Details

Time bar (total: 10.1s)

analyze2.8s (27.9%)

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
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)

sample2.6s (25.4%)

Symmetry

(sort x y)

(sort z t)

Results
1.8s8256×body128valid
650.0ms3094×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify48.0ms (0.5%)

Algorithm
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

prune5.0ms (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)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z t))
7.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

series78.0ms (0.8%)

Counts
2 → 108
Calls

2 calls:

53.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
25.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

rewrite122.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
420×fma-def_binary64
224×egg-rr
220×fma-neg_binary64
214×expm1-udef_binary64
214×log1p-udef_binary64
Counts
2 → 224
Calls

2 calls:

112.0ms
(-.f64 (*.f64 x y) (*.f64 z t))
112.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01023
122323
2311223
3497323
000
100

simplify200.0ms (2%)

Algorithm
egg-herbie
Rules
1168×fma-def_binary64
351×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
93×associate-/l*_binary64
92×unsub-neg_binary64
Counts
332 → 234
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0191140
1491140
2961140
32021140
43561140
55931140
68191140
79081140
89821140
99961140
1010011140
119281140

prune414.0ms (4.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New22311234
Fresh000
Picked101
Done000
Total22411235
Error
4.9b
Counts
235 → 11
Alt Table
StatusErrorProgram
37.0b
(fma.f64 (/.f64 x (sqrt.f64 a)) (/.f64 y (sqrt.f64 a)) (neg.f64 (/.f64 (*.f64 z t) a)))
8.3b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
37.8b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) 3))
8.7b
(pow.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) -1)
36.4b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
8.2b
(/.f64 (+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
9.0b
(*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) 2))
10.1b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
32.7b
(/.f64 (*.f64 y x) a)
10.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
25.2b
(/.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) x) (neg.f64 (*.f64 z t))) a)
Compiler

Compiled 4918 to 1258 computations (74.4% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t))))
7.7b
(/.f64 (+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
52.0b
(fma.f64 z (neg.f64 t) (*.f64 z t))

series127.0ms (1.3%)

Counts
3 → 132
Calls

3 calls:

75.0ms
(/.f64 (+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
27.0ms
(+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t))))
25.0ms
(fma.f64 z (neg.f64 t) (*.f64 z t))

rewrite113.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
383×fma-def_binary64
242×expm1-udef_binary64
242×log1p-udef_binary64
226×fma-neg_binary64
217×log-pow_binary64
Counts
3 → 134
Calls

3 calls:

107.0ms
(+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t))))
107.0ms
(/.f64 (+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
107.0ms
(fma.f64 z (neg.f64 t) (*.f64 z t))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01353
127740
2334840
3505240
000
100

simplify98.0ms (1%)

Algorithm
egg-herbie
Rules
1168×fma-def_binary64
351×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
93×associate-/l*_binary64
92×unsub-neg_binary64
Counts
266 → 145
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0201164
1501164
2961164
32021164
43561164
55931164
68191164
79081164
89821164
99961164
1010011164
119281164

prune101.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1450145
Fresh01010
Picked011
Done000
Total14511156
Error
4.9b
Counts
156 → 11
Alt Table
StatusErrorProgram
37.0b
(fma.f64 (/.f64 x (sqrt.f64 a)) (/.f64 y (sqrt.f64 a)) (neg.f64 (/.f64 (*.f64 z t) a)))
8.3b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
37.8b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) 3))
8.7b
(pow.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) -1)
36.4b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
8.2b
(/.f64 (+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
9.0b
(*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) 2))
10.1b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
32.7b
(/.f64 (*.f64 y x) a)
10.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
25.2b
(/.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) x) (neg.f64 (*.f64 z t))) a)
Compiler

Compiled 3292 to 922 computations (72% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z t))
7.8b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

series27.0ms (0.3%)

Counts
1 → 60
Calls

1 calls:

27.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

rewrite67.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
459×fma-def_binary64
228×expm1-udef_binary64
228×log1p-udef_binary64
204×log-pow_binary64
199×fma-neg_binary64
Counts
1 → 95
Calls

1 calls:

64.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01213
125613
2318213
3501413
000
100

simplify74.0ms (0.7%)

