Details

Time bar (total: 3.0s)

analyze1.0s (34.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
6.2%93.6%0.2%9
12.5%87.3%0.2%10
15.6%80.3%4.1%11
31.2%63.9%4.9%12
39%50.9%10.1%13
44.8%44.4%10.7%14
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample35.0ms (1.2%)

Algorithm
1×intervals
Results
11.0ms256×body128valid
1.0ms34×body128invalid
Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify15.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
171×fma-def_binary64
87×fma-neg_binary64
36×cancel-sign-sub-inv_binary64
23×distribute-rgt-neg-in_binary64
20×sub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11610
22710
34410
46610
510010
615210
721310
825710
927910
1029910
1130510
1227410

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
(-.f64 (*.f64 x y) (*.f64 z t))
Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 x y) (*.f64 z t))

series9.0ms (0.3%)

Counts
1 → 48
Calls

1 calls:

9.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

rewrite6.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
3×add-log-exp_binary64
1×cancel-sign-sub-inv_binary64
1×flip--_binary64
1×sub-neg_binary64
1×*-un-lft-identity_binary64
Counts
1 → 16
Calls

1 calls:

3.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

simplify120.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
480×times-frac_binary64
463×fma-def_binary64
444×unsub-neg_binary64
265×sub-neg_binary64
232×distribute-rgt-neg-in_binary64
Counts
64 → 32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043682
1113658
2347652
3974652
42183652
53451652
64489652
74961652
84995652
94859652

prune20.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New30232
Fresh000
Picked101
Done000
Total31233
Error
0.0b
Counts
33 → 2
Alt Table
StatusErrorProgram
32.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))
▶0.0b
(fma.f64 x y (neg.f64 (*.f64 z t)))
Compiler

Compiled 477 to 125 computations (73.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 x y (neg.f64 (*.f64 z t)))

series10.0ms (0.3%)

Counts
1 → 48
Calls

1 calls:

9.0ms
(fma.f64 x y (neg.f64 (*.f64 z t)))

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 → 10
Calls

1 calls:

0.0ms
(fma.f64 x y (neg.f64 (*.f64 z t)))

simplify87.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
967×unsub-neg_binary64
792×times-frac_binary64
421×fma-neg_binary64
384×neg-sub0_binary64
364×neg-mul-1_binary64
Counts
58 → 22
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
023568
137547
265547
3215547
4895547
51760547
63723547
74512547
85729547

prune10.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New22022
Fresh011
Picked011
Done000
Total22224
Error
0.0b
Counts
24 → 2
Alt Table
StatusErrorProgram
▶32.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))
✓0.0b
(fma.f64 x y (neg.f64 (*.f64 z t)))
Compiler

Compiled 302 to 77 computations (74.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z t))
✓0.3b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))
✓0.9b
(sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))

series124.0ms (4.1%)

Counts
2 → 56
Calls

2 calls:

76.0ms
(sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))
48.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))

rewrite22.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
18×pow1_binary64
14×sqrt-div_binary64
11×*-un-lft-identity_binary64
Counts
2 → 78
Calls

2 calls:

9.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))
3.0ms
(sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))

simplify92.0ms (3%)

Algorithm
1×egg-herbie
Rules
557×times-frac_binary64
537×fma-neg_binary64
342×*-commutative_binary64
337×associate-/r*_binary64
330×fma-def_binary64
Counts
134 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01382631
13352448
211842366
343732332
449602332

prune78.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2251226
Fresh000
Picked011
Done011
Total2253228
Error
0.0b
Counts
228 → 3
Alt Table
StatusErrorProgram
▶42.8b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3)))
✓32.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))
✓0.0b
(fma.f64 x y (neg.f64 (*.f64 z t)))
Compiler

Compiled 6007 to 1072 computations (82.2% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3)))
0.9b
(sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))
✓0.9b
(sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))
✓11.5b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3))

series195.0ms (6.4%)

Counts
3 → 72
Calls

3 calls:

77.0ms
(sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))
72.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3))
46.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3)))

rewrite34.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
48×cbrt-prod_binary64
44×add-sqr-sqrt_binary64
29×sqrt-prod_binary64
21×associate-*r*_binary64
17×*-un-lft-identity_binary64
Counts
3 → 110
Calls

3 calls:

14.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3)))
4.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3))
3.0ms
(sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))

simplify174.0ms (5.7%)

Algorithm
1×egg-herbie
Rules
589×times-frac_binary64
341×fma-def_binary64
315×associate-/l*_binary64
279×unswap-sqr_binary64
204×cancel-sign-sub-inv_binary64
Counts
182 → 135
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02014161
14133872
214803753
345373721
448263721
549913721
649513721

prune72.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1760176
Fresh000
Picked011
Done022
Total1763179
Error
0.0b
Counts
179 → 3
Alt Table
StatusErrorProgram
✓42.8b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) 3)))
✓32.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))
✓0.0b
(fma.f64 x y (neg.f64 (*.f64 z t)))
Compiler

Compiled 5683 to 1495 computations (73.7% saved)

regimes158.0ms (5.2%)

Accuracy

Total 0.0b remaining (15%)

Threshold costs 0.0b (15%)

Counts
17 → 1
Compiler

Compiled 2434 to 1471 computations (39.6% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
12222
23022
33422
43522
53522

end21.0ms (0.7%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 95 to 50 computations (47.4% saved)

sample689.0ms (22.6%)

Algorithm
1×intervals
Results
273.0ms8000×body128valid
42.0ms1405×body128invalid
Compiler

Compiled 91 to 54 computations (40.7% saved)

Profiling

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