Details

Time bar (total: 6.5s)

analyze1.2s (18.3%)

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 (23.3%)

Symmetry

(sort x y)

(sort z t)

Results
949.0ms8256×body128valid
477.0ms3039×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify47.0ms (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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
8.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶8.6b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
Compiler

Compiled 42 to 27 computations (35.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.5b
(-.f64 (*.f64 x y) (*.f64 z t))
✓8.1b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

series34.0ms (0.5%)

Counts
2 → 108
Calls

2 calls:

25.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
9.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

rewrite9.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
9×times-frac_binary64
4×add-cbrt-cube_binary64
Counts
2 → 48
Calls

2 calls:

4.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
2.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

simplify117.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
644×distribute-rgt-in_binary64
301×fma-neg_binary64
270×associate-*l*_binary64
223×fma-def_binary64
213×associate-*r*_binary64
Counts
156 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0992115
12512035
27432029
323552029
445902029
549962029
649232029

prune75.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New821193
Fresh000
Picked101
Done000
Total831194
Error
8.3b
Counts
94 → 11
Alt Table
StatusErrorProgram
9.5b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) a)
36.9b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
33.4b
(/.f64 (*.f64 y x) a)
35.4b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
34.1b
(neg.f64 (/.f64 (*.f64 t z) a))
9.6b
(/.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
9.5b
(/.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)))))
32.6b
(/.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))))
▶8.8b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
8.9b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
43.1b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
Compiler

Compiled 2088 to 535 computations (74.4% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(-.f64 (*.f64 x y) (*.f64 z t))
✓8.3b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

series39.0ms (0.6%)

Counts
1 → 60
Calls

1 calls:

39.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

rewrite10.0ms (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:

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

simplify87.0ms (1.3%)

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

prune80.0ms (1.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1005105
Fresh2810
Picked011
Done000
Total10214116
Error
8.3b
Counts
116 → 14
Alt Table
StatusErrorProgram
35.4b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 1 a)))
✓8.8b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
31.4b
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))) (/.f64 1 a)) (+.f64 (*.f64 x y) (*.f64 z t)))
▶8.9b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
9.5b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) a)
36.9b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
33.4b
(/.f64 (*.f64 y x) a)
34.1b
(neg.f64 (/.f64 (*.f64 t z) a))
9.6b
(/.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
9.5b
(/.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)))))
32.6b
(/.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))))
34.1b
(*.f64 (neg.f64 (*.f64 t z)) (/.f64 1 a))
33.5b
(*.f64 (*.f64 y x) (/.f64 1 a))
43.1b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
Compiler

Compiled 2538 to 887 computations (65.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
0.5b
(-.f64 (*.f64 x y) (*.f64 z t))
✓8.2b
(/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))

series82.0ms (1.3%)

Counts
2 → 120
Calls

2 calls:

55.0ms
(/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))
26.0ms
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))

rewrite24.0ms (0.4%)

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 a (-.f64 (*.f64 x y) (*.f64 z t)))
6.0ms
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))

simplify144.0ms (2.2%)

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

prune192.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2298237
Fresh6612
Picked101
Done101
Total23714251
Error
8.3b
Counts
251 → 14
Alt Table
StatusErrorProgram
31.4b
(/.f64 (/.f64 1 (/.f64 a (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))))) (+.f64 (*.f64 x y) (*.f64 z t)))
9.5b
(/.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)))))
36.9b
(/.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (sqrt.f64 a) (-.f64 (*.f64 x y) (*.f64 z t))))
36.3b
(/.f64 (/.f64 1 (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))) (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))))
33.6b
(/.f64 1 (*.f64 (+.f64 (/.f64 (*.f64 t z) (*.f64 y x)) 1) (/.f64 a (*.f64 y x))))
33.5b
(*.f64 (*.f64 y x) (/.f64 1 a))
8.9b
(/.f64 1 (/.f64 1 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
33.4b
(/.f64 (*.f64 y x) a)
▶8.8b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))
35.4b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 1 a)))
32.6b
(/.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))))
34.1b
(*.f64 (neg.f64 (*.f64 t z)) (/.f64 1 a))
33.5b
(/.f64 1 (/.f64 a (*.f64 y x)))
34.4b
(/.f64 1 (*.f64 (/.f64 a (*.f64 t z)) (-.f64 -1 (/.f64 (*.f64 y x) (*.f64 t z)))))
Compiler

Compiled 6015 to 1834 computations (69.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.5b
(-.f64 (*.f64 x y) (*.f64 z t))
✓0.8b
(/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t)))
✓7.4b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))

series56.0ms (0.9%)

Counts
2 → 108
Calls

2 calls:

29.0ms
(/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t)))
26.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))

rewrite63.0ms (1%)

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:

11.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))
4.0ms
(/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t)))

simplify275.0ms (4.2%)

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

prune315.0ms (4.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New3992401
Fresh11213
Picked011
Done000
Total40015415
Error
8.3b
Counts
415 → 15
Alt Table
StatusErrorProgram
31.4b
(/.f64 (/.f64 1 (/.f64 a (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))))) (+.f64 (*.f64 x y) (*.f64 z t)))
9.5b
(/.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)))))
32.3b
(*.f64 (/.f64 1 (/.f64 1 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))))) (/.f64 (/.f64 1 a) (+.f64 (*.f64 x y) (*.f64 z t))))
36.9b
(/.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (sqrt.f64 a) (-.f64 (*.f64 x y) (*.f64 z t))))
36.3b
(/.f64 (/.f64 1 (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))) (sqrt.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t)))))
33.6b
(/.f64 1 (*.f64 (+.f64 (/.f64 (*.f64 t z) (*.f64 y x)) 1) (/.f64 a (*.f64 y x))))
33.5b
(*.f64 (*.f64 y x) (/.f64 1 a))
8.9b
(/.f64 1 (/.f64 1 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
33.4b
(/.f64 (*.f64 y x) a)
✓8.8b
(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (*.f64 x y) (*.f64 z t))))
33.5b
(/.f64 (/.f64 1 a) (/.f64 1 (*.f64 y x)))
35.4b
(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 1 a)))
32.6b
(/.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))))
34.1b
(*.f64 (neg.f64 (*.f64 t z)) (/.f64 1 a))
34.4b
(/.f64 1 (*.f64 (/.f64 a (*.f64 t z)) (-.f64 -1 (/.f64 (*.f64 y x) (*.f64 t z)))))
Compiler

Compiled 11779 to 4863 computations (58.7% saved)

regimes1.9s (29.7%)

Accuracy

Total 0.3b remaining (4.5%)

Threshold costs 0.3b (4.5%)

Counts
179 → 1
Compiler

Compiled 41654 to 26516 computations (36.3% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11913
22713
33213
43413
53413

end181.0ms (2.8%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 416 to 242 computations (41.8% saved)

Profiling

Loading profile data...