Details

Time bar (total: 17.1s)

analyze205.0ms (1.2%)

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
12.5%87.4%0.1%4
25%74.9%0.1%5
31.2%68.7%0.1%6
67.1%32.8%0.1%7
71%28.9%0.1%8
82.3%17.6%0.1%9
84.9%15%0.1%10
90.8%9.1%0.1%11
92.2%7.7%0.1%12
95.3%4.6%0.1%13
96%3.9%0.1%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample21.0ms (0.1%)

Algorithm
intervals
Results
8.0ms202×body128valid
3.0ms21×body1024valid
2.0ms21×body512valid
1.0ms11×body256valid
0.0msbody2048valid
Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify201.0ms (1.2%)

Algorithm
egg-herbie
Rules
1996×fma-def_binary64
1626×fma-neg_binary64
1098×div-sub_binary64
733×sub-neg_binary64
664×associate-/l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0916
11916
24316
310214
427414
565214
6127214
7169714
8241614
9293314
10327814
11346114
12198014
13199614
14265914
15253914
16249714
17253114
18253114
19472314
20490314
21594214

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
14.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
22.2b
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
14.5b
(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (+.f64 x -1) (+.f64 1 y))
14.5b
(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series18.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

10.0ms
(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms
(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity_binary64
20×times-frac_binary64
18×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
11×distribute-lft-out_binary64
Counts
2 → 57
Calls

2 calls:

6.0ms
(/.f64 (+.f64 x -1) (+.f64 1 y))
0.0ms
(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify77.0ms (0.5%)

Algorithm
egg-herbie
Rules
780×fma-neg_binary64
491×associate--l+_binary64
425×associate--r+_binary64
390×associate-+l+_binary64
315×fma-def_binary64
Counts
105 → 102
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01602086
14161897
212751850
347011850
454021850

prune94.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1011102
Fresh011
Picked101
Done000
Total1022104
Error
0.0b
Counts
104 → 2
Alt Table
StatusErrorProgram
28.7b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))
22.2b
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
Compiler

Compiled 1882 to 1289 computations (31.5% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (-.f64 1 x) y)
2.4b
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
7.3b
(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

series27.0ms (0.2%)

Counts
3 → 60
Calls

3 calls:

10.0ms
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
9.0ms
(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
8.0ms
(*.f64 (-.f64 1 x) y)

rewrite30.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity_binary64
34×add-sqr-sqrt_binary64
30×prod-diff_binary64
26×add-cube-cbrt_binary64
20×times-frac_binary64
Counts
3 → 113
Calls

3 calls:

8.0ms
(*.f64 (-.f64 1 x) y)
8.0ms
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
7.0ms
(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

simplify121.0ms (0.7%)

Algorithm
egg-herbie
Rules
395×fma-neg_binary64
383×cancel-sign-sub-inv_binary64
261×sub-neg_binary64
216×distribute-rgt-neg-in_binary64
160×exp-prod_binary64
Counts
173 → 202
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02483950
16903374
227342924
345402924
448602924

prune165.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2020202
Fresh011
Picked011
Done000
Total2022204
Error
0.0b
Counts
204 → 2
Alt Table
StatusErrorProgram
28.7b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))
22.2b
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
Compiler

Compiled 4898 to 3489 computations (28.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.2b
(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
5.7b
(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
7.5b
(/.f64 x (*.f64 y y))
7.6b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))

series172.0ms (1%)

Counts
4 → 96
Calls

4 calls:

75.0ms
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))
36.0ms
(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
33.0ms
(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
27.0ms
(/.f64 x (*.f64 y y))

rewrite138.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
276×*-un-lft-identity_binary64
158×distribute-lft-out_binary64
57×times-frac_binary64
51×div-inv_binary64
50×add-log-exp_binary64
Counts
4 → 237
Calls

4 calls:

47.0ms
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))
29.0ms
(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
17.0ms
(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
3.0ms
(/.f64 x (*.f64 y y))

simplify230.0ms (1.3%)

Algorithm
egg-herbie
Rules
487×distribute-rgt-in_binary64
478×associate-*l*_binary64
467×distribute-lft-in_binary64
224×fma-def_binary64
103×sub-neg_binary64
Counts
333 → 258
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033818732
1119313212
2502513212

prune297.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2571258
Fresh000
Picked011
Done011
Total2573260
Error
0b
Counts
260 → 3
Alt Table
StatusErrorProgram
28.7b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))
28.8b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))))
22.2b
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
Compiler

Compiled 16007 to 8277 computations (48.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.7b
(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
7.5b
(/.f64 x (*.f64 y y))
7.6b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))))
14.8b
(cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))

series178.0ms (1%)

Counts
2 → 48
Calls

2 calls:

107.0ms
(cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))
70.0ms
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))))

rewrite1.5s (9%)

Algorithm
rewrite-expression-head
Rules
2165×cbrt-div_binary64
2162×frac-add_binary64
1300×frac-times_binary64
1296×flip-+_binary64
1296×flip3-+_binary64
Counts
2 → 913
Calls

2 calls:

74.0ms
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))))
24.0ms
(cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))

simplify4.3s (24.8%)

Algorithm
egg-herbie
Rules
869×fma-neg_binary64
fma-udef_binary64
Counts
961 → 937
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03852430581
15597430581

prune5.7s (33.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New126701267
Fresh000
Picked011
Done022
Total126731270
Error
0b
Counts
1270 → 3
Alt Table
StatusErrorProgram
28.7b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))
28.8b
(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))))
22.2b
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
Compiler

Compiled 318908 to 176660 computations (44.6% saved)

regimes2.8s (16.2%)

Accuracy

Total 0.0b remaining (52.4%)

Threshold costs 0.0b (52.4%)

Counts
201 → 3
Compiler

Compiled 33005 to 22677 computations (31.3% saved)

bsearch32.0ms (0.2%)

Steps
ItersRangePoint
9
83.01073491701408
3581014701.3406816
225276.2828618436
5
-416460.5630576568
-113717.4146418128
-115615.37911247845
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0%)

Algorithm
egg-herbie
Rules
21×+-commutative_binary64
13×sub-neg_binary64
12×*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038121
159121
276121
395121
4114121
5126121
6131121
7132121
8129121

end1.0ms (0%)

Compiler

Compiled 84 to 53 computations (36.9% saved)

sample781.0ms (4.6%)

Algorithm
intervals
Results
241.0ms6299×body128valid
119.0ms593×body1024valid
77.0ms674×body512valid
30.0ms428×body256valid
1.0msbody2048valid
Compiler

Compiled 218 to 143 computations (34.4% saved)

Profiling

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