Details

Time bar (total: 6.1s)

analyze1.6s (25.7%)

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)

sample103.0ms (1.7%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
19.0ms256×body128valid
6.0ms115×body128invalid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify206.0ms (3.4%)

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
9.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
10.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
10.0b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 100 to 69 computations (31% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 z 9) t)
0.3b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
9.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series64.0ms (1.1%)

Counts
3 → 132
Calls

3 calls:

45.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
7.0ms
(*.f64 (*.f64 z 9) t)

rewrite16.0ms (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:

6.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
5.0ms
(*.f64 (*.f64 z 9) t)
3.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

simplify98.0ms (1.6%)

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

prune138.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1078115
Fresh011
Picked101
Done000
Total1089117
Error
9.6b
Counts
117 → 9
Alt Table
StatusErrorProgram
36.3b
(*.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))
34.1b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
34.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
10.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
32.0b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (+.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))
10.6b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
34.9b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
33.7b
(*.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))))
10.0b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
Compiler

Compiled 2649 to 1515 computations (42.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 z (*.f64 9 t))
0.3b
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
9.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))

series71.0ms (1.2%)

Counts
3 → 132
Calls

3 calls:

53.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
13.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
5.0ms
(*.f64 z (*.f64 9 t))

rewrite16.0ms (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:

7.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
4.0ms
(*.f64 z (*.f64 9 t))
3.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))

simplify97.0ms (1.6%)

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

prune106.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1141115
Fresh178
Picked101
Done000
Total1168124
Error
9.6b
Counts
124 → 8
Alt Table
StatusErrorProgram
36.3b
(*.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))
34.1b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
34.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
10.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
10.6b
(/.f64 1 (/.f64 (*.f64 a 2) (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))))
32.0b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (+.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))
34.9b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
33.7b
(*.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))))
Compiler

Compiled 2626 to 1492 computations (43.2% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.4b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
9.5b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series56.0ms (0.9%)

Counts
2 → 108
Calls

2 calls:

43.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
12.0ms
(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))

simplify113.0ms (1.9%)

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

prune87.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New82688
Fresh167
Picked101
Done000
Total841296
Error
9.6b
Counts
96 → 12
Alt Table
StatusErrorProgram
11.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
36.2b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 a)) (/.f64 1/2 (sqrt.f64 a)))
34.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
10.6b
(/.f64 1 (/.f64 (*.f64 a 2) (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))))
34.1b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
32.0b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (+.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))
34.9b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
10.0b
(/.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2) a)
36.3b
(*.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))
33.7b
(*.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))))
34.9b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
10.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
Compiler

Compiled 2198 to 1214 computations (44.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)
0.4b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
9.2b
(/.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2) a)

series62.0ms (1%)

Counts
2 → 108
Calls

2 calls:

43.0ms
(/.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2) a)
19.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2)

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 43
Calls

2 calls:

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

simplify97.0ms (1.6%)

Algorithm
egg-herbie
Rules
672×fma-def_binary64
610×div-sub_binary64
429×associate-/l*_binary64
331×times-frac_binary64
277×associate-*l*_binary64
Counts
151 → 83
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01012629
12282297
27412297
332972296
457372296

prune95.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1051106
Fresh11011
Picked011
Done000
Total10612118
Error
9.6b
Counts
118 → 12
Alt Table
StatusErrorProgram
11.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
36.2b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 a)) (/.f64 1/2 (sqrt.f64 a)))
34.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
10.6b
(/.f64 1 (/.f64 (*.f64 a 2) (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))))
34.1b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
32.0b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (+.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))
10.0b
(/.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) 1/2) a)
36.3b
(*.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))
34.9b
(/.f64 (*.f64 -9/2 (*.f64 t z)) a)
33.7b
(*.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))))
34.9b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
10.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
Compiler

Compiled 2138 to 1091 computations (49% saved)

regimes1.7s (28.2%)

Accuracy

Total 0.4b remaining (5.3%)

Threshold costs 0.4b (5.3%)

Counts
112 → 1
Compiler

Compiled 32356 to 22943 computations (29.1% 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
01419
12419
23219
34219
44919
55419
65619
75519

end21.0ms (0.4%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 90 to 65 computations (27.8% saved)

sample1.3s (21.2%)

Algorithm
intervals
Results
465.0ms8000×body128valid
187.0ms3137×body128invalid
Compiler

Compiled 302 to 213 computations (29.5% saved)

Profiling

Loading profile data...