Details

Time bar (total: 6.5s)

sample127.0ms

Algorithm
intervals
Results
60.0ms48×body2560valid
37.0ms86×body1280valid
15.0ms64×body640valid
5.0ms36×body320valid
1.0ms14×body80valid
1.0ms8×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

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: 33.2b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
1.5b
(- 1.0 (cos x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
12.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series56.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ (- 1.0 (cos x)) (sin x))
20.0ms
(- 1.0 (cos x))

simplify36.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0289569
1941460
25001460

prune156.0ms

Filtered
74 candidates to 51 candidates (31.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New601474
Fresh000
Picked101
Done000
Total611475

Merged error: 0.2b

Counts
75 → 14

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

series190.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
128.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

simplify35.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
060148
1184130
2979130
35001130

prune83.0ms

Filtered
26 candidates to 21 candidates (19.2%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New26026
Fresh01313
Picked011
Done000
Total261440

Merged error: 0.2b

Counts
40 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
0.2b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b
(- 1.0 (cos x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-exp-log add-log-exp
6×add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff rem-log-exp flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp clear-num rem-exp-log
Counts
4 → 133
Calls
4 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
8.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
11.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms
(- 1.0 (cos x))

series145.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (- 1.0 (cos x)) (sin x))
44.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
41.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms
(- 1.0 (cos x))

simplify43.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03651009
11075873
25001871

prune499.0ms

Filtered
145 candidates to 102 candidates (29.7%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1405145
Fresh3912
Picked101
Done011
Total14415159

Merged error: 0.2b

Counts
159 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b
(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.1b
(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.5b
(- 1.0 (cos x))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
339×times-frac
243×*-un-lft-identity
242×add-sqr-sqrt
174×add-cube-cbrt
156×exp-prod
79×log-pow
53×associate-/r/
36×associate-/r*
34×distribute-lft-out-- difference-of-squares
16×add-exp-log
13×div-inv associate-/l*
11×flip3-- flip--
9×prod-diff add-cbrt-cube
7×div-exp add-log-exp
6×pow1
5×clear-num
4×expm1-log1p-u frac-2neg log1p-expm1-u
3×cbrt-undiv log-prod fma-neg
2×rec-exp 1-exp rem-log-exp remove-double-div
1×sub-neg pow-flip diff-log rem-exp-log inv-pow
Counts
4 → 331
Calls
4 calls:
10.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
17.0ms
(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
19.0ms
(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
4.0ms
(- 1.0 (cos x))

series140.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
48.0ms
(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
36.0ms
(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
20.0ms
(- 1.0 (cos x))

simplify88.0ms

Algorithm
egg-herbie
Counts
343 → 343
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
07142891
128722548
250022299

prune547.0ms

Filtered
343 candidates to 216 candidates (37.0%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New3367343
Fresh7613
Picked011
Done011
Total34315358

Merged error: 0.2b

Counts
358 → 15

regimes69.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.8b

bsearch62.0ms

Steps
ItersRangePoint
9
0.0004381094517774334
96283.49646244562
0.01916768720892558
6
-0.04448272872103196
-0.010589856477353462
-0.022467842987435108

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03212
13212

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.1s1594×body2560valid
1.2s2719×body1280valid
447.0ms1937×body640valid
138.0ms914×body320valid
52.0ms489×body160valid
22.0ms345×body80valid
8.0ms2×body5120valid