Details

Time bar (total: 3.0s)

analyze21.0ms (0.7%)

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

Compiled 9 to 7 computations (22.2% saved)

sample34.0ms (1.2%)

Algorithm
intervals
Results
15.0ms63×body2048valid
6.0ms142×body128valid
5.0ms33×body1024valid
1.0ms11×body512valid
1.0msbody256valid
Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify11.0ms (0.4%)

Algorithm
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

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
13.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
13.6b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(atan.f64 (+.f64 N 1))
0.7b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series3.0ms (0.1%)

Counts
2 → 0
Calls

2 calls:

2.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms
(atan.f64 (+.f64 N 1))

rewrite8.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
add-log-exp_binary64
Counts
2 → 40
Calls

2 calls:

5.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms
(atan.f64 (+.f64 N 1))

simplify73.0ms (2.5%)

Algorithm
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
40 → 48
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
072836
1128555
2354501
31262498
42924498
54651491
64824491

prune31.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New46248
Fresh000
Picked101
Done000
Total47249
Error
0.6b
Counts
49 → 2
Alt Table
StatusErrorProgram
13.6b
(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
Compiler

Compiled 926 to 513 computations (44.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series2.0ms (0.1%)

Counts
1 → 0
Calls

1 calls:

2.0ms
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

rewrite1.0ms (0%)

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

1 calls:

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

simplify135.0ms (4.5%)

Algorithm
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

prune9.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New8210
Fresh101
Picked011
Done000
Total9312
Error
0.6b
Counts
12 → 3
Alt Table
StatusErrorProgram
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1.2b
(*.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)))))
2.0b
(*.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)))))
Compiler

Compiled 256 to 158 computations (38.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.6b
(*.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)))))
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
13.6b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series6.0ms (0.2%)

Counts
2 → 12
Calls

2 calls:

4.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
2.0ms
(*.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)))))

rewrite11.0ms (0.4%)

Algorithm
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))))

simplify115.0ms (3.9%)

Algorithm
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

prune126.0ms (4.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1056111
Fresh101
Picked011
Done011
Total1068114
Error
0.6b
Counts
114 → 8
Alt Table
StatusErrorProgram
1.3b
(*.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))))))
1.2b
(*.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)))))
1.3b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (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 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
1.8b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.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)))))))
2.2b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.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)))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
6.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (*.f64 (*.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 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
2.1b
(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 5/2) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
Compiler

Compiled 3216 to 2011 computations (37.5% saved)

localize9.0ms (0.3%)

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
(*.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)))))
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
13.6b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series536.0ms (18%)

Counts
2 → 24
Calls

2 calls:

534.0ms
(*.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))))))

rewrite34.0ms (1.1%)

Algorithm
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:

12.0ms
(*.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))))))
7.0ms
(*.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)))))

simplify138.0ms (4.6%)

Algorithm
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

prune261.0ms (8.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1924196
Fresh325
Picked101
Done022
Total1968204
Error
0.6b
Counts
204 → 8
Alt Table
StatusErrorProgram
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
0.9b
(*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (*.f64 (*.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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))))))))
1.8b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.f64 (cbrt.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)))))))
6.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (*.f64 (*.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 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
0.8b
(*.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))))) 3))
0.8b
(*.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))))) 7/2))
1.2b
(*.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)))))
0.8b
(pow.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 4)
Compiler

Compiled 7098 to 4555 computations (35.8% saved)

regimes122.0ms (4.1%)

Accuracy

Total 0.0b remaining (13.1%)

Threshold costs 0.0b (13.1%)

Counts
58 → 1
Compiler

Compiled 3070 to 2068 computations (32.6% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
1911
2811

end1.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.3s (42.6%)

Algorithm
intervals
Results
440.0ms2117×body2048valid
208.0ms1042×body1024valid
190.0ms4103×body128valid
64.0ms522×body512valid
18.0ms216×body256valid
Compiler

Compiled 259 to 174 computations (32.8% saved)

Profiling

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