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)

sample1.8s (51.4%)

Results
846.0ms2125×body2048valid
435.0ms4308×body128valid
305.0ms1007×body1024valid
124.0ms547×body512valid
45.0ms269×body256valid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (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
13.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶13.3b
(-.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%)

Counts
1 → 0
Calls

1 calls:

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

rewrite5.0ms (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))

simplify66.0ms (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
0.2b
Counts
38 → 1
Alt Table
StatusErrorProgram
▶0.2b
(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
✓0.2b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series1.0ms (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)))

simplify136.0ms (3.9%)

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

prune12.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New7310
Fresh000
Picked011
Done000
Total7411
Error
0.2b
Counts
11 → 4
Alt Table
StatusErrorProgram
8.1b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
✓0.2b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶0.8b
(*.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)))))
1.5b
(*.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 280 to 176 computations (37.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓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)))))
✓12.9b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series5.0ms (0.1%)

Counts
2 → 12
Calls

2 calls:

4.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms
(*.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)))))

rewrite16.0ms (0.5%)

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))))

simplify111.0ms (3.2%)

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

prune122.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1065111
Fresh112
Picked011
Done011
Total1078115
Error
0.1b
Counts
115 → 8
Alt Table
StatusErrorProgram
✓0.2b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶1.2b
(*.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (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))))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
8.1b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
2.3b
(*.f64 (*.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)))))) (*.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))))))) (*.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)))))))
6.6b
(sqrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 4))
✓0.8b
(*.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 (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)))))))
1.7b
(*.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)))))))
Compiler

Compiled 3202 to 2005 computations (37.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓6.7b
(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))))))
12.9b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
✓13.3b
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series700.0ms (20.1%)

Counts
2 → 24
Calls

2 calls:

351.0ms
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
349.0ms
(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))))))

rewrite5.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
10×pow1_binary64
9×sqrt-pow1_binary64
7×pow1/3_binary64
3×*-un-lft-identity_binary64
3×add-sqr-sqrt_binary64
Counts
2 → 34
Calls

2 calls:

3.0ms
(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))))))
1.0ms
(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify78.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
813×associate-/r/_binary64
619×log-prod_binary64
451×associate-*l*_binary64
350×distribute-rgt-out_binary64
295×associate-*r*_binary64
Counts
58 → 35
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
044736
154722
276722
3139722
4382714
51660714
62951714
73836714
85314714

prune156.0ms (4.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1230123
Fresh055
Picked011
Done022
Total1238131
Error
0.1b
Counts
131 → 8
Alt Table
StatusErrorProgram
✓0.2b
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓1.2b
(*.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (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))))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
8.1b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
2.3b
(*.f64 (*.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)))))) (*.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))))))) (*.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)))))))
6.6b
(sqrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 4))
✓0.8b
(*.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 (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)))))))
1.7b
(*.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)))))))
Compiler

Compiled 6137 to 3842 computations (37.4% saved)

regimes61.0ms (1.8%)

Accuracy

Total 0.0b remaining (11.6%)

Threshold costs 0.0b (11.6%)

Counts
30 → 1
Compiler

Compiled 1676 to 1054 computations (37.1% 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

end148.0ms (4.3%)

Compiler

Compiled 254 to 168 computations (33.9% saved)

Profiling

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