Details

Time bar (total: 4.7s)

analyze709.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
50%50%0%5
50%50%0%6
50%50%0%7
50%50%0%8
50%50%0%9
50%50%0%10
50%50%0%11
50%50%0%12
50%50%0%13
50%49.9%0%14

sample41.0ms

Algorithm
intervals
Results
11.0ms40×body1280valid
8.0ms45×body640valid
6.0ms144×body80valid
3.0ms22×body320valid
0.0ms5×body160valid

simplify421.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01615
11615

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.3b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1.0 (* (tan x) (tan x)))
0.2b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×pow1
12×times-frac
10×add-exp-log add-cbrt-cube
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×associate-/l*
3×associate-/r*
2×pow2 frac-times flip3-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
4 → 104
Calls
4 calls:
3.0ms
(- 1.0 (* (tan x) (tan x)))
5.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms
(* (tan x) (tan x))
7.0ms
(* (tan x) (tan x))

series85.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- 1.0 (* (tan x) (tan x)))
31.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
8.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))

simplify45.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050701206

prune217.0ms

Filtered
82 candidates to 116 candidates (-41.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10511116
Fresh000
Picked101
Done000
Total10611117

Merged error: 0.0b

Counts
117 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
0.2b
(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
0.3b
(pow (tan x) 2)
0.3b
(pow (tan x) 2)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
274×times-frac
239×add-sqr-sqrt
237×*-un-lft-identity
113×add-cube-cbrt
84×difference-of-squares
46×associate-/r*
41×distribute-lft-out
27×unpow-prod-down
23×unpow2 sqr-pow
21×distribute-lft-out--
19×add-exp-log
11×associate-/r/ add-cbrt-cube
8×div-exp
7×pow1 associate-/l*
6×pow-unpow div-inv
5×flip3-- flip--
4×cbrt-undiv add-log-exp
2×pow-to-exp rec-exp pow-pow frac-2neg 1-exp pow-exp clear-num associate-/l/
1×pow-flip flip3-+ flip-+ inv-pow
Counts
4 → 272
Calls
4 calls:
11.0ms
(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
14.0ms
(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
2.0ms
(pow (tan x) 2)
3.0ms
(pow (tan x) 2)

series81.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
34.0ms
(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
8.0ms
(pow (tan x) 2)
8.0ms
(pow (tan x) 2)

simplify96.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
050405487

prune407.0ms

Filtered
137 candidates to 284 candidates (-107.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2795284
Fresh5510
Picked011
Done000
Total28411295

Merged error: 0.0b

Counts
295 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (pow (tan x) 2)) (+ (pow (tan x) 2) 1.0))
0.3b
(log (exp (/ (- 1.0 (pow (tan x) 2)) (+ (pow (tan x) 2) 1.0))))
0.3b
(pow (tan x) 2)
0.3b
(pow (tan x) 2)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
88×*-un-lft-identity
64×times-frac
39×log-pow
38×exp-prod
36×add-cube-cbrt difference-of-squares
17×distribute-lft-out
15×unpow-prod-down
11×unpow2 sqr-pow
9×distribute-lft-out--
8×add-exp-log associate-/l*
7×pow1
6×pow-unpow add-cbrt-cube
4×associate-/r* associate-/r/ add-log-exp
3×log-prod
2×pow-to-exp pow-pow flip3-+ div-sub pow-exp flip-+ div-inv associate-/l/
1×cbrt-undiv log-div flip3-- frac-2neg exp-diff div-exp rem-log-exp clear-num flip--
Counts
4 → 148
Calls
4 calls:
11.0ms
(/ (- 1.0 (pow (tan x) 2)) (+ (pow (tan x) 2) 1.0))
14.0ms
(log (exp (/ (- 1.0 (pow (tan x) 2)) (+ (pow (tan x) 2) 1.0))))
3.0ms
(pow (tan x) 2)
3.0ms
(pow (tan x) 2)

series79.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (- 1.0 (pow (tan x) 2)) (+ (pow (tan x) 2) 1.0))
30.0ms
(log (exp (/ (- 1.0 (pow (tan x) 2)) (+ (pow (tan x) 2) 1.0))))
11.0ms
(pow (tan x) 2)
8.0ms
(pow (tan x) 2)

simplify67.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050312244

prune290.0ms

Filtered
103 candidates to 160 candidates (-55.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1591160
Fresh189
Picked011
Done011
Total16011171

Merged error: 0.0b

Counts
171 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (tan x) 2)
0.3b
(pow (tan x) 2)
0.3b
(pow (tan x) 2)
0.3b
(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
36×*-un-lft-identity
25×times-frac
12×add-cube-cbrt
11×unpow-prod-down
10×difference-of-squares
9×pow-unpow
7×pow1 add-exp-log distribute-lft-out--
6×add-log-exp
5×unpow2 sqr-pow
4×associate-/r/ add-cbrt-cube distribute-lft-out
3×pow-to-exp distribute-rgt-out-- pow-pow pow-exp
2×flip3-+ flip-+ div-inv
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 87
Calls
4 calls:
2.0ms
(pow (tan x) 2)
2.0ms
(pow (tan x) 2)
2.0ms
(pow (tan x) 2)
36.0ms
(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(pow (tan x) 2)
8.0ms
(pow (tan x) 2)
8.0ms
(pow (tan x) 2)
52.0ms
(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049301408
149301408

prune157.0ms

Filtered
66 candidates to 99 candidates (-50.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New98199
Fresh088
Picked101
Done022
Total9911110

Merged error: 0.0b

Counts
110 → 11

regimes133.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01215
11215

end0.0ms

analyze495.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
50%50%0%5
50%50%0%6
50%50%0%7
50%50%0%8
50%50%0%9
50%50%0%10
50%50%0%11
50%50%0%12
50%50%0%13
50%49.9%0%14

sample1.0s

Algorithm
intervals
Results
404.0ms1515×body1280valid
222.0ms1273×body640valid
169.0ms4309×body80valid
81.0ms632×body320valid
24.0ms271×body160valid

Profiling

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