Details

Time bar (total: 8.3s)

analyze258.0ms (3.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
46.8%53.1%0.1%6
70.2%29.7%0.1%7
76.5%23.4%0.1%8
83.5%16.4%0.1%9
87%12.9%0.1%10
91.1%8.8%0.1%11
93.2%6.7%0.1%12
95.4%4.5%0.1%13
96.5%3.4%0.1%14
Compiler

Compiled 20 to 10 computations (50% saved)

sample28.0ms (0.3%)

Algorithm
intervals
Results
9.0ms256×body128valid
Compiler

Compiled 41 to 21 computations (48.8% saved)

simplify167.0ms (2%)

Algorithm
egg-herbie
Rules
985×associate-/l*_binary64
739×distribute-lft-out_binary64
723×*-commutative_binary64
475×distribute-rgt-out_binary64
464×+-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01025
13925
213125
344025
4127525
5186125
6232825
7230625
8235925
9241625
10250925
11369525
12382725
13419325
14457825
15469725
16479925
17493325

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
20.4b
Counts
1 → 1
Alt Table
StatusErrorProgram
20.4b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
Compiler

Compiled 38 to 18 computations (52.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (+.f64 x y) (+.f64 x y))
0.1b
(*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
20.1b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

rewrite248.0ms (3%)

Algorithm
rewrite-expression-head
Error
5.7b
Rules
60×flip3-+_binary64 frac-times_binary64 flip-+_binary64
31×add-exp-log_binary64 add-cbrt-cube_binary64
30×associate-*l/_binary64
27×*-un-lft-identity_binary64
26×associate-/r/_binary64
Counts
3 → 140
Calls

3 calls:

20.0ms
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
17.0ms
(*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
10.0ms
(*.f64 (+.f64 x y) (+.f64 x y))
Compiler

Compiled 4492 to 1383 computations (69.2% saved)

series242.0ms (2.9%)

Error
3.9b
Counts
3 → 65
Calls

3 calls:

115.0ms
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
40.0ms
(*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
29.0ms
(*.f64 (+.f64 x y) (+.f64 x y))
Compiler

Compiled 3909 to 2828 computations (27.7% saved)

simplify131.0ms (1.6%)

Algorithm
egg-herbie
Rules
615×times-frac_binary64
391×associate-/r*_binary64
368×distribute-rgt-in_binary64
348×distribute-lft-in_binary64
345×associate-/l*_binary64
Counts
205 → 182
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04027013
112856465
250096465

prune137.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1766182
Fresh000
Picked101
Done000
Total1776183
Error
3.5b
Counts
183 → 6
Alt Table
StatusErrorProgram
30.5b
(/.f64 (*.f64 x y) (+.f64 (*.f64 y (+.f64 (*.f64 3 (*.f64 x x)) (*.f64 2 x))) (+.f64 (pow.f64 y 3) (+.f64 (*.f64 (+.f64 (*.f64 3 x) 1) (*.f64 y y)) (+.f64 (*.f64 x x) (pow.f64 x 3))))))
31.4b
(/.f64 y (+.f64 x (*.f64 x x)))
7.4b
(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))
8.5b
(*.f64 (/.f64 x (*.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 x (+.f64 y 1))))
20.6b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (*.f64 (+.f64 x y) (cbrt.f64 (+.f64 x y))) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (+.f64 (+.f64 x y) 1)))
22.6b
(/.f64 (*.f64 x y) (/.f64 (*.f64 (+.f64 x (+.f64 y 1)) (*.f64 (+.f64 x y) (-.f64 (*.f64 x x) (*.f64 y y)))) (-.f64 x y)))
Compiler

Compiled 4122 to 1758 computations (57.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (+.f64 x y) 3)
0.0b
(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y)))))
3.7b
(/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
7.2b
(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))

rewrite393.0ms (4.8%)

Algorithm
rewrite-expression-head
Error
3.5b
Rules
131×*-un-lft-identity_binary64
70×times-frac_binary64
61×add-sqr-sqrt_binary64
45×add-cube-cbrt_binary64 associate-*r*_binary64
41×distribute-lft-out_binary64
Counts
4 → 213
Calls

4 calls:

44.0ms
(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y)))))
38.0ms
(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))
20.0ms
(/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
5.0ms
(pow.f64 (+.f64 x y) 3)
Compiler

Compiled 6595 to 2363 computations (64.2% saved)

series466.0ms (5.7%)

Error
3.5b
Counts
4 → 79
Calls

4 calls:

182.0ms
(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))
88.0ms
(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y)))))
86.0ms
(/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
34.0ms
(pow.f64 (+.f64 x y) 3)
Compiler

