Details

Time bar (total: 1.7s)

analyze737.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 78.161621%

sample68.0ms

Algorithm
intervals
Results
30.0ms58×body2560valid
13.0ms46×body1280valid
6.0ms22×body160valid
6.0ms33×body640valid
4.0ms34×body320valid
2.0ms63×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.6b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.5b
(- 1.0 (cos x))
18.7b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

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:
3.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune92.0ms

Filtered
34 candidates to 48 candidates (-41.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New381048
Fresh000
Picked101
Done000
Total391049

Merged error: 0.1b

Counts
49 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/720 (pow x 4)) 1/2)
0.1b
(* 1/720 (pow x 4))
0.4b
(* 1/24 (pow x 2))
10.6b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×associate-*r*
14×add-exp-log
11×add-log-exp
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 sqr-pow
2×pow-to-exp diff-log pow-exp sum-log *-commutative cbrt-unprod unpow2
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ flip-- flip-+
Counts
4 → 77
Calls
4 calls:
4.0ms
(+ (* 1/720 (pow x 4)) 1/2)
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
6.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series19.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(+ (* 1/720 (pow x 4)) 1/2)
4.0ms
(* 1/720 (pow x 4))
3.0ms
(* 1/24 (pow x 2))
5.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify44.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0312408
11312376
25001369

prune151.0ms

Filtered
56 candidates to 89 candidates (-58.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New88189
Fresh099
Picked101
Done000
Total891099

Merged error: 0.1b

Counts
99 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.4b
(* 1/24 (pow x 2))
10.6b
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×sqr-pow
3×pow1
2×pow-to-exp associate-+r+ pow-exp sum-log *-commutative cbrt-unprod unpow2
1×+-commutative associate-+r- sub-neg flip3-+ diff-log flip-+
Counts
3 → 67
Calls
3 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
5.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series11.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* 1/720 (pow x 4))
3.0ms
(* 1/24 (pow x 2))
5.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify38.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0274345
11103314
25001314

prune126.0ms

Filtered
47 candidates to 76 candidates (-61.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh099
Picked011
Done000
Total761086

Merged error: 0.1b

Counts
86 → 10

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))
3.5b
(- 1.0 (cos x))

rewrite30.0ms

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:
6.0ms
(/ (- 1.0 (cos x)) x)
16.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

series14.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ (- 1.0 (cos x)) x)
5.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

simplify60.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0521814
12334726
25003690

prune118.0ms

Filtered
82 candidates to 123 candidates (-50.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1194123
Fresh358
Picked101
Done011
Total12310133

Merged error: 0.0b

Counts
133 → 10

regimes67.0ms

bsearch1.0ms

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