Details

Time bar (total: 3.9s)

sample69.0ms

Algorithm
intervals
Results
27.0ms49×body2560valid
13.0ms41×body1280valid
9.0ms45×body640valid
6.0ms36×body320valid
4.0ms69×body80valid
2.0ms16×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: 32.9b

localize10.0ms

Local error

Found 2 expressions with local error:

2.5b
(- 1.0 (cos x))
13.6b
(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

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:
3.0ms
(- 1.0 (cos x))
10.0ms
(/ (- 1.0 (cos x)) (* x x))

series67.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(- 1.0 (cos x))
44.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify31.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0279446
11006326
25001317

prune144.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 1/24 (pow x 2))
11.1b
(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:
6.0ms
(* 1/24 (pow x 2))
0.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series74.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(* 1/24 (pow x 2))
48.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify103.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0139194
1532171
22601171
35001170

prune124.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* 1/24 (pow x 2)))
0.2b
(* 1/24 (pow x 2))
2.8b
(log (exp (* 1/24 (pow x 2))))
23.1b
(fma (pow x 4) 1/720 (- 1/2 (log (exp (* 1/24 (pow x 2))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×add-exp-log
8×add-cube-cbrt *-un-lft-identity associate-*r*
7×add-log-exp
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u unpow-prod-down log1p-expm1-u unswap-sqr
3×log-prod associate-*l* prod-exp log-pow
2×exp-prod exp-to-pow unpow2 sqr-pow
1×pow-to-exp rem-log-exp pow-exp *-commutative cbrt-unprod fma-udef rem-exp-log
Counts
4 → 67
Calls
4 calls:
2.0ms
(exp (* 1/24 (pow x 2)))
6.0ms
(* 1/24 (pow x 2))
1.0ms
(log (exp (* 1/24 (pow x 2))))
0.0ms
(fma (pow x 4) 1/720 (- 1/2 (log (exp (* 1/24 (pow x 2))))))

series120.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(exp (* 1/24 (pow x 2)))
31.0ms
(* 1/24 (pow x 2))
27.0ms
(log (exp (* 1/24 (pow x 2))))
49.0ms
(fma (pow x 4) 1/720 (- 1/2 (log (exp (* 1/24 (pow x 2))))))

simplify113.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0180348
1625300
22920299
35002298

prune226.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) x)
0.1b
(/ (/ (- 1.0 (cos x)) x) x)
2.5b
(- 1.0 (cos x))

rewrite31.0ms

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:
9.0ms
(/ (- 1.0 (cos x)) x)
12.0ms
(/ (/ (- 1.0 (cos x)) x) x)
3.0ms
(- 1.0 (cos x))

series114.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(/ (- 1.0 (cos x)) x)
50.0ms
(/ (/ (- 1.0 (cos x)) x) x)
20.0ms
(- 1.0 (cos x))

simplify64.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05921453
122121292
250011283

prune309.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes40.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.6b

bsearch93.0ms

Steps
ItersRangePoint
9
0.00035723662727133143
33.11368705657117
0.032805924782194386
10
-29.541817090935037
-6.322351620237733e-11
-0.028665245890189286

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03724
13724

end0.0ms

sample2.1s

Algorithm
intervals
Results
914.0ms1621×body2560valid
384.0ms1238×body1280valid
338.0ms1531×body640valid
157.0ms954×body320valid
129.0ms2193×body80valid
56.0ms463×body160valid