Details

Time bar (total: 11.5s)

analyze1.6s (13.6%)

Algorithm
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
0%99.8%0.2%9
1.6%98.2%0.2%10
3.1%90.4%6.5%11
9.2%84.4%6.5%12
13%80.6%6.5%13
24.8%68.7%6.5%14
Compiler

Compiled 20 to 13 computations (35% saved)

sample1.7s (15%)

Symmetry

(sort x y)

(sort t a)

Results
1.2s8256×body128valid
421.0ms3090×body128invalid
Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify59.0ms (0.5%)

Algorithm
egg-herbie
Rules
1034×fma-def_binary64
336×fma-neg_binary64
138×distribute-rgt-in_binary64
130×cancel-sign-sub-inv_binary64
128×associate-/r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01321
12621
25221
38721
412821
516121
620321
724721
846421
982221
10123421
11116921
12123721
13131121
14137521
15137521
16128221

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
24.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
24.3b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
Compiler

Compiled 57 to 36 computations (36.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.0b
(-.f64 (*.f64 z z) (*.f64 t a))
6.9b
(*.f64 (*.f64 x y) z)
9.2b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
24.2b
(sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))

series268.0ms (2.3%)

Counts
4 → 136
Calls

4 calls:

207.0ms
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
42.0ms
(sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))
10.0ms
(*.f64 (*.f64 x y) z)
9.0ms
(-.f64 (*.f64 z z) (*.f64 t a))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube_binary64
18×add-exp-log_binary64
11×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
4 → 86
Calls

4 calls:

8.0ms
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
4.0ms
(*.f64 (*.f64 x y) z)
3.0ms
(sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))
3.0ms
(-.f64 (*.f64 z z) (*.f64 t a))

simplify135.0ms (1.2%)

Algorithm
egg-herbie
Rules
731×fma-def_binary64
379×times-frac_binary64
318×associate-*r*_binary64
293×associate-*l*_binary64
277×associate-/l*_binary64
Counts
222 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02834463
18424196
238994138
349614138
449764138

prune158.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1828190
Fresh000
Picked101
Done000
Total1838191
Error
2.7b
Counts
191 → 8
Alt Table
StatusErrorProgram
24.0b
(/.f64 (*.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z))
37.0b
(neg.f64 (*.f64 y x))
35.5b
(*.f64 y x)
44.6b
(*.f64 y (*.f64 (sqrt.f64 (/.f64 -1 (*.f64 a t))) (*.f64 z x)))
24.3b
(*.f64 (*.f64 (*.f64 x y) z) (/.f64 1 (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))))
24.3b
(*.f64 (/.f64 (*.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 a t))))))
25.4b
(/.f64 (*.f64 x (*.f64 y z)) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
24.9b
(/.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
Compiler

Compiled 4988 to 1507 computations (69.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z)
3.4b
(/.f64 (*.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z))
12.8b
(sqrt.f64 (neg.f64 (*.f64 a t)))

series704.0ms (6.1%)

Counts
3 → 52
Calls

3 calls:

517.0ms
(/.f64 (*.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z))
165.0ms
(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z)
21.0ms
(sqrt.f64 (neg.f64 (*.f64 a t)))

rewrite16.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
40×times-frac_binary64
27×add-sqr-sqrt_binary64
26×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64
17×add-cbrt-cube_binary64
Counts
3 → 95
Calls

3 calls:

6.0ms
(/.f64 (*.f64 x y) (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z))
2.0ms
(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z)
1.0ms
(sqrt.f64 (neg.f64 (*.f64 a t)))

simplify100.0ms (0.9%)

Algorithm
egg-herbie
Rules
641×associate-/r/_binary64
607×associate-*r/_binary64
266×fma-def_binary64
200×cancel-sign-sub-inv_binary64
157×associate-/l*_binary64
Counts
147 → 175
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02684134
16543630
224023587
352063587

prune121.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1732175
Fresh077
Picked101
Done000
Total1749183
Error
0.3b
Counts
183 → 9
Alt Table
StatusErrorProgram
24.8b
(/.f64 (*.f64 x y) (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z))
25.4b
(/.f64 (*.f64 x (*.f64 y z)) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
37.0b
(neg.f64 (*.f64 y x))
35.5b
(*.f64 y x)
44.6b
(*.f64 y (*.f64 (sqrt.f64 (/.f64 -1 (*.f64 a t))) (*.f64 z x)))
24.3b
(*.f64 (*.f64 (*.f64 x y) z) (/.f64 1 (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))))
24.3b
(*.f64 (/.f64 (*.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 a t))))))
23.2b
(/.f64 x (/.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z) y))
24.9b
(/.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
Compiler

Compiled 4705 to 1289 computations (72.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z)
1.7b
(/.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z) y)
1.8b
(/.f64 x (/.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z) y))
12.8b
(sqrt.f64 (neg.f64 (*.f64 a t)))

series722.0ms (6.3%)