Compiled 6892 to 4838 computations (29.8% saved)

simplify241.0ms (2.9%)

Algorithm
egg-herbie
Rules
484×times-frac_binary64
407×associate-/r*_binary64
314×associate-/l*_binary64
211×distribute-rgt-in_binary64
192×distribute-lft-in_binary64
Counts
292 → 264
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
051110143
115559218
249279218
350749218

prune251.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2613264
Fresh145
Picked101
Done000
Total2637270
Error
3.5b
Counts
270 → 7
Alt Table
StatusErrorProgram
6.5b
(/.f64 (*.f64 (-.f64 (+.f64 y x) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))) (+.f64 x y))
30.5b
(/.f64 (*.f64 x y) (+.f64 (*.f64 y (+.f64 (*.f64 3 (*.f64 x x)) (*.f64 2 x))) (+.f64 (pow.f64 y 3) (+.f64 (*.f64 (+.f64 (*.f64 3 x) 1) (*.f64 y y)) (+.f64 (*.f64 x x) (pow.f64 x 3))))))
31.4b
(/.f64 y (+.f64 x (*.f64 x x)))
8.5b
(*.f64 (/.f64 x (*.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 x (+.f64 y 1))))
7.4b
(*.f64 (/.f64 (*.f64 y (/.f64 x (+.f64 y x))) (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y)))) (-.f64 (+.f64 x y) 1))
7.8b
(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))) (-.f64 (+.f64 x y) 1))
22.6b
(/.f64 (*.f64 x y) (/.f64 (*.f64 (+.f64 x (+.f64 y 1)) (*.f64 (+.f64 x y) (-.f64 (*.f64 x x) (*.f64 y y)))) (-.f64 x y)))
Compiler

Compiled 6535 to 2956 computations (54.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (*.f64 (-.f64 (+.f64 y x) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))) (+.f64 x y))
3.7b
(/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))
5.3b
(*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))
15.9b
(*.f64 (-.f64 (+.f64 y x) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))

rewrite395.0ms (4.8%)

Algorithm
rewrite-expression-head
Error
3.0b
Rules
105×*-un-lft-identity_binary64
97×add-sqr-sqrt_binary64
71×times-frac_binary64
44×associate-*r*_binary64
39×add-cube-cbrt_binary64
Counts
4 → 191
Calls

4 calls:

32.0ms
(/.f64 (*.f64 (-.f64 (+.f64 y x) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))) (+.f64 x y))
30.0ms
(*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))
29.0ms
(*.f64 (-.f64 (+.f64 y x) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))
18.0ms
(/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))
Compiler

Compiled 5939 to 2398 computations (59.6% saved)

series547.0ms (6.6%)

Error
0.4b
Counts
4 → 78
Calls

4 calls:

182.0ms
(/.f64 (*.f64 (-.f64 (+.f64 y x) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))) (+.f64 x y))
118.0ms
(*.f64 (-.f64 (+.f64 y x) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))
89.0ms
(/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))
73.0ms
(*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))
Compiler

Compiled 7804 to 5596 computations (28.3% saved)

simplify239.0ms (2.9%)

Algorithm
egg-herbie
Rules
472×times-frac_binary64
452×associate-/l*_binary64
291×associate-/r*_binary64
151×associate-*l/_binary64
139×sub-neg_binary64
Counts
269 → 245
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
055310187
115969478
248449433
349899433

prune267.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2396245
Fresh426
Picked101
Done000
Total2448252
Error
0.2b
Counts
252 → 8
Alt Table
StatusErrorProgram
6.5b
(/.f64 (*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))) (+.f64 x y))
21.1b
(/.f64 (*.f64 (*.f64 x (-.f64 (+.f64 x y) 1)) (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))) (+.f64 x y))
7.4b
(*.f64 (-.f64 (+.f64 x y) 1) (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))))
34.5b
(/.f64 (*.f64 (-.f64 (+.f64 y x) 1) (*.f64 (*.f64 x (/.f64 (sqrt.f64 y) (*.f64 (+.f64 1 (+.f64 x y)) (sqrt.f64 (+.f64 x y))))) (/.f64 (sqrt.f64 y) (-.f64 (pow.f64 (sqrt.f64 (+.f64 y x)) 3) (sqrt.f64 (+.f64 y x)))))) (+.f64 x y))
31.4b
(/.f64 y (+.f64 x (*.f64 x x)))
40.1b
(/.f64 (-.f64 (/.f64 y x) (+.f64 (/.f64 y (*.f64 x x)) (*.f64 2 (*.f64 (/.f64 y x) (/.f64 y x))))) (+.f64 x y))
42.0b
(/.f64 (-.f64 (/.f64 x y) (+.f64 (/.f64 x (*.f64 y y)) (*.f64 2 (*.f64 (/.f64 x y) (/.f64 x y))))) (+.f64 x y))
7.8b
(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))) (-.f64 (+.f64 x y) 1))
Compiler

