Details

Time bar (total: 3.8s)

sample52.0ms

Algorithm
intervals
Results
27.0ms62×body2560valid
6.0ms48×body640valid
6.0ms27×body1280valid
3.0ms77×body80valid
3.0ms26×body320valid
1.0ms16×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: 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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
2.0ms
(- 1.0 (cos x))
8.0ms
(/ (- 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))

simplify59.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune105.0ms

Filtered
48 candidates to 34 candidates (70.8%)
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
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
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×associate-/r* 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 → 114
Calls
3 calls:
7.0ms
(/ (- 1.0 (cos x)) x)
23.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

series101.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(/ (- 1.0 (cos x)) x)
43.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
17.0ms
(- 1.0 (cos x))

simplify59.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0521814
12334726
25003690

prune210.0ms

Filtered
123 candidates to 80 candidates (65.0%)
Pruning

10 alts after pruning (9 fresh and 1 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))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
283×times-frac
227×add-sqr-sqrt
191×*-un-lft-identity
128×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-- flip--
6×cbrt-unprod associate-/l* add-log-exp
3×pow-flip 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 → 304
Calls
4 calls:
5.0ms
(/ x (- 1.0 (cos x)))
48.0ms
(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
10.0ms
(/ 1 (/ x (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))

series144.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ x (- 1.0 (cos x)))
42.0ms
(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
40.0ms
(/ 1 (/ x (- 1.0 (cos x))))
22.0ms
(- 1.0 (cos x))

simplify51.0ms

Algorithm
egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011062673
150012310

prune501.0ms

Filtered
316 candidates to 188 candidates (59.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/120 (pow x 3))
0.1b
(* (/ 1 x) (/ 1 (+ (+ (* 1/6 x) (/ 2 x)) (* 1/120 (pow x 3)))))
0.3b
(* 1/6 x)
0.4b
(/ 1 (+ (+ (* 1/6 x) (/ 2 x)) (* 1/120 (pow x 3))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
55×add-exp-log
39×times-frac
38×*-un-lft-identity
32×add-cube-cbrt
30×associate-*r*
22×add-cbrt-cube
20×prod-exp
19×associate-*l*
18×div-exp
14×unswap-sqr
11×pow1
9×rec-exp 1-exp
6×cbrt-unprod
5×cbrt-undiv
4×unpow-prod-down cube-prod pow-prod-down associate-/r/ add-log-exp
3×pow-flip associate-/r* *-commutative div-inv associate-/l* inv-pow
2×flip3-+ flip-+ sqr-pow
1×cube-mult frac-times pow-to-exp frac-2neg unpow3 associate-*r/ associate-*l/ pow-exp clear-num un-div-inv
Counts
4 → 154
Calls
4 calls:
7.0ms
(* 1/120 (pow x 3))
96.0ms
(* (/ 1 x) (/ 1 (+ (+ (* 1/6 x) (/ 2 x)) (* 1/120 (pow x 3)))))
3.0ms
(* 1/6 x)
41.0ms
(/ 1 (+ (+ (* 1/6 x) (/ 2 x)) (* 1/120 (pow x 3))))

series170.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 1/120 (pow x 3))
62.0ms
(* (/ 1 x) (/ 1 (+ (+ (* 1/6 x) (/ 2 x)) (* 1/120 (pow x 3)))))
16.0ms
(* 1/6 x)
54.0ms
(/ 1 (+ (+ (* 1/6 x) (/ 2 x)) (* 1/120 (pow x 3))))

simplify77.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06941476
133841273
250011242

prune292.0ms

Filtered
166 candidates to 95 candidates (57.2%)
Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

99.1% (0.1b remaining)

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

bsearch55.0ms

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
03517
13517

end0.0ms

sample1.5s

Algorithm
intervals
Results
724.0ms1614×body2560valid
276.0ms1214×body1280valid
210.0ms1523×body640valid
92.0ms893×body320valid
75.0ms2304×body80valid
31.0ms452×body160valid