Details

Time bar (total: 1.6s)

analyze18.0ms (1.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0.1%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample14.0ms (0.9%)

Algorithm
1×intervals
Results
7.0ms256×body128valid
Compiler

Compiled 16 to 12 computations (25% saved)

simplify6.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64
1×associate-*r*_binary64
1×associate-*l*_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
199
2119
3119

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
32.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶32.0b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Compiler

Compiled 21 to 15 computations (28.6% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 2 (*.f64 x x))
✓30.9b
(sqrt.f64 (*.f64 2 (*.f64 x x)))

series5.0ms (0.3%)

Counts
2 → 24
Calls

2 calls:

3.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
2.0ms
(*.f64 2 (*.f64 x x))

rewrite9.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
13×pow1_binary64
7×add-cbrt-cube_binary64
7×add-exp-log_binary64
6×pow-prod-down_binary64
4×add-sqr-sqrt_binary64
Counts
2 → 35
Calls

2 calls:

4.0ms
(*.f64 2 (*.f64 x x))
3.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))

simplify75.0ms (4.7%)

Algorithm
1×egg-herbie
Rules
597×distribute-rgt-out_binary64
429×fma-def_binary64
339×*-commutative_binary64
318×times-frac_binary64
249×fma-neg_binary64
Counts
59 → 47
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
053514
197472
2229461
3599461
4904401
51456401
63025401
74826401
84904401

prune28.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New41647
Fresh000
Picked011
Done000
Total41748
Error
0.1b
Counts
48 → 7
Alt Table
StatusErrorProgram
2.7b
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
31.6b
(neg.f64 (*.f64 (sqrt.f64 2) x))
31.3b
(*.f64 (sqrt.f64 2) x)
53.0b
(sqrt.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 2 (*.f64 x x)) (*.f64 2 (*.f64 x x))) (*.f64 2 (*.f64 x x)))))
▶0.6b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓32.0b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
1.3b
(*.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x)))
Compiler

Compiled 584 to 339 computations (42% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(hypot.f64 x x)
✓0.1b
(sqrt.f64 (hypot.f64 x x))
✓0.5b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series18.0ms (1.1%)

Counts
3 → 24
Calls

3 calls:

10.0ms
(sqrt.f64 (hypot.f64 x x))
5.0ms
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
3.0ms
(hypot.f64 x x)

rewrite10.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
19×pow1_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
Counts
3 → 78
Calls

3 calls:

5.0ms
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms
(sqrt.f64 (hypot.f64 x x))
0.0ms
(hypot.f64 x x)

simplify88.0ms (5.6%)

Algorithm
1×egg-herbie
Rules
951×fma-def_binary64
446×unswap-sqr_binary64
308×sqr-pow_binary64
263×associate-+l+_binary64
259×associate-/l*_binary64
Counts
102 → 83
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
061802
185752
2199739
3402701
4728701
51353701
62551685
74580685
85171685

prune46.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1004104
Fresh325
Picked011
Done101
Total1047111
Error
0.0b
Counts
111 → 7
Alt Table
StatusErrorProgram
41.6b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (*.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
31.6b
(neg.f64 (*.f64 (sqrt.f64 2) x))
1.3b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
31.3b
(*.f64 (sqrt.f64 2) x)
0.9b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓0.6b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
▶0.1b
(hypot.f64 x x)
Compiler

Compiled 1518 to 364 computations (76% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 x x)

prune6.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New404
Fresh055
Picked011
Done011
Total4711
Error
0.0b
Counts
11 → 7
Alt Table
StatusErrorProgram
41.6b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (*.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
31.6b
(neg.f64 (*.f64 (sqrt.f64 2) x))
1.3b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
31.3b
(*.f64 (sqrt.f64 2) x)
▶0.9b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓0.6b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓0.1b
(hypot.f64 x x)
Compiler

Compiled 195 to 78 computations (60% saved)

localize7.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓0.5b
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
✓0.5b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓0.6b
(cbrt.f64 (hypot.f64 x x))

series455.0ms (28.9%)

Counts
4 → 36
Calls

4 calls:

226.0ms
(cbrt.f64 (hypot.f64 x x))
216.0ms
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
10.0ms
(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
4.0ms
(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))

rewrite20.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
27×cbrt-prod_binary64
14×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
12×associate-*l*_binary64
Counts
4 → 89
Calls

4 calls:

8.0ms
(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
5.0ms
(*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
1.0ms
(cbrt.f64 (sqrt.f64 (hypot.f64 x x)))
1.0ms
(cbrt.f64 (hypot.f64 x x))

simplify112.0ms (7.1%)

Algorithm
1×egg-herbie
Rules
459×unswap-sqr_binary64
433×fma-def_binary64
360×fma-neg_binary64
325×*-commutative_binary64
311×sqr-pow_binary64
Counts
125 → 138
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01072157
12081998
25361829
39231329
411771298
524561298
642661298
749381298

prune48.0ms (3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1371138
Fresh134
Picked011
Done022
Total1387145
Error
0.0b
Counts
145 → 7
Alt Table
StatusErrorProgram
41.5b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))) (*.f64 (hypot.f64 x x) (sqrt.f64 (hypot.f64 x x)))))
31.6b
(neg.f64 (*.f64 (sqrt.f64 2) x))
1.3b
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
31.3b
(*.f64 (sqrt.f64 2) x)
✓0.9b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓0.6b
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
✓0.1b
(hypot.f64 x x)
Compiler

Compiled 2748 to 540 computations (80.3% saved)

regimes122.0ms (7.8%)

Accuracy

Total 0.1b remaining (76.8%)

Threshold costs 0.1b (76.8%)

Counts
34 → 1
Compiler

Compiled 2187 to 1108 computations (49.3% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034
134

end0.0ms (0%)

Compiler

Compiled 4 to 2 computations (50% saved)

sample476.0ms (30.2%)

Algorithm
1×intervals
Results
237.0ms8000×body128valid
Compiler

Compiled 91 to 45 computations (50.5% saved)

Profiling

Loading profile data...