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 (53.9%)

Results
891.0ms2064×body2048valid
435.0ms4324×body128valid
328.0ms1024×body1024valid
149.0ms555×body512valid
52.0ms289×body256valid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
15.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶15.0b
(-.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
✓1.5b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series2.0ms (0.1%)

Counts
1 → 0
Calls

1 calls:

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

rewrite6.0ms (0.2%)

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:

4.0ms
(-.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

prune26.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New35237
Fresh000
Picked101
Done000
Total36238
Error
0.3b
Counts
38 → 2
Alt Table
StatusErrorProgram
▶0.3b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
15.6b
(log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
Compiler

Compiled 796 to 422 computations (47% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (fma.f64 N N N))
✓0.3b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series4.0ms (0.1%)

Counts
2 → 12
Calls

2 calls:

2.0ms
(+.f64 1 (fma.f64 N N N))
1.0ms
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

rewrite4.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
5×*-un-lft-identity_binary64
4×add-log-exp_binary64
3×fma-def_binary64
3×add-sqr-sqrt_binary64
3×add-cube-cbrt_binary64
Counts
2 → 27
Calls

2 calls:

2.0ms
(+.f64 1 (fma.f64 N N N))
0.0ms
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

simplify66.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
832×sub-neg_binary64
634×distribute-rgt-in_binary64
538×distribute-lft-in_binary64
319×associate-*l*_binary64
301×associate-*r*_binary64
Counts
39 → 53
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
046435
198377
2243377
3899377
42950377
54669377
65438377

prune42.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New50353
Fresh101
Picked011
Done000
Total51455
Error
0.3b
Counts
55 → 4
Alt Table
StatusErrorProgram
✓0.3b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶0.6b
(atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
9.3b
(atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3)))
1.0b
(*.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 807 to 490 computations (39.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))
✓0.2b
(*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))
✓0.3b
(atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
✓12.0b
(cbrt.f64 (+.f64 1 (fma.f64 N N N)))

series15.0ms (0.4%)

Counts
4 → 48
Calls

4 calls:

5.0ms
(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
5.0ms
(*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))
2.0ms
(*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))
2.0ms
(atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))

rewrite41.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
68×cbrt-div_binary64
34×flip-+_binary64
34×flip3-+_binary64
33×*-un-lft-identity_binary64
33×cbrt-prod_binary64
Counts
4 → 145
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))
9.0ms
(*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))
2.0ms
(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
0.0ms
(atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))

simplify224.0ms (6.4%)

Algorithm
1×egg-herbie
Rules
862×fma-neg_binary64
372×sub-neg_binary64
318×fma-def_binary64
309×*-commutative_binary64
258×+-commutative_binary64
Counts
193 → 221
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01984773
13944589
210214255
324964193
436423815
547163815
648793815
748873815

prune287.0ms (8.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2881289
Fresh022
Picked011
Done011
Total2885293
Error
0.3b
Counts
293 → 5
Alt Table
StatusErrorProgram
✓0.3b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓0.6b
(atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
9.3b
(atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3)))
▶1.0b
(*.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)))))
1.1b
(*.f64 (sqrt.f64 (atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))))
Compiler

Compiled 10287 to 5628 computations (45.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (fma.f64 N N N))
0.3b
(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)))))
✓11.8b
(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)))))

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))))

simplify108.0ms (3.1%)

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

prune200.0ms (5.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1943197
Fresh022
Picked101
Done022
Total1957202
Error
0.3b
Counts
202 → 7
Alt Table
StatusErrorProgram
✓0.3b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓0.6b
(atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
9.3b
(atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3)))
0.5b
(*.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)))))))
1.6b
(*.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 (*.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))
1.1b
(*.f64 (sqrt.f64 (atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (atan2.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))))
Compiler

Compiled 4973 to 3078 computations (38.1% saved)

regimes324.0ms (9.2%)

Accuracy

Total 0.0b remaining (14.1%)

Threshold costs 0.0b (14.1%)

Counts
169 → 1
Compiler

Compiled 7184 to 4902 computations (31.8% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
1911
2811

end139.0ms (4%)

Compiler

Compiled 216 to 137 computations (36.6% saved)

Profiling

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