Details

Time bar (total: 5.8s)

sample160.0ms

Algorithm
intervals
Results
84.0ms60×body2560valid
39.0ms84×body1280valid
20.0ms61×body640valid
4.0ms25×body320valid
2.0ms17×body160valid
1.0ms9×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.5b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.9b
(- 1.0 (cos x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series11.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

simplify80.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune111.0ms

Filtered
58 candidates to 42 candidates (27.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New481058
Fresh000
Picked101
Done000
Total491059

Merged error: 0.2b

Counts
59 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/240 (pow x 5)) (* 1/2 x))
0.0b
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.0b
(* 1/240 (pow x 5))
0.3b
(* 1/24 (pow x 3))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sum-log sqr-pow
2×+-commutative pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+
1×cube-mult associate-+r+ unpow3
Counts
4 → 80
Calls
4 calls:
4.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
9.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))

series26.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
6.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify52.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0355458
11538429
25002428

prune150.0ms

Filtered
92 candidates to 59 candidates (35.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh099
Picked011
Done000
Total9210102

Merged error: 0.2b

Counts
102 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.2b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.2b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b
(- 1.0 (cos x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt *-un-lft-identity
45×times-frac
38×exp-prod
33×add-cube-cbrt
20×log-pow
11×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
3×log-prod div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms
(- 1.0 (cos x))

series29.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
11.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms
(- 1.0 (cos x))

simplify90.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0303818
1799768
22970766
35001766

prune184.0ms

Filtered
124 candidates to 89 candidates (28.2%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1204124
Fresh088
Picked101
Done011
Total12113134

Merged error: 0.2b

Counts
134 → 13

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b
(/ (sin x) (- 1.0 (cos x)))
1.9b
(- 1.0 (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
105×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 159
Calls
3 calls:
9.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms
(/ (sin x) (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series18.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
8.0ms
(/ (sin x) (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))

simplify65.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05101595
123961450
250011337

prune114.0ms

Filtered
168 candidates to 83 candidates (50.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1644168
Fresh4711
Picked101
Done011
Total16912181

Merged error: 0.2b

Counts
181 → 12

regimes190.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.8b

bsearch39.0ms

Steps
ItersRangePoint
10
1.6467731241392944e-08
62869179882.65231
0.022639579152446066
9
-3.3701171682469404
-2.708263725627834e-09
-0.02084294767391905

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04936
14936

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.1s1575×body2560valid
1.3s2792×body1280valid
477.0ms1898×body640valid
162.0ms906×body320valid
55.0ms480×body160valid
24.0ms347×body80valid
5.0ms2×body5120valid

Profiling

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