Details

Time bar (total: 12.2s)

analyze2.1s (17.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
24.9%74.7%0.3%8
24.9%74.7%0.3%9
24.9%74.7%0.3%10
37.4%62.3%0.3%11
37.4%62.3%0.3%12
37.4%62.3%0.3%13
37.4%62.3%0.3%14
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample2.0s (16.2%)

Symmetry

(sort x y)

(sort t a)

Results
1.8s8256×body128valid
Compiler

Compiled 80 to 56 computations (30% saved)

simplify90.0ms (0.7%)

Algorithm
egg-herbie
Rules
828×fma-def_binary64
568×div-sub_binary64
502×associate-/r/_binary64
476×distribute-neg-frac_binary64
465×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01928
14228
211624
335224
488023
5204121
6415421
7436521
8494121

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
3.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
14.1b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
8.1b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
Compiler

Compiled 137 to 92 computations (32.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x (*.f64 9 y) b)
0.5b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
3.4b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
5.2b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)

series224.0ms (1.8%)

Counts
4 → 240
Calls

4 calls:

109.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
87.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
20.0ms
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
7.0ms
(fma.f64 x (*.f64 9 y) b)

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
18×times-frac_binary64
add-cbrt-cube_binary64
Counts
4 → 78
Calls

4 calls:

6.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c)
2.0ms
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
0.0ms
(fma.f64 x (*.f64 9 y) b)
0.0ms
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))

simplify190.0ms (1.6%)

Algorithm
egg-herbie
Rules
913×div-sub_binary64
630×fma-def_binary64
477×fma-neg_binary64
332×associate-/l/_binary64
274×distribute-rgt-in_binary64
Counts
318 → 171
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01516685
12966160
27255908
319955341
442785341
564635341

prune316.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1638171
Fresh011
Picked101
Done000
Total1649173
Error
3.3b
Counts
173 → 9
Alt Table
StatusErrorProgram
21.5b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
14.1b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
35.8b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
26.4b
(/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 z c))
40.5b
(/.f64 b (*.f64 c z))
36.2b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
26.9b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
8.6b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
8.1b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
Compiler

Compiled 4292 to 2306 computations (46.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x (*.f64 9 y) b)
0.5b
(fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z))
3.4b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
5.2b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

series160.0ms (1.3%)

Counts
1 → 84
Calls

1 calls:

160.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

rewrite11.0ms (0.1%)

Algorithm
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 → 38
Calls

1 calls:

6.0ms
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))

simplify102.0ms (0.8%)

Algorithm
egg-herbie
Rules
893×fma-def_binary64
740×distribute-rgt-in_binary64
236×associate-*l*_binary64
202×associate-*r*_binary64
162×fma-neg_binary64
Counts
122 → 78
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01003557
12313078
25992942
319012744
451822744

prune513.0ms (4.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1801181
Fresh088
Picked011
Done000
Total18010190
Error
3.3b
Counts
190 → 10
Alt Table
StatusErrorProgram
21.5b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
35.8b
(*.f64 (*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 (/.f64 1 c))) (sqrt.f64 (/.f64 1 c)))
14.1b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
35.8b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
26.4b
(/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 z c))
40.5b
(/.f64 b (*.f64 c z))
36.2b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
26.9b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
8.6b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
8.1b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
Compiler

Compiled 4705 to 2705 computations (42.5% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 c)
0.8b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
3.4b
(/.f64 (fma.f64 x (*.f64 9 y) b) z)
4.5b
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c)))

series1.3s (10.4%)

Counts
3 → 180
Calls

3 calls:

980.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c)))
232.0ms
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
49.0ms
(cbrt.f64 c)

rewrite24.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
66×times-frac_binary64
36×*-un-lft-identity_binary64
36×add-sqr-sqrt_binary64
36×add-cube-cbrt_binary64
27×cbrt-prod_binary64
Counts
3 → 110
Calls

3 calls:

7.0ms
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
4.0ms
(/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c)))
2.0ms
(cbrt.f64 c)

simplify269.0ms (2.2%)

