Details

Time bar (total: 6.3s)

analyze1.2s (18.8%)

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
0%99.8%0.2%9
0%99.8%0.2%10
16.4%83.4%0.2%11
19.9%79.9%0.2%12
21.6%77.2%1.2%13
24.8%73.7%1.4%14
Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.5s (24.1%)

Symmetry

(sort x y)

(sort z t)

Results
1.1s8256×body128valid
340.0ms2935×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify44.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
828×fma-def_binary64
389×fma-neg_binary64
130×cancel-sign-sub-inv_binary64
113×distribute-rgt-in_binary64
103×associate-/l*_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
12113
24213
37313
414413
522313
631913
749513
867813
983313
1088913
1197613
1298213
1398713
1491413

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
8.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶8.1b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
Compiler

Compiled 42 to 27 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓7.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

series27.0ms (0.4%)

Counts
1 → 60
Calls

1 calls:

27.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

rewrite7.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×*-un-lft-identity_binary64
9×times-frac_binary64
9×add-sqr-sqrt_binary64
9×add-cube-cbrt_binary64
3×associate-/r*_binary64
Counts
1 → 32
Calls

1 calls:

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

simplify78.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
742×fma-def_binary64
440×distribute-rgt-in_binary64
432×distribute-lft-in_binary64
335×associate-/l/_binary64
300×neg-mul-1_binary64
Counts
92 → 61
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0801433
12041377
25521377
316691377
446351377
551531377

prune51.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New511061
Fresh000
Picked101
Done000
Total521062
Error
7.8b
Counts
62 → 10
Alt Table
StatusErrorProgram
51.1b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (-.f64 (*.f64 x y) (*.f64 z t))) (-.f64 (*.f64 x y) (*.f64 z t))) (*.f64 (*.f64 a a) a)))
35.5b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
9.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
36.6b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
9.0b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
30.6b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))) (*.f64 a (fma.f64 t z (*.f64 y x))))
33.4b
(/.f64 (*.f64 y x) a)
▶8.2b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
8.3b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
33.7b
(neg.f64 (/.f64 (*.f64 t z) a))
Compiler

Compiled 1575 to 421 computations (73.3% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓7.8b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

series26.0ms (0.4%)

Counts
1 → 60
Calls

1 calls:

26.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

rewrite11.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
13×associate-*r*_binary64
11×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-exp-log_binary64
Counts
1 → 42
Calls

1 calls:

8.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

simplify87.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
493×associate-*l*_binary64
488×fma-neg_binary64
416×associate-*r*_binary64
344×distribute-lft-neg-out_binary64
344×distribute-rgt-neg-out_binary64
Counts
102 → 73
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0921553
12431454
27771454
327121454
449761454
552171454

prune54.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New71273
Fresh189
Picked011
Done000
Total721183
Error
7.8b
Counts
83 → 11
Alt Table
StatusErrorProgram
36.6b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
30.6b
(/.f64 (*.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (fma.f64 t z (*.f64 y x))) (*.f64 a (fma.f64 t z (*.f64 y x))))
33.7b
(neg.f64 (/.f64 (*.f64 t z) a))
9.0b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1 (cbrt.f64 a)))
51.1b
(cbrt.f64 (/.f64 (*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (-.f64 (*.f64 x y) (*.f64 z t))) (-.f64 (*.f64 x y) (*.f64 z t))) (*.f64 (*.f64 a a) a)))
35.5b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
9.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
9.0b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
33.4b
(/.f64 (*.f64 y x) a)
✓8.2b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
▶8.3b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
Compiler

Compiled 1893 to 667 computations (64.8% saved)

localize35.0ms (0.6%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
✓7.6b
(/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))

series86.0ms (1.4%)

Counts
2 → 120
Calls

2 calls:

60.0ms
(/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))
25.0ms
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))

rewrite21.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
90×times-frac_binary64
54×*-un-lft-identity_binary64
54×add-sqr-sqrt_binary64
54×add-cube-cbrt_binary64
18×associate-/r*_binary64
Counts
2 → 117
Calls

2 calls:

7.0ms
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
4.0ms
(/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))

simplify155.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
770×fma-def_binary64
372×fma-neg_binary64
341×times-frac_binary64
322×associate-/l/_binary64
189×cancel-sign-sub-inv_binary64
Counts
237 → 205
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02035987
15585614
223745371
348495371
451075371

prune179.0ms (2.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New19411205
Fresh549
Picked101
Done011
Total20016216
Error
7.7b
Counts
216 → 16
Alt Table
StatusErrorProgram
36.9b
(/.f64 1 (cbrt.f64 (*.f64 (*.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))))
33.9b
(/.f64 1 (neg.f64 (/.f64 a (*.f64 t z))))
9.0b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
9.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 a (-.f64 (*.f64 y x) (*.f64 t z)))) (cbrt.f64 (/.f64 a (-.f64 (*.f64 y x) (*.f64 t z)))))) (/.f64 1 (cbrt.f64 (/.f64 a (-.f64 (*.f64 y x) (*.f64 t z))))))
✓8.2b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
34.0b
(/.f64 1 (*.f64 (+.f64 (/.f64 (*.f64 t z) (*.f64 y x)) 1) (/.f64 a (*.f64 y x))))
37.0b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))))
34.2b
(/.f64 1 (*.f64 (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))) (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))))
34.9b
(/.f64 1 (*.f64 (/.f64 a (*.f64 t z)) (-.f64 -1 (/.f64 (*.f64 y x) (*.f64 t z)))))
29.7b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (fma.f64 y x (*.f64 t z))) a) (+.f64 (*.f64 x y) (*.f64 z t)))
▶8.4b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))
35.7b
(/.f64 1 (/.f64 (/.f64 a (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
30.4b
(*.f64 (/.f64 1 (/.f64 a (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))))) (/.f64 1 (+.f64 (*.f64 x y) (*.f64 z t))))
9.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
33.4b
(/.f64 (*.f64 y x) a)
9.0b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1 (cbrt.f64 a)))
Compiler

Compiled 5738 to 1758 computations (69.4% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t)))
✓7.8b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))

series61.0ms (1%)

Counts
2 → 108
Calls

2 calls:

35.0ms
(/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t)))
26.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))

rewrite89.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
474×times-frac_binary64
220×*-un-lft-identity_binary64
220×add-sqr-sqrt_binary64
220×add-cube-cbrt_binary64
46×add-exp-log_binary64
Counts
2 → 292
Calls

2 calls:

12.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))
4.0ms
(/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t)))

simplify284.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
722×fma-def_binary64
283×fma-neg_binary64
217×distribute-rgt-in_binary64
199×distribute-lft-in_binary64
197×cancel-sign-sub-inv_binary64
Counts
400 → 369
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
022912199
163511258
2238511054
3468911054
4496711054

prune301.0ms (4.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New3690369
Fresh01414
Picked011
Done011
Total36916385
Error
7.7b
Counts
385 → 16
Alt Table
StatusErrorProgram
36.9b
(/.f64 1 (cbrt.f64 (*.f64 (*.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))))
33.9b
(/.f64 1 (neg.f64 (/.f64 a (*.f64 t z))))
9.0b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
9.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 a (-.f64 (*.f64 y x) (*.f64 t z)))) (cbrt.f64 (/.f64 a (-.f64 (*.f64 y x) (*.f64 t z)))))) (/.f64 1 (cbrt.f64 (/.f64 a (-.f64 (*.f64 y x) (*.f64 t z))))))
✓8.2b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
34.0b
(/.f64 1 (*.f64 (+.f64 (/.f64 (*.f64 t z) (*.f64 y x)) 1) (/.f64 a (*.f64 y x))))
37.0b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))) (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))))
34.2b
(/.f64 1 (*.f64 (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))) (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))))
34.9b
(/.f64 1 (*.f64 (/.f64 a (*.f64 t z)) (-.f64 -1 (/.f64 (*.f64 y x) (*.f64 t z)))))
29.7b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (fma.f64 y x (*.f64 t z))) a) (+.f64 (*.f64 x y) (*.f64 z t)))
✓8.4b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))
35.7b
(/.f64 1 (/.f64 (/.f64 a (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
30.4b
(*.f64 (/.f64 1 (/.f64 a (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))))) (/.f64 1 (+.f64 (*.f64 x y) (*.f64 z t))))
9.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
33.4b
(/.f64 (*.f64 y x) a)
9.0b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1 (cbrt.f64 a)))
Compiler

Compiled 11278 to 4664 computations (58.6% saved)

regimes1.8s (28.3%)

Accuracy

Total 0.4b remaining (4.7%)

Threshold costs 0.4b (4.7%)

Counts
169 → 1
Compiler

Compiled 38051 to 23949 computations (37.1% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01116
11516
22216
33216
43916
54416
64616
74616

end192.0ms (3%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 528 to 275 computations (47.9% saved)

Profiling

Loading profile data...