Details

Time bar (total: 1.6s)

analyze3.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50%13
49.9%0%50%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample700.0ms (44.3%)

Infinites
0% of outputs are infinite.
Results
457.0ms8256×body128valid
Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify203.0ms (12.8%)

Algorithm
1×egg-herbie
Rules
1115×distribute-rgt-neg-in_binary64
788×distribute-rgt-out--_binary64
692×unsub-neg_binary64
492×fma-neg_binary64
461×distribute-neg-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1139
2199
3299
4459
5689
61089
72429
84479
97249
1015319
1123119
1223659
1326019
1427499
1527479
1628249
1730839
1836469
1946389
2048839
2149259
2249369
2349339
2461859

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 1 (*.f64 x x))
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))

series7.0ms (0.4%)

Counts
2 → 24
Calls

2 calls:

5.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms
(-.f64 1 (*.f64 x x))

rewrite8.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64
7×*-un-lft-identity_binary64
5×sqrt-prod_binary64
5×add-cube-cbrt_binary64
4×difference-of-squares_binary64
Counts
2 → 41
Calls

2 calls:

2.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms
(-.f64 1 (*.f64 x x))

simplify69.0ms (4.4%)

Algorithm
1×egg-herbie
Rules
508×fma-neg_binary64
320×times-frac_binary64
300×neg-mul-1_binary64
296×neg-sub0_binary64
260×unswap-sqr_binary64
Counts
65 → 76
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0100827
1239777
2655750
32266746
44452746
54914746

prune52.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New74276
Fresh000
Picked101
Done000
Total75277
Error
0b
Counts
77 → 2
Alt Table
StatusErrorProgram
0.4b
(fma.f64 (*.f64 x x) -1/2 1)
▶0.0b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))
Compiler

Compiled 1030 to 710 computations (31.1% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 1 (*.f64 x x))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓0.0b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))
✓0.0b
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)

series12.0ms (0.8%)

Counts
2 → 24
Calls

2 calls:

8.0ms
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)
4.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))

rewrite12.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
22×cbrt-prod_binary64
20×sqrt-prod_binary64
16×cube-prod_binary64
16×*-un-lft-identity_binary64
16×add-sqr-sqrt_binary64
Counts
2 → 75
Calls

2 calls:

4.0ms
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)
3.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))

simplify96.0ms (6.1%)

Algorithm
1×egg-herbie
Rules
787×fma-neg_binary64
472×fma-def_binary64
352×times-frac_binary64
230×cancel-sign-sub-inv_binary64
226×associate-/r*_binary64
Counts
99 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01551652
14071608
211351537
332901523
448581523
548951523

prune129.0ms (8.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1961197
Fresh101
Picked011
Done000
Total1972199
Error
0b
Counts
199 → 2
Alt Table
StatusErrorProgram
▶0.0b
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
✓0.0b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))
Compiler

Compiled 3237 to 2429 computations (25% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 1 (*.f64 x x))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓1.0b
(expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

series3.0ms (0.2%)

Counts
1 → 12
Calls

1 calls:

3.0ms
(expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
2×log1p-expm1-u_binary64
1×*-un-lft-identity_binary64
1×add-sqr-sqrt_binary64
1×add-cube-cbrt_binary64
1×add-cbrt-cube_binary64
Counts
1 → 11
Calls

1 calls:

0.0ms
(expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify82.0ms (5.2%)

Algorithm
1×egg-herbie
Rules
647×sub-neg_binary64
558×fma-def_binary64
446×associate-*l*_binary64
364×associate-*r*_binary64
343×cancel-sign-sub-inv_binary64
Counts
23 → 21
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
045343
197314
2270308
3840300
43169300
54662300
65218300

prune65.0ms (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New97097
Fresh000
Picked011
Done011
Total97299
Error
0b
Counts
99 → 2
Alt Table
StatusErrorProgram
✓0.0b
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
✓0.0b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))
Compiler

Compiled 1451 to 1052 computations (27.5% saved)

regimes70.0ms (4.4%)

Accuracy

Total 0.0b remaining (42.4%)

Threshold costs 0.0b (42.4%)

Counts
27 → 1
Compiler

Compiled 926 to 716 computations (22.7% saved)

simplify6.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
3×+-commutative_binary64
3×sub-neg_binary64
2×*-commutative_binary64
2×neg-sub0_binary64
2×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11513
22113
32513
42713
52613

end43.0ms (2.7%)

Compiler

Compiled 37 to 29 computations (21.6% saved)

Profiling

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