Algorithm
egg-herbie
Rules
1163×fma-def_binary64
349×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
92×associate-/l*_binary64
92×unsub-neg_binary64
Counts
155 → 101
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
018720
146720
293720
3198720
4354720
5593720
6819720
7908720
8982720
9996720
101001720
11928720

prune241.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2715276
Fresh369
Picked101
Done011
Total27512287
Error
4.9b
Counts
287 → 12
Alt Table
StatusErrorProgram
8.2b
(/.f64 (+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
8.2b
(fma.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a) (*.f64 (fma.f64 z (neg.f64 t) (*.f64 z t)) (/.f64 1 a)))
25.2b
(*.f64 (fma.f64 (*.f64 x (sqrt.f64 y)) (sqrt.f64 y) (neg.f64 (*.f64 z t))) (/.f64 1 a))
10.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
28.3b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 z t) 2)) (*.f64 a (fma.f64 x y (*.f64 z t))))
8.7b
(pow.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) -1)
20.5b
(*.f64 (fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 t)) (sqrt.f64 t) (*.f64 x y)) (/.f64 1 a))
32.8b
(*.f64 (*.f64 y x) (/.f64 1 a))
10.1b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
37.0b
(fma.f64 (/.f64 x (sqrt.f64 a)) (/.f64 y (sqrt.f64 a)) (neg.f64 (/.f64 (*.f64 z t) a)))
32.7b
(/.f64 (*.f64 y x) a)
25.2b
(/.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) x) (neg.f64 (*.f64 z t))) a)
Compiler

Compiled 6663 to 2047 computations (69.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z t))
7.8b
(fma.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a) (*.f64 (fma.f64 z (neg.f64 t) (*.f64 z t)) (/.f64 1 a)))
52.0b
(fma.f64 z (neg.f64 t) (*.f64 z t))

series39.0ms (0.4%)

Counts
1 → 60
Calls

1 calls:

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

rewrite66.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
475×fma-def_binary64
260×fma-neg_binary64
256×expm1-udef_binary64
256×log1p-udef_binary64
161×add-sqr-sqrt_binary64
Counts
1 → 39
Calls

1 calls:

64.0ms
(fma.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a) (*.f64 (fma.f64 z (neg.f64 t) (*.f64 z t)) (/.f64 1 a)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01529
131811
2354911
3496811
000
100

simplify76.0ms (0.8%)

Algorithm
egg-herbie
Rules
1163×fma-def_binary64
349×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
92×associate-/l*_binary64
92×unsub-neg_binary64
Counts
99 → 45
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
018720
146720
293720
3198720
4354720
5593720
6819720
7908720
8982720
9996720
101001720
11928720

prune223.0ms (2.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2510251
Fresh01010
Picked011
Done011
Total25112263
Error
4.9b
Counts
263 → 12
Alt Table
StatusErrorProgram
8.2b
(/.f64 (+.f64 (*.f64 x y) (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
8.2b
(fma.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a) (*.f64 (fma.f64 z (neg.f64 t) (*.f64 z t)) (/.f64 1 a)))
25.2b
(*.f64 (fma.f64 (*.f64 x (sqrt.f64 y)) (sqrt.f64 y) (neg.f64 (*.f64 z t))) (/.f64 1 a))
10.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
28.3b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 2) (pow.f64 (*.f64 z t) 2)) (*.f64 a (fma.f64 x y (*.f64 z t))))
8.7b
(pow.f64 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))) -1)
20.5b
(*.f64 (fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 t)) (sqrt.f64 t) (*.f64 x y)) (/.f64 1 a))
32.8b
(*.f64 (*.f64 y x) (/.f64 1 a))
10.1b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
37.0b
(fma.f64 (/.f64 x (sqrt.f64 a)) (/.f64 y (sqrt.f64 a)) (neg.f64 (/.f64 (*.f64 z t) a)))
32.7b
(/.f64 (*.f64 y x) a)
25.2b
(/.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) x) (neg.f64 (*.f64 z t))) a)
Compiler

Compiled 7588 to 2313 computations (69.5% saved)

regimes2.2s (21.7%)

Accuracy

Total 0.5b remaining (11%)

Threshold costs 0.5b (11%)

Counts
139 → 3
Compiler

Compiled 26746 to 17391 computations (35% saved)

bsearch4.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02466
13866
24866
35466
45666
55566

end353.0ms (3.5%)

Remove

(sort z t)

Compiler

Compiled 626 to 311 computations (50.3% saved)

Profiling

Loading profile data...