Details

Time bar (total: 4.0s)

sample53.0ms

Algorithm
intervals
Results
27.0ms62×body2560valid
7.0ms48×body640valid
6.0ms27×body1280valid
3.0ms77×body80valid
2.0ms26×body320valid
1.0ms16×body160valid

simplify8.0ms

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: 29.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.9b
(- 1.0 (cos x))
17.3b
(/ (- 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:
18.0ms
(- 1.0 (cos x))
49.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify33.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0279446
11006326
25001317

prune133.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) x)
0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.9b
(- 1.0 (cos x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
54×*-un-lft-identity
46×times-frac
36×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp prod-diff
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×expm1-log1p-u fma-neg associate-/r* log1p-expm1-u div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 132
Calls
3 calls:
9.0ms
(/ (- 1.0 (cos x)) x)
21.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

series112.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ (- 1.0 (cos x)) x)
42.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
23.0ms
(- 1.0 (cos x))

simplify73.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0582999
12640823
25001787

prune246.0ms

Filtered
141 candidates to 91 candidates (64.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ x (- 1.0 (cos x)))
0.1b
(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
0.2b
(/ 1 (/ x (- 1.0 (cos x))))
0.9b
(- 1.0 (cos x))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
283×times-frac
234×add-sqr-sqrt
198×*-un-lft-identity
135×add-cube-cbrt
100×add-exp-log
68×associate-*r*
50×div-exp
32×add-cbrt-cube
28×prod-exp
26×associate-/r* distribute-lft-out-- difference-of-squares
18×associate-/r/
17×rec-exp 1-exp
15×unswap-sqr
13×cbrt-undiv associate-*l*
11×div-inv
9×pow1 flip3-- prod-diff flip--
6×cbrt-unprod associate-/l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-flip fma-neg pow-prod-down inv-pow
2×frac-2neg clear-num
1×frac-times sub-neg diff-log associate-*r/ associate-*l/ un-div-inv *-commutative
Counts
4 → 324
Calls
4 calls:
5.0ms
(/ x (- 1.0 (cos x)))
49.0ms
(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
10.0ms
(/ 1 (/ x (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))

series145.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ x (- 1.0 (cos x)))
45.0ms
(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
41.0ms
(/ 1 (/ x (- 1.0 (cos x))))
18.0ms
(- 1.0 (cos x))

simplify184.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011702869
150012418

prune543.0ms

Filtered
336 candidates to 203 candidates (60.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x)))
0.1b
(* (/ 1 x) (/ 1 (fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x)))))
0.2b
(fma x 1/6 (/ 2 x))
0.4b
(/ 1 (fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
48×add-exp-log
39×times-frac
32×*-un-lft-identity
26×add-cube-cbrt
18×div-exp add-cbrt-cube
16×prod-exp
13×associate-*r* associate-*l*
9×pow1 rec-exp 1-exp unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×pow-flip pow-prod-down associate-/r* div-inv associate-/l* inv-pow
2×fma-udef
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num un-div-inv *-commutative
Counts
4 → 125
Calls
4 calls:
0.0ms
(fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x)))
14.0ms
(* (/ 1 x) (/ 1 (fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x)))))
0.0ms
(fma x 1/6 (/ 2 x))
2.0ms
(/ 1 (fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x))))

series220.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x)))
69.0ms
(* (/ 1 x) (/ 1 (fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x)))))
47.0ms
(fma x 1/6 (/ 2 x))
58.0ms
(/ 1 (fma (pow x 3) 1/120 (fma x 1/6 (/ 2 x))))

simplify61.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05301159
122261007
25001952

prune266.0ms

Filtered
137 candidates to 82 candidates (59.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes47.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 15.2b

bsearch52.0ms

Steps
ItersRangePoint
7
0.0008659720100092236
0.04032056371688071
0.024673669128913823
9
-3875183.9477288676
-0.008763241487176904
-0.03128865823944801

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03110
13110

end0.0ms

sample1.6s

Algorithm
intervals
Results
741.0ms1614×body2560valid
289.0ms1214×body1280valid
208.0ms1523×body640valid
95.0ms893×body320valid
69.0ms2304×body80valid
31.0ms452×body160valid