Algorithm
egg-herbie
Rules
643×associate-/l*_binary64
499×associate-/l/_binary64
447×fma-def_binary64
413×associate-/r/_binary64
356×associate-*l/_binary64
Counts
290 → 218
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
020811145
14658796
214588495
345278495
449928495
549698495

prune453.0ms (3.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New3082310
Fresh178
Picked011
Done011
Total30911320
Error
3.3b
Counts
320 → 11
Alt Table
StatusErrorProgram
35.8b
(*.f64 (*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 (/.f64 1 c))) (sqrt.f64 (/.f64 1 c)))
14.1b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
35.8b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
26.4b
(/.f64 (fma.f64 9 (*.f64 y x) b) (*.f64 z c))
40.5b
(/.f64 b (*.f64 c z))
11.9b
(fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c))
36.2b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
40.9b
(/.f64 (*.f64 -4 (*.f64 (pow.f64 (/.f64 1 (pow.f64 c 2)) 1/3) (*.f64 a t))) (cbrt.f64 c))
26.9b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
8.6b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
8.1b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
Compiler

Compiled 10420 to 5007 computations (51.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(fma.f64 (*.f64 a t) -4 (/.f64 b z))
2.1b
(fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c))
4.8b
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
9.0b
(/.f64 (*.f64 y x) (*.f64 c z))

series188.0ms (1.5%)

Counts
4 → 192
Calls

4 calls:

99.0ms
(fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c))
42.0ms
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
30.0ms
(/.f64 (*.f64 y x) (*.f64 c z))
16.0ms
(fma.f64 (*.f64 a t) -4 (/.f64 b z))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube_binary64
18×add-exp-log_binary64
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
Counts
4 → 72
Calls

4 calls:

4.0ms
(/.f64 (*.f64 y x) (*.f64 c z))
3.0ms
(/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c)
0.0ms
(fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c))
0.0ms
(fma.f64 (*.f64 a t) -4 (/.f64 b z))

simplify278.0ms (2.3%)

Algorithm
egg-herbie
Rules
623×associate-/r*_binary64
523×fma-def_binary64
493×associate-*l*_binary64
460×associate-*l/_binary64
371×associate-*r/_binary64
Counts
264 → 107
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01535571
13514619
212474619
344964619
449994619

prune241.0ms (2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1034107
Fresh268
Picked101
Done022
Total10612118
Error
1.0b
Counts
118 → 12
Alt Table
StatusErrorProgram
35.8b
(*.f64 (*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 (/.f64 1 c))) (sqrt.f64 (/.f64 1 c)))
14.1b
(/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))
10.8b
(fma.f64 9 (/.f64 (/.f64 (*.f64 y x) c) z) (/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c))
35.8b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (sqrt.f64 c)) (sqrt.f64 c))
12.4b
(fma.f64 9 (/.f64 y (/.f64 (*.f64 c z) x)) (/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c))
8.1b
(*.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (/.f64 1 c))
11.7b
(fma.f64 9 (*.f64 (/.f64 y c) (/.f64 x z)) (/.f64 (fma.f64 (*.f64 a t) -4 (/.f64 b z)) c))
36.2b
(*.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) (/.f64 (sqrt.f64 (fma.f64 a (*.f64 t -4) (/.f64 (fma.f64 9 (*.f64 y x) b) z))) c))
40.9b
(/.f64 (*.f64 -4 (*.f64 (pow.f64 (/.f64 1 (pow.f64 c 2)) 1/3) (*.f64 a t))) (cbrt.f64 c))
26.9b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) z) (/.f64 b z)) c)
26.9b
(/.f64 (fma.f64 9 (/.f64 (*.f64 y x) c) (/.f64 b c)) z)
8.6b
(/.f64 (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))
Compiler

Compiled 2982 to 1085 computations (63.6% saved)

regimes3.2s (26.5%)

Accuracy

Total 4.3b remaining (72.1%)

Threshold costs 0b (0%)

Counts
155 → 5
Compiler

Compiled 42038 to 28942 computations (31.2% saved)

bsearch6.0ms (0%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify12.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
049265
173265
293265
3112265
4121265
5124265
6123265

end419.0ms (3.4%)

Remove

(sort t a)

Compiler

Compiled 1800 to 1084 computations (39.8% saved)

Profiling

Loading profile data...