Details

Time bar (total: 4.6s)

analyze711.0ms (15.5%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
25%75%0%4
37.5%62.5%0%5
43.7%56.2%0%6
46.9%53.1%0%7
46.9%53.1%0%8
46.9%53.1%0%9
47.2%52.7%0%10
47.2%52.7%0%11
47.3%52.7%0%12
47.3%52.7%0%13
47.3%52.6%0%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (43.2%)

Results
945.0ms2187×body2048valid
430.0ms4211×body128valid
340.0ms1066×body1024valid
189.0ms525×body512valid
44.0ms267×body256valid
Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify10.0ms (0.2%)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
14.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶14.4b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(atan.f64 (+.f64 N 1))
✓1.9b
(-.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))

rewrite7.0ms (0.1%)

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

2 calls:

3.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms
(atan.f64 (+.f64 N 1))

simplify70.0ms (1.5%)

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
40 → 48
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
072836
1128555
2354501
31262498
42924498
54651491
64824491

prune31.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New47148
Fresh000
Picked011
Done000
Total47249
Error
0.6b
Counts
49 → 2
Alt Table
StatusErrorProgram
▶0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓14.4b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 916 to 505 computations (44.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0%)

Counts
1 → 0
Calls

1 calls:

2.0ms
(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)))

simplify133.0ms (2.9%)

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

prune13.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New7310
Fresh000
Picked011
Done011
Total7512
Error
0.6b
Counts
12 → 5
Alt Table
StatusErrorProgram
✓0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓14.4b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 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)))))
1.9b
(*.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)))))
10.3b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
Compiler

Compiled 288 to 182 computations (36.8% saved)

localize7.0ms (0.1%)

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)))
✓15.0b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series6.0ms (0.1%)

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)))))

rewrite12.0ms (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 (2.3%)

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

prune120.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1074111
Fresh112
Picked011
Done022
Total1088116
Error
0.6b
Counts
116 → 8
Alt Table
StatusErrorProgram
1.6b
(*.f64 (sqrt.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)))))) (*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓14.4b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 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)))))))
2.1b
(*.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)))))))
✓0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
10.3b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
Compiler

Compiled 3140 to 1963 computations (37.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.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))))))
✓0.6b
(*.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)))))))
0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
15.0b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series7.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

4.0ms
(*.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))))))
2.0ms
(*.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)))))))

rewrite141.0ms (3.1%)

Algorithm
1×rewrite-expression-head
Rules
480×sqrt-pow1_binary64
360×pow1_binary64
253×pow-prod-up_binary64
240×pow1/2_binary64
188×add-sqr-sqrt_binary64
Counts
2 → 296
Calls

2 calls:

41.0ms
(*.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)))))))
9.0ms
(*.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))))))

simplify194.0ms (4.2%)

Algorithm
1×egg-herbie
Rules
963×fma-def_binary64
458×associate-*l*_binary64
350×*-commutative_binary64
342×log-prod_binary64
341×exp-prod_binary64
Counts
320 → 249
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0883038
11252773
23462617
310792560
417252538
533492528
642712510
748832510
849792510

prune650.0ms (14.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New4282430
Fresh134
Picked011
Done033
Total4299438
Error
0.6b
Counts
438 → 9
Alt Table
StatusErrorProgram
1.6b
(*.f64 (sqrt.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)))))) (*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓14.4b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 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)))))))
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))
10.3b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
2.1b
(*.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)))))))
✓0.6b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
0.8b
(*.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 (*.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 17514 to 11677 computations (33.3% saved)

regimes175.0ms (3.8%)

Accuracy

Total 0.0b remaining (12.4%)

Threshold costs 0.0b (12.4%)

Counts
77 → 1
Compiler

Compiled 4506 to 3080 computations (31.6% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
1911
2811

end184.0ms (4%)

Compiler

Compiled 285 to 189 computations (33.7% saved)

Profiling

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