Counts
2 → 64
Calls

2 calls:

513.0ms
(/.f64 x (/.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z) y))
209.0ms
(/.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z) y)

rewrite61.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
468×times-frac_binary64
228×*-un-lft-identity_binary64
228×add-sqr-sqrt_binary64
228×add-cube-cbrt_binary64
46×associate-/r*_binary64
Counts
2 → 266
Calls

2 calls:

9.0ms
(/.f64 x (/.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z) y))
7.0ms
(/.f64 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) z) y)

simplify344.0ms (3%)

Algorithm
egg-herbie
Rules
697×associate-/r/_binary64
529×associate-/l/_binary64
381×associate-*l/_binary64
356×*-commutative_binary64
228×fma-def_binary64
Counts
330 → 539
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057213139
1139012128
2472812118
3499912118
4498012118

prune336.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New6102612
Fresh178
Picked101
Done000
Total6129621
Error
0.3b
Counts
621 → 9
Alt Table
StatusErrorProgram
24.3b
(*.f64 (*.f64 (*.f64 x y) z) (/.f64 1 (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))))
35.6b
(/.f64 x (/.f64 1 y))
37.0b
(neg.f64 (*.f64 y x))
35.5b
(*.f64 y x)
44.6b
(*.f64 y (*.f64 (sqrt.f64 (/.f64 -1 (*.f64 a t))) (*.f64 z x)))
24.3b
(*.f64 (/.f64 (*.f64 y x) (fabs.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 a t))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 a t))))))
24.8b
(/.f64 (*.f64 x y) (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z))
24.3b
(/.f64 x (/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y))
24.9b
(/.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
Compiler

Compiled 18567 to 3397 computations (81.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z)
0.2b
(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))
1.7b
(/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y)
1.8b
(/.f64 x (/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y))

series921.0ms (8%)

Counts
4 → 78
Calls

4 calls:

517.0ms
(/.f64 x (/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y))
219.0ms
(/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y)
168.0ms
(/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z)
17.0ms
(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))

rewrite71.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
477×times-frac_binary64
254×add-sqr-sqrt_binary64
244×*-un-lft-identity_binary64
244×add-cube-cbrt_binary64
49×associate-/r*_binary64
Counts
4 → 335
Calls

4 calls:

9.0ms
(/.f64 x (/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y))
6.0ms
(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))
4.0ms
(/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y)
2.0ms
(/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z)

simplify336.0ms (2.9%)

Algorithm
egg-herbie
Rules
695×associate-/r/_binary64
529×associate-/l/_binary64
414×associate-*l/_binary64
259×associate-*r/_binary64
255×associate-/l*_binary64
Counts
413 → 667
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
069515587
1173214439
2493614431
3498314431

prune347.0ms (3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New6643667
Fresh268
Picked011
Done000
Total66610676
Error
0.0b
Counts
676 → 10
Alt Table
StatusErrorProgram
24.9b
(/.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
24.4b
(*.f64 (/.f64 x (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z)) y)
37.0b
(neg.f64 (*.f64 y x))
35.5b
(*.f64 y x)
44.6b
(*.f64 y (*.f64 (sqrt.f64 (/.f64 -1 (*.f64 a t))) (*.f64 z x)))
35.6b
(/.f64 x (/.f64 1 y))
42.4b
(/.f64 x (/.f64 (*.f64 (/.f64 (sqrt.f64 (neg.f64 t)) z) (sqrt.f64 a)) y))
41.9b
(/.f64 x (*.f64 (/.f64 (sqrt.f64 (neg.f64 t)) (*.f64 y z)) (sqrt.f64 a)))
24.8b
(/.f64 (*.f64 x y) (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z))
24.3b
(/.f64 x (/.f64 (/.f64 (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z) z) y))
Compiler

Compiled 20912 to 3958 computations (81.1% saved)

regimes2.8s (24.3%)

Accuracy

Total 6.3b remaining (94.7%)

Threshold costs 0b (0%)

Counts
130 → 5
Compiler

Compiled 26128 to 15687 computations (40% saved)

bsearch170.0ms (1.5%)

Steps
ItersRangePoint
4
1.2989047507070077e+138
8.459611311231945e+143
1.2689282843189357e+142
7
1.2104245460289898e-173
4.677002156473703e-172
1.2271992071220414e-173
8
3.777965263235588e-262
1.2197554429266104e-257
1.1954013876901866e-257
8
-2.3747563862881755e-35
-1.3053004514730204e-39
-1.2154716544061854e-37
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
056137
179137
295137
3104137
4107137
5106137

end459.0ms (4%)

Compiler

Compiled 712 to 426 computations (40.2% saved)

Profiling

Loading profile data...