Details

Time bar (total: 1.5s)

analyze133.0ms (8.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
37.5%62.4%0.1%6
50%46.8%3.2%7
59.3%35.9%4.8%8
67.1%25.8%7.1%9
72.6%19.1%8.3%10
76.9%13.5%9.7%11
79.8%9.9%10.3%12
82%6.9%11.1%13
83.6%5%11.4%14
Compiler

Compiled 12 to 9 computations (25% saved)

sample1.1s (69.7%)

Results
551.0ms6180×body128valid
213.0ms734×body1024valid
188.0ms800×body512valid
79.0ms533×body256valid
8.0ms89×body128invalid
3.0msbody2048valid
Compiler

Compiled 24 to 18 computations (25% saved)

preprocess53.0ms (3.4%)

Algorithm
egg-herbie
Rules
1016×fma-def_binary64
368×fma-neg_binary64
337×unsub-neg_binary64
317×associate--l+_binary64
241×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
11922
24222
313222
451216
5222116
022
Stop Event
saturated
node limit
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))
(+.f64 y (*.f64 (-.f64 1 y) (-.f64 1 x)))
Outputs
(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))
(fma.f64 (-.f64 1 x) (-.f64 1 y) x)
(fma.f64 y (+.f64 x -1) 1)
(-.f64 (fma.f64 x y 1) y)
(+.f64 y (*.f64 (-.f64 1 y) (-.f64 1 x)))
(+.f64 y (*.f64 (-.f64 1 x) (-.f64 1 y)))
(fma.f64 (-.f64 1 x) (-.f64 1 y) y)
(fma.f64 x y (-.f64 1 x))
(-.f64 (fma.f64 x y 1) x)
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify27.0ms (1.8%)

Algorithm
egg-herbie
Rules
736×fma-def_binary64
523×unsub-neg_binary64
291×distribute-neg-in_binary64
256×sub-neg_binary64
254×fma-neg_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0813
11611
23711
311311
44098
516868
640868
Stop Event
node limit
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))
Outputs
(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))
(fma.f64 (-.f64 1 x) (-.f64 1 y) x)
(fma.f64 y (+.f64 x -1) 1)
(-.f64 (fma.f64 x y 1) y)

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
14.4b
(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))
0.0b
(-.f64 (fma.f64 x y 1) y)
Compiler

Compiled 55 to 37 computations (32.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (fma.f64 x y 1) y)

series3.0ms (0.2%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(-.f64 (fma.f64 x y 1) y)
1.0ms
x
@0
(-.f64 (fma.f64 x y 1) y)
1.0ms
y
@inf
(-.f64 (fma.f64 x y 1) y)
1.0ms
y
@-inf
(-.f64 (fma.f64 x y 1) y)
0.0ms
x
@inf
(-.f64 (fma.f64 x y 1) y)

rewrite42.0ms (2.7%)

Algorithm
batch-egg-rewrite
Rules
672×pow1_binary64
624×add-log-exp_binary64
624×log1p-expm1-u_binary64
624×expm1-log1p-u_binary64
65×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11248
216328
Stop Event
node limit
Counts
1 → 38
Calls
Call 1
Inputs
(-.f64 (fma.f64 x y 1) y)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x y 1) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x y 1) (*.f64 (neg.f64 y) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (fma.f64 x y 1) y) (fma.f64 (neg.f64 y) 1 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (fma.f64 x y 1) y) (fma.f64 (neg.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 y) 2) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (fma.f64 x y 1) y) (fma.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 y) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x y) (-.f64 1 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x y) (+.f64 1 (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 y) (fma.f64 x y 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (fma.f64 x y 1) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (fma.f64 x y 1) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (fma.f64 x y 1) y)) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y 1) y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y 1) y)) 2) (cbrt.f64 (-.f64 (fma.f64 x y 1) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (fma.f64 x y 1) y)) (sqrt.f64 (-.f64 (fma.f64 x y 1) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 x y 1) 3) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y (+.f64 y (fma.f64 x y 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y y)) (/.f64 1 (+.f64 y (fma.f64 x y 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 x y 1)) (sqrt.f64 y)) (-.f64 (sqrt.f64 (fma.f64 x y 1)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y (+.f64 y (fma.f64 x y 1)))) (-.f64 (pow.f64 (fma.f64 x y 1) 3) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 y (fma.f64 x y 1)) (-.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x y 1) 3) (pow.f64 y 3)) (+.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y (+.f64 y (fma.f64 x y 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y y)) (+.f64 y (fma.f64 x y 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x y 1) 3) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y (+.f64 y (fma.f64 x y 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 y y))) (neg.f64 (+.f64 y (fma.f64 x y 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x y 1) 3) (pow.f64 (neg.f64 y) 3)) (+.f64 (pow.f64 (fma.f64 x y 1) 2) (-.f64 (*.f64 (neg.f64 y) (neg.f64 y)) (*.f64 (fma.f64 x y 1) (neg.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x y 1) 2) (*.f64 (neg.f64 y) (neg.f64 y))) (-.f64 (fma.f64 x y 1) (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (fma.f64 x y 1) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (fma.f64 x y 1) y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (fma.f64 x y 1) y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y 1) y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (fma.f64 x y 1) y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (fma.f64 x y 1) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (fma.f64 x y 1) y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (fma.f64 x y 1) y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (fma.f64 x y 1) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (fma.f64 x y 1) y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x y 1) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x y 1)) 2) (cbrt.f64 (fma.f64 x y 1)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x y 1)) (sqrt.f64 (fma.f64 x y 1)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (fma.f64 x y 1) y)))))))

simplify20.0ms (1.3%)

