Details

Time bar (total: 3.5s)

analyze1.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.9s (53.3%)

Results
909.0ms2146×body2048valid
425.0ms4257×body128valid
335.0ms1068×body1024valid
136.0ms551×body512valid
38.0ms234×body256valid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43011
54711
67211
79211
810911
911911
1012311
1112511
1211111

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
16.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶16.8b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓2.0b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series2.0ms (0%)

Counts
1 → 0
Calls

1 calls:

2.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite4.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
9×prod-diff_binary64
9×add-cube-cbrt_binary64
3×cancel-sign-sub-inv_binary64
Counts
1 → 31
Calls

1 calls:

3.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify68.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
719×fma-def_binary64
392×unsub-neg_binary64
319×distribute-rgt-in_binary64
308×unswap-sqr_binary64
275×times-frac_binary64
Counts
31 → 37
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
068753
1125472
2351418
31250415
42898415
54629415
64801415

prune24.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New36137
Fresh000
Picked101
Done000
Total37138
Error
0.1b
Counts
38 → 1
Alt Table
StatusErrorProgram
▶0.1b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
Compiler

Compiled 776 to 406 computations (47.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.1b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series2.0ms (0%)

Counts
1 → 0
Calls

1 calls:

1.0ms
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1×*-un-lft-identity_binary64
1×add-sqr-sqrt_binary64
1×add-cube-cbrt_binary64
1×add-cbrt-cube_binary64
1×add-exp-log_binary64
Counts
1 → 9
Calls

1 calls:

0.0ms
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

simplify142.0ms (4%)

Algorithm
1×egg-herbie
Rules
1333×sqr-pow_binary64
715×pow-sqr_binary64
529×cube-prod_binary64
481×fabs-mul_binary64
362×unswap-sqr_binary64
Counts
9 → 10
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
015156
121133
229133
341133
454133
561133
693133
7157133
8335133
9641133
10645133
11775133
12929133
131097133
141326133
151627133
161975133
172450133
183068133
193264133
203438133
213552133
223599133
233651133
244529133
254833133

prune14.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New7310
Fresh000
Picked011
Done000
Total7411
Error
0.1b
Counts
11 → 4
Alt Table
StatusErrorProgram
✓0.1b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶0.7b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
1.4b
(*.f64 (*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
10.6b
(cbrt.f64 (*.f64 (*.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
Compiler

Compiled 312 to 192 computations (38.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓0.7b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓13.7b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series7.0ms (0.2%)

Counts
2 → 12
Calls

2 calls:

4.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
4.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite10.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
18×pow1_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
2 → 68
Calls

2 calls:

5.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
1.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify105.0ms (3%)

Algorithm
1×egg-herbie
Rules
498×log-prod_binary64
465×*-commutative_binary64
441×unswap-sqr_binary64
425×log-div_binary64
306×sqr-pow_binary64
Counts
80 → 75
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0521385
1751281
21811233
33891149
47201054
513241054
625191040
742851040
849941040
948351040

prune107.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1074111
Fresh202
Picked101
Done011
Total1105115
Error
0.0b
Counts
115 → 5
Alt Table
StatusErrorProgram
✓0.1b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1.7b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
▶0.7b
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
1.4b
(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
6.4b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))
Compiler

Compiled 2990 to 1868 computations (37.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
0.1b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓0.2b
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
13.7b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series332.0ms (9.4%)

Counts
2 → 24
Calls

2 calls:

331.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
2.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))

rewrite29.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
51×sqrt-pow1_binary64
48×pow1_binary64
42×add-sqr-sqrt_binary64
37×sqrt-prod_binary64
36×pow-prod-up_binary64
Counts
2 → 100
Calls

2 calls:

11.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
6.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

simplify136.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
429×unswap-sqr_binary64
359×log-div_binary64
358×cube-div_binary64
273×associate-*r/_binary64
260×log-prod_binary64
Counts
124 → 118
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
0812735
11372079
22891866
33931866
47201832
511021828
626651828
738861705
849331705
948821705

prune214.0ms (6.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1933196
Fresh213
Picked101
Done011
Total1965201
Error
0.0b
Counts
201 → 5
Alt Table
StatusErrorProgram
✓0.1b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1.7b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (pow.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 5/2)))
6.4b
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3))))
1.0b
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))
Compiler

Compiled 7027 to 4509 computations (35.8% saved)

regimes300.0ms (8.5%)

Accuracy

Total 0.0b remaining (9%)

Threshold costs 0.0b (9%)

Counts
152 → 1
Compiler

Compiled 9334 to 6266 computations (32.9% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
1911
2811

end111.0ms (3.2%)

Compiler

Compiled 187 to 126 computations (32.6% saved)

Profiling

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