Details

Time bar (total: 3.9s)

sample53.0ms

Algorithm
intervals
Results
23.0ms50×body2560valid
10.0ms48×body1280valid
6.0ms42×body640valid
4.0ms38×body320valid
2.0ms59×body80valid
1.0ms19×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize6.0ms

Local error

Found 2 expressions with local error:

2.5b
(- 1.0 (cos x))
14.5b
(/ (- 1.0 (cos x)) (* x x))

rewrite16.0ms

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:
4.0ms
(- 1.0 (cos x))
11.0ms
(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
48.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify31.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0279446
11006326
25001317

prune143.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

7 alts after pruning (7 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))
9.6b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite8.0ms

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))))

series71.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(* 1/24 (pow x 2))
42.0ms
(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
0139203
1565171
22616171
35001170

prune114.0ms

Filtered
45 candidates to 30 candidates (66.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
181×add-sqr-sqrt
157×*-un-lft-identity
156×times-frac
104×sqrt-prod
103×add-cube-cbrt
40×swap-sqr
28×associate-*r* associate-*l*
24×distribute-lft-out--
18×add-exp-log prod-diff add-cbrt-cube difference-of-squares
11×pow1
9×unswap-sqr
8×associate-/l* add-log-exp
6×fma-neg
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×flip3-- associate-/r* flip--
2×sub-neg sqrt-div diff-log associate-/l/
1×pow2 frac-times frac-2neg pow-plus associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr *-commutative pow-prod-up
Counts
4 → 238
Calls
4 calls:
11.0ms
(/ (sqrt (- 1.0 (cos x))) x)
45.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series176.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (sqrt (- 1.0 (cos x))) x)
48.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
18.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))

simplify98.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07292762
135882273
250022108

prune475.0ms

Filtered
250 candidates to 141 candidates (56.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
2.5b
(- 1.0 (cos x))
2.5b
(- 1.0 (cos x))
2.6b
(log (exp (- 1.0 (cos x))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
111×add-sqr-sqrt
81×*-un-lft-identity
72×times-frac
63×add-cube-cbrt
48×sqrt-prod
40×associate-*r*
28×associate-*l*
27×prod-diff
24×log-pow
20×exp-prod
16×add-exp-log add-cbrt-cube
14×log-prod
11×exp-sum
10×pow1
9×distribute-lft-out-- difference-of-squares unswap-sqr
8×add-log-exp
6×fma-neg
4×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u
3×sub-neg
2×flip3-- diff-log flip-- div-inv
1×frac-times log-div exp-diff associate-*r/ rem-log-exp pow-prod-down associate-*l/ *-commutative
Counts
4 → 186
Calls
4 calls:
71.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))
10.0ms
(log (exp (- 1.0 (cos x))))

series103.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
23.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))
19.0ms
(log (exp (- 1.0 (cos x))))

simplify70.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06882088
128411468
250011375

prune462.0ms

Filtered
198 candidates to 121 candidates (61.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes64.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 32.4b

bsearch71.0ms

Steps
ItersRangePoint
10
7.712829756242493e-08
8770343.893451896
0.023960596481684263
9
-1827977.1926269082
-0.00043085380315138777
-0.030927381235145903

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03010
13210
23210

end0.0ms

sample1.6s

Algorithm
intervals
Results
749.0ms1615×body2560valid
267.0ms1171×body1280valid
216.0ms1519×body640valid
97.0ms943×body320valid
91.0ms2276×body80valid
40.0ms476×body160valid