Details

Time bar (total: 2.8s)

sample64.0ms

Algorithm
intervals
Results
31.0ms55×body2560valid
9.0ms55×body640valid
9.0ms34×body1280valid
3.0ms29×body320valid
3.0ms71×body80valid
1.0ms12×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0288
1288

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.7b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b
(- 1.0 (cos x))
16.5b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify30.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
05441441

prune91.0ms

Filtered
34 candidates to 48 candidates (-41.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New381048
Fresh000
Picked101
Done000
Total391049

Merged error: 0.1b

Counts
49 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow x 4) 1/720)
0.1b
(* x (* x -1/24))
0.3b
(* x -1/24)
12.4b
(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×add-exp-log
13×associate-*l* add-cbrt-cube
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-log-exp
7×associate-*r* prod-exp
5×cbrt-unprod
4×unpow-prod-down pow-prod-down unswap-sqr
3×sum-log *-commutative
2×sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-+ pow-exp flip-+
Counts
4 → 74
Calls
4 calls:
4.0ms
(* (pow x 4) 1/720)
4.0ms
(* x (* x -1/24))
3.0ms
(* x -1/24)
6.0ms
(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))

series13.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (pow x 4) 1/720)
3.0ms
(* x (* x -1/24))
2.0ms
(* x -1/24)
5.0ms
(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))

simplify54.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
05044646

prune114.0ms

Filtered
53 candidates to 86 candidates (-62.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New85186
Fresh099
Picked101
Done000
Total861096

Merged error: 0.1b

Counts
96 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow x 4) 1/720)
0.1b
(* x (* x -1/24))
0.3b
(* x -1/24)
12.4b
(+ (+ (* (pow x 4) 1/720) 1/2) (* x (* x -1/24)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×add-exp-log
13×associate-*l* add-cbrt-cube
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-log-exp
7×associate-*r* prod-exp
5×cbrt-unprod
4×unpow-prod-down pow-prod-down unswap-sqr
3×sum-log *-commutative
2×sqr-pow
1×+-commutative pow-to-exp associate-+l+ flip3-+ pow-exp flip-+
Counts
4 → 74
Calls
4 calls:
5.0ms
(* (pow x 4) 1/720)
4.0ms
(* x (* x -1/24))
3.0ms
(* x -1/24)
9.0ms
(+ (+ (* (pow x 4) 1/720) 1/2) (* x (* x -1/24)))

series13.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (pow x 4) 1/720)
3.0ms
(* x (* x -1/24))
2.0ms
(* x -1/24)
5.0ms
(+ (+ (* (pow x 4) 1/720) 1/2) (* x (* x -1/24)))

simplify54.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
04895646
14895646

prune113.0ms

Filtered
53 candidates to 86 candidates (-62.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New86086
Fresh099
Picked011
Done000
Total861096

Merged error: 0.1b

Counts
96 → 10

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (/ x (- 1.0 (cos x))))
0.1b
(/ x (- 1.0 (cos x)))
0.2b
(/ 1 (* x (/ x (- 1.0 (cos x)))))
2.6b
(- 1.0 (cos x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
42×*-un-lft-identity
34×times-frac
32×add-exp-log
26×add-cube-cbrt
21×associate-*r*
20×add-cbrt-cube
11×div-exp
9×pow1
8×prod-exp distribute-lft-out-- difference-of-squares
6×cbrt-undiv associate-/r* associate-/l* add-log-exp
5×associate-/r/
4×cbrt-unprod
3×rec-exp flip3-- 1-exp associate-*l* flip-- div-inv
2×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num unswap-sqr
1×sub-neg diff-log *-commutative inv-pow
Counts
4 → 124
Calls
4 calls:
9.0ms
(* x (/ x (- 1.0 (cos x))))
5.0ms
(/ x (- 1.0 (cos x)))
8.0ms
(/ 1 (* x (/ x (- 1.0 (cos x)))))
3.0ms
(- 1.0 (cos x))

series25.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* x (/ x (- 1.0 (cos x))))
9.0ms
(/ x (- 1.0 (cos x)))
5.0ms
(/ 1 (* x (/ x (- 1.0 (cos x)))))
3.0ms
(- 1.0 (cos x))

simplify42.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050211248

prune114.0ms

Filtered
88 candidates to 136 candidates (-54.5%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1342136
Fresh088
Picked011
Done011
Total13412146

Merged error: 0.1b

Counts
146 → 12

regimes73.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 31.1b

bsearch24.0ms

Steps
ItersRangePoint
7
0.003810670139712195
0.06592465963988953
0.036660421940451667
8
-0.6973264211480649
-0.00018277710226217338
-0.029842379482625983

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03543
13543

end0.0ms

sample1.8s

Algorithm
intervals
Results
845.0ms1629×body2560valid
349.0ms1257×body1280valid
251.0ms1447×body640valid
114.0ms963×body320valid
79.0ms2250×body80valid
37.0ms454×body160valid

Profiling

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