Details

Time bar (total: 3.9s)

sample56.0ms

Algorithm
intervals
Results
25.0ms57×body2560valid
9.0ms41×body1280valid
6.0ms84×body80valid
5.0ms37×body640valid
3.0ms26×body320valid
1.0ms11×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b
(- 1.0 (cos x))
17.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

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:
7.0ms
(- 1.0 (cos x))
20.0ms
(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
46.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune135.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

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:
21.0ms
(/ (/ (- 1.0 (cos x)) x) x)
17.0ms
(/ (- 1.0 (cos x)) x)
7.0ms
(- 1.0 (cos x))

series110.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(/ (/ (- 1.0 (cos x)) x) x)
40.0ms
(/ (- 1.0 (cos x)) x)
23.0ms
(- 1.0 (cos x))

simplify58.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05921453
122121292
250011283

prune311.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- 1.0 (cos x)))
0.1b
(/ (log (exp (- 1.0 (cos x)))) x)
1.5b
(- 1.0 (cos x))
1.6b
(log (exp (- 1.0 (cos x))))

rewrite97.0ms

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:
17.0ms
(exp (- 1.0 (cos x)))
49.0ms
(/ (log (exp (- 1.0 (cos x)))) x)
10.0ms
(- 1.0 (cos x))
16.0ms
(log (exp (- 1.0 (cos x))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(exp (- 1.0 (cos x)))
45.0ms
(/ (log (exp (- 1.0 (cos x)))) x)
17.0ms
(- 1.0 (cos x))
18.0ms
(log (exp (- 1.0 (cos x))))

simplify43.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03931192
11234873
25001725

prune277.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b
(/ (cos x) x)
1.6b
(- (/ 1.0 x) (/ (cos x) x))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
338×times-frac
287×add-sqr-sqrt
267×*-un-lft-identity
227×add-cube-cbrt
169×prod-diff
39×div-inv
20×distribute-lft-out-- difference-of-squares
15×associate-/l*
13×fma-neg
7×add-exp-log add-cbrt-cube
6×associate-/r*
5×distribute-rgt-out-- add-log-exp
4×associate-/l/
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
1×sub-neg diff-log div-sub
Counts
3 → 306
Calls
3 calls:
83.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
11.0ms
(/ (cos x) x)
34.0ms
(- (/ 1.0 x) (/ (cos x) x))

series186.0ms

Counts
3 → 9
Calls
3 calls:
99.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
27.0ms
(/ (cos x) x)
60.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify103.0ms

Algorithm
egg-herbie
Counts
315 → 315
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
010096352
132214216
250013627

prune394.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.9b

bsearch54.0ms

Steps
ItersRangePoint
9
1.3330246063773173e-09
3.618674152218468
0.030875615092221424
7
-0.23317146499959118
-0.002309702793432406
-0.029930317430197608

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03418
13418

end0.0ms

sample1.6s

Algorithm
intervals
Results
742.0ms1596×body2560valid
282.0ms1322×body1280valid
210.0ms1458×body640valid
96.0ms898×body320valid
69.0ms2255×body80valid
33.0ms471×body160valid