Algorithm
egg-herbie
Rules
162×fma-def_binary64
148×fma-neg_binary64
27×associate--r+_binary64
25×sub-neg_binary64
24×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
014171
133171
271171
3144171
4279171
5475171
6650171
7730171
8741171
Stop Event
saturated
Counts
62 → 46
Calls
Call 1
Inputs
(-.f64 1 y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(*.f64 y x)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(*.f64 y x)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
1
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(*.f64 y (-.f64 x 1))
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(*.f64 -1 (*.f64 (-.f64 1 x) y))
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
Outputs
(-.f64 1 y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(*.f64 y x)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(*.f64 y x)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
1
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(*.f64 y (-.f64 x 1))
(*.f64 y (+.f64 x -1))
(-.f64 (*.f64 y x) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(*.f64 -1 (*.f64 (-.f64 1 x) y))
(*.f64 y (+.f64 x -1))
(-.f64 (*.f64 y x) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)
(-.f64 (+.f64 (*.f64 y x) 1) y)
(-.f64 (fma.f64 y x 1) y)

prune32.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New45146
Fresh101
Picked011
Done000
Total46248
Error
0b
Counts
48 → 2
Alt Table
StatusErrorProgram
25.9b
(*.f64 y (-.f64 x 1))
0.0b
(-.f64 (fma.f64 x y 1) y)
Compiler

Compiled 591 to 354 computations (40.1% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(*.f64 y (-.f64 x 1))

series4.0ms (0.2%)

Counts
1 → 12
Calls

6 calls:

TimeVariablePointExpression
1.0ms
y
@0
(*.f64 y (-.f64 x 1))
1.0ms
y
@-inf
(*.f64 y (-.f64 x 1))
0.0ms
y
@inf
(*.f64 y (-.f64 x 1))
0.0ms
x
@-inf
(*.f64 y (-.f64 x 1))
0.0ms
x
@inf
(*.f64 y (-.f64 x 1))

rewrite33.0ms (2.2%)

Algorithm
batch-egg-rewrite
Rules
599×pow1_binary64
556×add-log-exp_binary64
555×log1p-expm1-u_binary64
555×expm1-log1p-u_binary64
63×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11247
215407
Stop Event
node limit
Counts
1 → 20
Calls
Call 1
Inputs
(*.f64 y (-.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x y) (*.f64 -1 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y x) (*.f64 y -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) -1) y) (fma.f64 x x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 x x -1) y) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 y (+.f64 (pow.f64 x 3) -1)) (fma.f64 x x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 y (fma.f64 x x -1)) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (+.f64 x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (+.f64 x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (+.f64 x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (+.f64 x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 y (+.f64 x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 x -1)) y))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (+.f64 x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 (+.f64 x -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (+.f64 x -1))))))))

simplify14.0ms (0.9%)

Algorithm
egg-herbie
Rules
123×fma-def_binary64
78×fma-neg_binary64
28×cancel-sign-sub-inv_binary64
16×distribute-rgt-neg-in_binary64
16×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0774
11274
21874
32874
44374
57174
615474
729774
844174
947574
1047774
Stop Event
saturated
Counts
32 → 25
Calls
Call 1
Inputs
(*.f64 -1 y)
(-.f64 (*.f64 y x) y)
(-.f64 (*.f64 y x) y)
(-.f64 (*.f64 y x) y)
(*.f64 y x)
(-.f64 (*.f64 y x) y)
(-.f64 (*.f64 y x) y)
(-.f64 (*.f64 y x) y)
(*.f64 y x)
(-.f64 (*.f64 y x) y)
(-.f64 (*.f64 y x) y)
(-.f64 (*.f64 y x) y)
Outputs
(*.f64 -1 y)
(neg.f64 y)
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(*.f64 y x)
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(*.f64 y x)
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))
(-.f64 (*.f64 y x) y)
(*.f64 y (+.f64 x -1))
(*.f64 y (+.f64 -1 x))

prune17.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New25025
Fresh000
Picked011
Done011
Total25227
Error
0b
Counts
27 → 2
Alt Table
StatusErrorProgram
25.9b
(*.f64 y (-.f64 x 1))
0.0b
(-.f64 (fma.f64 x y 1) y)
Compiler

Compiled 211 to 143 computations (32.2% saved)

regimes35.0ms (2.3%)

Accuracy

Total 0.0b remaining (69.3%)

Threshold costs 0.0b (69.3%)

Counts
9 → 1
Compiler

Compiled 77 to 50 computations (35.1% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1108
2148
3168
4178
Stop Event
saturated
Calls
Call 1
Inputs
(-.f64 (fma.f64 x y 1) y)
Outputs
(-.f64 (fma.f64 x y 1) y)

end37.0ms (2.4%)

Stop Event
done
Compiler

Compiled 31 to 20 computations (35.5% saved)

Profiling

Loading profile data...