Details

Time bar (total: 2.3s)

sample53.0ms

Algorithm
intervals
Results
25.0ms56×body2560valid
8.0ms36×body1280valid
6.0ms38×body640valid
3.0ms79×body80valid
3.0ms25×body320valid
2.0ms22×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.0b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b
(- 1.0 (cos x))
16.0b
(/ (- 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:
4.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series68.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
50.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify63.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune104.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New41748
Fresh000
Picked011
Done000
Total41849

Merged error: 0.1b

Counts
49 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
2.1b
(- 1.0 (cos x))

rewrite29.0ms

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:
15.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series111.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
42.0ms
(/ (- 1.0 (cos x)) x)
23.0ms
(- 1.0 (cos x))

simplify63.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0521814
12337726
25001700

prune179.0ms

Filtered
123 candidates to 82 candidates (66.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1212123
Fresh066
Picked101
Done011
Total1229131

Merged error: 0.1b

Counts
131 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.4b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
89×*-un-lft-identity
80×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
25×associate-/l* distribute-lft-out--
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
3×pow-unpow associate-/r*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num sum-log div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 189
Calls
4 calls:
24.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
3.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
13.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series220.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
28.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify98.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06172953
126992889
250022810

prune360.0ms

Filtered
201 candidates to 105 candidates (52.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1992201
Fresh167
Picked101
Done011
Total2019210

Merged error: 0.0b

Counts
210 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
0.4b
(+ (cos x) 1.0)
2.0b
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
70×times-frac
53×*-un-lft-identity
25×unpow-prod-down cube-prod difference-of-squares
17×add-cube-cbrt
16×distribute-lft-out--
11×sqr-pow
10×add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×flip3-+ associate-/r/ flip-+
3×pow-unpow distribute-rgt-out--
2×+-commutative sum-log div-inv distribute-lft-out
1×cube-mult pow-to-exp sub-neg flip3-- pow-pow diff-log unpow3 pow-exp frac-sub flip-- sub-div rem-cube-cbrt
Counts
4 → 105
Calls
4 calls:
3.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
4.0ms
(+ (cos x) 1.0)
89.0ms
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (cos x) 3)
9.0ms
(+ (cos x) 1.0)
14.0ms
(+ (cos x) 1.0)
260.0ms
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04432054
116541994
250021970

prune242.0ms

Filtered
117 candidates to 70 candidates (59.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1161117
Fresh077
Picked101
Done011
Total1179126

Merged error: 0.0b

Counts
126 → 9

regimes81.0ms

bsearch2.0ms

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