Details

Time bar (total: 3.4s)

sample60.0ms

Algorithm
intervals
Results
28.0ms58×body2560valid
11.0ms46×body1280valid
7.0ms47×body640valid
3.0ms28×body320valid
3.0ms67×body80valid
1.0ms10×body160valid

simplify7.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.7b

Counts
2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.4b
(- 1.0 (cos x))
16.8b
(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

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))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series58.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
41.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify37.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune124.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New541064
Fresh000
Picked101
Done000
Total551065

Merged error: 0.1b

Counts
65 → 10

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b
(* 1/24 (pow x 2))
12.4b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×associate-*r*
7×add-exp-log
5×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 39
Calls
2 calls:
5.0ms
(* 1/24 (pow x 2))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series68.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(* 1/24 (pow x 2))
40.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify102.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0139194
1532171
22601171
35001170

prune99.0ms

Filtered
45 candidates to 30 candidates (66.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New44145
Fresh099
Picked101
Done000
Total451055

Merged error: 0.1b

Counts
55 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/24 (pow x 2))
0.5b
(expm1 (log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))))
12.4b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
22.8b
(log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×add-exp-log
8×associate-*r*
7×add-cube-cbrt *-un-lft-identity
6×add-cbrt-cube
5×expm1-log1p-u
4×pow1 unpow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l* prod-exp
2×unpow2 sqr-pow
1×pow-to-exp log1p-udef expm1-log1p log1p-expm1 pow-exp *-commutative cbrt-unprod fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
5.0ms
(* 1/24 (pow x 2))
1.0ms
(expm1 (log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
1.0ms
(log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 1/24 (pow x 2))
138.0ms
(expm1 (log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))))
40.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
95.0ms
(log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))

simplify38.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0285449
11022396
25001376

prune191.0ms

Filtered
73 candidates to 54 candidates (74.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New73073
Fresh099
Picked011
Done000
Total731083

Merged error: 0.1b

Counts
83 → 10

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)
1.4b
(- 1.0 (cos x))

rewrite27.0ms

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:
8.0ms
(/ (/ (- 1.0 (cos x)) x) x)
7.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series110.0ms

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

simplify59.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05921453
122121292
250011283

prune235.0ms

Filtered
174 candidates to 116 candidates (66.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1704174
Fresh268
Picked101
Done011
Total17311184

Merged error: 0.1b

Counts
184 → 11

regimes54.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch92.0ms

Steps
ItersRangePoint
10
0.0002141056345597589
3206628.0142593775
0.0320878512219627
11
-4.816760182774211e+16
-0.0014803844373699059
-0.034045814957462915

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03720
13720

end0.0ms

sample1.7s

Algorithm
intervals
Results
763.0ms1566×body2560valid
326.0ms1274×body1280valid
232.0ms1439×body640valid
120.0ms958×body320valid
78.0ms2308×body80valid
41.0ms455×body160valid