Compiled 7104 to 3187 computations (55.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))) (+.f64 x y))
3.7b
(/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))
5.3b
(*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))
15.9b
(*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))))

rewrite354.0ms (4.3%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
105×*-un-lft-identity_binary64
97×add-sqr-sqrt_binary64
71×times-frac_binary64
44×associate-*r*_binary64
39×add-cube-cbrt_binary64
Counts
4 → 191
Calls

4 calls:

31.0ms
(/.f64 (*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))) (+.f64 x y))
27.0ms
(*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))
27.0ms
(*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))))
20.0ms
(/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))
Compiler

Compiled 5939 to 2390 computations (59.8% saved)

series547.0ms (6.6%)

Error
0.2b
Counts
4 → 78
Calls

4 calls:

182.0ms
(/.f64 (*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))) (+.f64 x y))
121.0ms
(*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))))
88.0ms
(/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))
72.0ms
(*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))
Compiler

Compiled 7804 to 5550 computations (28.9% saved)

simplify294.0ms (3.6%)

Algorithm
egg-herbie
Rules
472×times-frac_binary64
452×associate-/l*_binary64
291×associate-/r*_binary64
152×associate-*l/_binary64
138×sub-neg_binary64
Counts
269 → 251
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054610187
115889478
248219433
349999433
449679433

prune265.0ms (3.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2510251
Fresh077
Picked011
Done000
Total2518259
Error
0.2b
Counts
259 → 8
Alt Table
StatusErrorProgram
6.5b
(/.f64 (*.f64 (-.f64 (+.f64 x y) 1) (*.f64 x (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y))))) (+.f64 x y))
21.1b
(/.f64 (*.f64 (*.f64 x (-.f64 (+.f64 x y) 1)) (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))) (+.f64 x y))
7.4b
(*.f64 (-.f64 (+.f64 x y) 1) (*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (-.f64 (pow.f64 (+.f64 x y) 3) (+.f64 x y)))))
34.5b
(/.f64 (*.f64 (-.f64 (+.f64 y x) 1) (*.f64 (*.f64 x (/.f64 (sqrt.f64 y) (*.f64 (+.f64 1 (+.f64 x y)) (sqrt.f64 (+.f64 x y))))) (/.f64 (sqrt.f64 y) (-.f64 (pow.f64 (sqrt.f64 (+.f64 y x)) 3) (sqrt.f64 (+.f64 y x)))))) (+.f64 x y))
31.4b
(/.f64 y (+.f64 x (*.f64 x x)))
40.1b
(/.f64 (-.f64 (/.f64 y x) (+.f64 (/.f64 y (*.f64 x x)) (*.f64 2 (*.f64 (/.f64 y x) (/.f64 y x))))) (+.f64 x y))
42.0b
(/.f64 (-.f64 (/.f64 x y) (+.f64 (/.f64 x (*.f64 y y)) (*.f64 2 (*.f64 (/.f64 x y) (/.f64 x y))))) (+.f64 x y))
7.8b
(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))) (-.f64 (+.f64 x y) 1))
Compiler

Compiled 7054 to 3155 computations (55.3% saved)

regimes1.7s (21.2%)

Accuracy

Total 1.8b remaining (88.3%)

Threshold costs 0b (0%)

Compiler

Compiled 22022 to 11682 computations (47% saved)

bsearch48.0ms (0.6%)

Steps
ItersRangePoint
9
2.4193580723950186e+148
4.6088448567525784e+154
1.927226550392451e+154
10
-2.9751191585681977e+94
-1.878233366103188e+76
-2.925834951620488e+94
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
19×+-commutative_binary64
17×*-commutative_binary64
16×sub-neg_binary64
12×neg-mul-1_binary64 neg-sub0_binary64
distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039123
156123
272123
3104123
4128123
5146123
6154123
7156123
8153123

end11.0ms (0.1%)

Compiler

Compiled 255 to 117 computations (54.1% saved)

sample915.0ms (11.1%)

Algorithm
intervals
Results
301.0ms8000×body128valid
Compiler

Compiled 315 to 154 computations (51.1% saved)

Profiling

Loading profile data...