Details

Time bar (total: 6.6s)

analyze1.6s (23.8%)

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
9.4%90.4%0.2%11
9.4%90.4%0.2%12
10.1%89.6%0.2%13
20.8%78.9%0.2%14
Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.6s (24.8%)

Symmetry

(sort x y)

(sort z t)

Results
1.1s8256×body128valid
462.0ms3280×body128invalid
Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify207.0ms (3.1%)

Algorithm
egg-herbie
Rules
2966×fma-def_binary64
757×fma-neg_binary64
541×cancel-sign-sub-inv_binary64
473×associate-/l/_binary64
472×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
13117
210317
331817
479417
5152617
6205417
7228117
8297517
9354017
10395417
11415817
12409717
13410817
14411817
15446217
16453117
17453617
18453617
19647417

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
9.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
9.3b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
9.3b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 100 to 69 computations (31% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
0.2b
(*.f64 (*.f64 z 9) t)
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series55.0ms (0.8%)

Counts
3 → 132
Calls

3 calls:

38.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
5.0ms
(*.f64 (*.f64 z 9) t)

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

6.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
4.0ms
(*.f64 (*.f64 z 9) t)
3.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

simplify94.0ms (1.4%)

Algorithm
egg-herbie
Rules
470×fma-def_binary64
445×*-commutative_binary64
325×div-sub_binary64
307×associate-/l*_binary64
287×fma-neg_binary64
Counts
194 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01482790
13962561
215062551
341282551
452472551

prune117.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10510115
Fresh011
Picked101
Done000
Total10611117
Error
8.6b
Counts
117 → 11
Alt Table
StatusErrorProgram
10.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 a 2))
32.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
35.2b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
9.4b
(/.f64 1 (/.f64 (*.f64 a 2) (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))
9.3b
(/.f64 (fma.f64 x y (*.f64 (*.f64 t z) -9)) (*.f64 a 2))
9.3b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
36.9b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)) 3))
30.8b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
9.3b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
32.7b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
40.4b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 (*.f64 z 9) t) 3)) (*.f64 (*.f64 a 2) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (+.f64 (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t)) (*.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))))
Compiler

Compiled 2783 to 1603 computations (42.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
0.2b
(*.f64 z (*.f64 9 t))
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))

series55.0ms (0.8%)

Counts
3 → 132
Calls

3 calls:

38.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
5.0ms
(*.f64 z (*.f64 9 t))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

5.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
5.0ms
(*.f64 z (*.f64 9 t))
3.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))

simplify91.0ms (1.4%)

Algorithm
egg-herbie
Rules
423×fma-def_binary64
421×*-commutative_binary64
320×div-sub_binary64
286×associate-/l*_binary64
251×fma-neg_binary64
Counts
194 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01462786
13882556
213912549
338852549
449522549

prune112.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1114115
Fresh3710
Picked101
Done000
Total11511126
Error
8.6b
Counts
126 → 11
Alt Table
StatusErrorProgram
35.2b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
35.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
10.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 a 2))
32.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
9.3b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
32.4b
(/.f64 (*.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 a 2))
9.3b
(/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))
9.3b
(/.f64 1 (/.f64 (*.f64 a 2) (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))))
32.7b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
30.8b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
40.4b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 (*.f64 z 9) t) 3)) (*.f64 (*.f64 a 2) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (+.f64 (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t)) (*.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))))
Compiler

Compiled 2844 to 1626 computations (42.8% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t))))
0.2b
(*.f64 z (*.f64 9 t))
8.7b
(/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))

series172.0ms (2.6%)

Counts
2 → 108
Calls

2 calls:

160.0ms
(/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))
12.0ms
(fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t))))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 33
Calls

2 calls:

3.0ms
(/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))
0.0ms
(fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t))))

simplify75.0ms (1.1%)

Algorithm
egg-herbie
Rules
635×distribute-rgt-in_binary64
453×fma-def_binary64
289×div-sub_binary64
249×associate-/l*_binary64
204×times-frac_binary64
Counts
141 → 68
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0892397
12062009
26042009
323132009
452622009

prune129.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New97198
Fresh1910
Picked011
Done000
Total9811109
Error
8.6b
Counts
109 → 11
Alt Table
StatusErrorProgram
35.2b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
35.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
10.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 a 2))
32.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
9.3b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
32.4b
(/.f64 (*.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 a 2))
9.3b
(/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))
9.3b
(/.f64 1 (/.f64 (*.f64 a 2) (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))))
32.7b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
10.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))))
30.8b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
Compiler

Compiled 2384 to 1477 computations (38% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
8.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series55.0ms (0.8%)

Counts
2 → 108
Calls

2 calls:

42.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
13.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

5.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
0.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

simplify106.0ms (1.6%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
487×associate-*l*_binary64
418×associate-*r*_binary64
225×associate-*r/_binary64
211×associate-*l/_binary64
Counts
152 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082547
12482243
28122243
332062242
449372242
550192242

prune98.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New79988
Fresh639
Picked101
Done011
Total861399
Error
8.6b
Counts
99 → 13
Alt Table
StatusErrorProgram
10.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) (*.f64 a 2))
32.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
35.7b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 a)) (/.f64 1/2 (sqrt.f64 a)))
35.2b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
9.3b
(/.f64 (fma.f64 x y (neg.f64 (*.f64 z (*.f64 9 t)))) (*.f64 a 2))
10.1b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
35.7b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
9.3b
(/.f64 1 (/.f64 (*.f64 a 2) (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))))
10.1b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (/.f64 (cbrt.f64 1/2) a))
9.3b
(/.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2) a)
32.8b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
32.4b
(*.f64 (*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)))) (/.f64 1/2 a))
9.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
Compiler

Compiled 1948 to 1040 computations (46.6% saved)

regimes1.6s (24.2%)

Accuracy

Total 0.5b remaining (5.9%)

Threshold costs 0.5b (5.9%)

Counts
116 → 1
Compiler

Compiled 33879 to 23370 computations (31% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
distribute-lft-neg-in_binary64
distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
12419
23419
34719
45419
55819
65919
75719

end335.0ms (5.1%)

Remove

(sort x y)

Compiler

Compiled 418 to 296 computations (29.2% saved)

Profiling

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