25×body320valid
1.0ms13×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b
(- 1.0 (cos x))
15.4b
(/ (- 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:
4.0ms
(- 1.0 (cos x))
8.0ms
(/ (- 1.0 (cos x)) (* x x))

series68.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
50.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune130.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.9b
(- 1.0 (cos x))

rewrite33.0ms

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:
14.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
10.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series109.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
47.0ms
(/ (- 1.0 (cos x)) x)
18.0ms
(- 1.0 (cos x))

simplify69.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0582999
12640823
25001787

prune250.0ms

Filtered
141 candidates to 91 candidates (64.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (exp (log (- 1.0 (cos x)))) x)
0.2b
(exp (log (- 1.0 (cos x))))
0.3b
(log (- 1.0 (cos x)))
1.9b
(- 1.0 (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt *-un-lft-identity
31×add-cube-cbrt
30×log-prod
25×exp-sum
24×times-frac
9×prod-diff
8×associate-/l*
7×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log log-div add-cbrt-cube add-log-exp
4×expm1-log1p-u exp-prod flip3-- exp-diff flip-- log1p-expm1-u
3×fma-neg associate-/r*
2×log-pow associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num div-inv rem-exp-log
Counts
4 → 118
Calls
4 calls:
8.0ms
(/ (exp (log (- 1.0 (cos x)))) x)
5.0ms
(exp (log (- 1.0 (cos x))))
4.0ms
(log (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series163.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (exp (log (- 1.0 (cos x)))) x)
18.0ms
(exp (log (- 1.0 (cos x))))
77.0ms
(log (- 1.0 (cos x)))
19.0ms
(- 1.0 (cos x))

simplify38.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0361939
11100784
25002738

prune291.0ms

Filtered
130 candidates to 86 candidates (66.2%)
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
(/ (log (exp (- 1.0 (cos x)))) x)
0.1b
(exp (- 1.0 (cos x)))
1.9b
(- 1.0 (cos x))
2.0b
(log (exp (- 1.0 (cos x))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
44×add-cube-cbrt
30×exp-prod log-pow
27×times-frac prod-diff
22×exp-sum
14×log-prod
9×pow1 associate-/l* add-log-exp
7×distribute-lft-out-- difference-of-squares
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×sub-neg exp-diff fma-neg associate-/r*
2×log-div diff-log rem-exp-log
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp rem-log-exp clear-num flip-- div-inv
Counts
4 → 141
Calls
4 calls:
9.0ms
(/ (log (exp (- 1.0 (cos x)))) x)
6.0ms
(exp (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))
6.0ms
(log (exp (- 1.0 (cos x))))

series125.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (log (exp (- 1.0 (cos x)))) x)
38.0ms
(exp (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))
19.0ms
(log (exp (- 1.0 (cos x))))

simplify41.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03931192
11234873
25001725

prune275.0ms

Filtered
153 candidates to 95 candidates (62.1%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes61.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch60.0ms

Steps
ItersRangePoint
7
0.007472435306926121
0.16151685480387348
0.03285064029015476
9
-0.10280128843953673
-1.4570494276460042e-08
-0.028907332605334953

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03624
13624

end0.0ms

sample1.5s

Algorithm
intervals
Results
708.0ms1550×body2560valid
287.0ms1284×body1280valid
207.0ms1500×body640valid
108.0ms921×body320valid
77.0ms2308×body80valid
35.0ms437×body160valid