Details

Time bar (total: 10.5s)

sample1.4s

Algorithm
intervals
Results
127.0ms45×body2560valid
49.0ms83×body1280valid
17.0ms61×body640valid
6.0ms36×body320valid
2.0ms15×body160valid
1.0ms16×body80valid

simplify373.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.5b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.8b
(- x (tan x))
1.8b
(- x (sin x))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt *-un-lft-identity
25×times-frac
15×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
5×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×flip3-- flip--
3×pow1
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv
Counts
3 → 80
Calls
3 calls:
7.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
5.0ms
(- x (sin x))

series54.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(/ (- x (sin x)) (- x (tan x)))
11.0ms
(- x (tan x))
13.0ms
(- x (sin x))

simplify147.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune96.0ms

Filtered
63 candidates to 89 candidates (-41.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New85489
Fresh000
Picked011
Done000
Total85590

Merged error: 0.0b

Counts
90 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x (tan x)))
0.1b
(* (- x (sin x)) (/ 1 (- x (tan x))))
1.8b
(- x (tan x))
1.8b
(- x (sin x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
45×*-un-lft-identity
32×times-frac
24×add-cube-cbrt
21×associate-*r*
17×add-exp-log
11×add-cbrt-cube
10×distribute-lft-out-- difference-of-squares
8×add-log-exp
7×pow1
6×flip3-- flip--
5×associate-*l* associate-/r*
4×div-exp prod-exp associate-/r/
3×associate-/l* unswap-sqr
2×cbrt-undiv frac-times sub-neg rec-exp diff-log 1-exp associate-*l/ cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 119
Calls
4 calls:
5.0ms
(/ 1 (- x (tan x)))
12.0ms
(* (- x (sin x)) (/ 1 (- x (tan x))))
3.0ms
(- x (tan x))
3.0ms
(- x (sin x))

series36.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ 1 (- x (tan x)))
13.0ms
(* (- x (sin x)) (/ 1 (- x (tan x))))
10.0ms
(- x (tan x))
5.0ms
(- x (sin x))

simplify52.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0462904
12072810
25002768

prune104.0ms

Filtered
80 candidates to 131 candidates (-63.8%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1310131
Fresh033
Picked011
Done011
Total1315136

Merged error: 0.0b

Counts
136 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.1b
(* 9/40 (pow x 2))
16.6b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite20.0ms

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 diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- sum-log flip-- associate--r+
Counts
3 → 66
Calls
3 calls:
7.0ms
(* 27/2800 (pow x 4))
5.0ms
(* 9/40 (pow x 2))
6.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series12.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* 27/2800 (pow x 4))
3.0ms
(* 9/40 (pow x 2))
6.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify40.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0273349
11123316
25001313

prune109.0ms

Filtered
46 candidates to 75 candidates (-63.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New75075
Fresh022
Picked011
Done022
Total75580

Merged error: 0.0b

Counts
80 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin x) 2)
1.8b
(- x (tan x))
1.8b
(- (pow x 2) (pow (sin x) 2))
15.5b
(/ (- (pow x 2) (pow (sin x) 2)) (+ x (sin x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
131×add-sqr-sqrt
103×*-un-lft-identity
97×difference-of-squares
84×times-frac
63×unpow-prod-down
49×unpow2 sqr-pow
33×add-cube-cbrt
22×distribute-lft-out
21×associate-/l*
13×distribute-lft-out--
8×add-log-exp
7×add-exp-log
6×add-cbrt-cube
5×pow1
4×associate-/r*
3×pow-unpow flip3-- flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv pow-to-exp pow-pow frac-2neg flip3-+ div-sub div-exp pow-exp clear-num flip-+ div-inv
Counts
4 → 188
Calls
4 calls:
2.0ms
(pow (sin x) 2)
3.0ms
(- x (tan x))
7.0ms
(- (pow x 2) (pow (sin x) 2))
14.0ms
(/ (- (pow x 2) (pow (sin x) 2)) (+ x (sin x)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin x) 2)
12.0ms
(- x (tan x))
8.0ms
(- (pow x 2) (pow (sin x) 2))
13.0ms
(/ (- (pow x 2) (pow (sin x) 2)) (+ x (sin x)))

simplify64.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06791963
120941722
250011705

prune185.0ms

Filtered
98 candidates to 200 candidates (-104.1%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1991200
Fresh011
Picked101
Done033
Total2005205

Merged error: 0.0b

Counts
205 → 5

regimes88.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch39.0ms

Steps
ItersRangePoint
9
6.661366802070807e-05
11.963514959293093
0.02775660499312673
9
-0.030526827651633566
-3.100103530908671e-11
-0.026422262747365307

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02911
12911

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.1s1623×body2560valid
1.6s2743×body1280valid
480.0ms1883×body640valid
156.0ms933×body320valid
66.0ms470×body160valid
25.0ms348×body80valid

Profiling

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