Details

Time bar (total: 7.0s)

analyze1.5s (22.1%)

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)

sample87.0ms (1.3%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
15.0ms256×body128valid
7.0ms81×body128invalid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify213.0ms (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
8.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.9b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 100 to 69 computations (31% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 z 9) t)
0.5b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series79.0ms (1.1%)

Counts
3 → 132
Calls

3 calls:

38.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
35.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
5.0ms
(*.f64 (*.f64 z 9) t)

rewrite16.0ms (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:

7.0ms
(/.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))

simplify93.0ms (1.3%)

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

prune114.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New10510115
Fresh011
Picked011
Done000
Total10512117
Error
8.4b
Counts
117 → 12
Alt Table
StatusErrorProgram
8.9b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
32.0b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
39.3b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
38.6b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)) 3))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
43.6b
(/.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))))))
35.4b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
35.6b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
8.8b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
Compiler

Compiled 2817 to 1628 computations (42.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 z (*.f64 9 t))
0.5b
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
8.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))

series66.0ms (0.9%)

Counts
3 → 132
Calls

3 calls:

49.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
4.0ms
(*.f64 z (*.f64 9 t))

rewrite21.0ms (0.3%)

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:

10.0ms
(*.f64 z (*.f64 9 t))
5.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
3.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))

simplify90.0ms (1.3%)

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

prune102.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1132115
Fresh3710
Picked011
Done101
Total11710127
Error
8.3b
Counts
127 → 10
Alt Table
StatusErrorProgram
8.9b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
32.0b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
39.3b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
35.2b
(/.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))
35.6b
(/.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
38.6b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)) 3))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
35.4b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
Compiler

Compiled 2718 to 1555 computations (42.8% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.6b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
8.4b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series53.0ms (0.8%)

Counts
2 → 108
Calls

2 calls:

40.0ms
(*.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))

rewrite8.0ms (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))

simplify112.0ms (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

prune82.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New85388
Fresh178
Picked101
Done011
Total871198
Error
8.3b
Counts
98 → 11
Alt Table
StatusErrorProgram
38.6b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)) 3))
32.1b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
39.3b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
35.5b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
35.2b
(/.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))
35.6b
(/.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
9.2b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
35.4b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
Compiler

Compiled 2152 to 1181 computations (45.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1))
0.4b
(/.f64 (sqrt.f64 1/2) a)
0.6b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
8.3b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))

series125.0ms (1.8%)

Counts
3 → 108
Calls

3 calls:

101.0ms
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
21.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1))
3.0ms
(/.f64 (sqrt.f64 1/2) a)

rewrite33.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
58×times-frac_binary64
57×add-sqr-sqrt_binary64
47×*-un-lft-identity_binary64
45×add-cube-cbrt_binary64
44×associate-*r*_binary64
Counts
3 → 140
Calls

3 calls:

11.0ms
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
6.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1))
3.0ms
(/.f64 (sqrt.f64 1/2) a)

simplify188.0ms (2.7%)

Algorithm
egg-herbie
Rules
772×fma-def_binary64
582×times-frac_binary64
408×*-commutative_binary64
289×associate-/l/_binary64
262×distribute-rgt-in_binary64
Counts
248 → 197
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01844969
14064213
215424213
344304213
452154213

prune210.0ms (3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2173220
Fresh189
Picked101
Done011
Total21912231
Error
8.3b
Counts
231 → 12
Alt Table
StatusErrorProgram
35.2b
(/.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))
35.8b
(*.f64 -9 (/.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 t z)) a))
38.6b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)) 3))
32.1b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
39.3b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
35.5b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
35.5b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
35.6b
(/.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2)))
8.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
35.6b
(*.f64 (*.f64 (*.f64 (*.f64 t z) -9) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
32.2b
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 y x)) (/.f64 (sqrt.f64 1/2) a))
Compiler

Compiled 5784 to 3725 computations (35.6% saved)

regimes2.4s (34.5%)

Accuracy

Total 0.5b remaining (6.7%)

Threshold costs 0.5b (6.7%)

Counts
168 → 1
Compiler

Compiled 48515 to 35968 computations (25.9% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
distribute-rgt-neg-in_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01419
12319
24019
34819
45419
55619
65519

end21.0ms (0.3%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 90 to 65 computations (27.8% saved)

sample1.3s (18.1%)

Algorithm
intervals
Results
443.0ms8000×body128valid
181.0ms3195×body128invalid
Compiler

Compiled 306 to 220 computations (28.1% saved)

Profiling

Loading profile data...