Details

Time bar (total: 1.9s)

analyze1.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0.1%99.9%0
0.1%0%99.9%1
Compiler

Compiled 33 to 24 computations (27.3% saved)

sample1.5s (79.9%)

Results
1.5s8256×body128valid
Compiler

Compiled 66 to 48 computations (27.3% saved)

preprocess41.0ms (2.2%)

Algorithm
2×egg-herbie
Rules
601×fma-def_binary32
498×fma-neg_binary32
174×cancel-sign-sub-inv_binary32
94×sub-neg_binary32
89×unsub-neg_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01640
14032
210632
322232
454032
5115332
6198732
7232532
8240532
9241632
033
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
1
2
Outputs
0
1
2
Call 2
Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(+.f32 (-.f32 1 uy) (*.f32 uy maxCos))
(+.f32 (-.f32 1 maxCos) (*.f32 maxCos ux))
(+.f32 (-.f32 1 ux) (*.f32 ux uy))
Outputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 ux))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (-.f32 1 uy) (*.f32 uy maxCos))
(-.f32 1 (-.f32 uy (*.f32 maxCos uy)))
(fma.f32 maxCos uy (-.f32 1 uy))
(-.f32 (fma.f32 maxCos uy 1) uy)
(+.f32 (-.f32 1 maxCos) (*.f32 maxCos ux))
(+.f32 (-.f32 1 maxCos) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 maxCos))
(-.f32 (fma.f32 ux maxCos 1) maxCos)
(+.f32 (-.f32 1 ux) (*.f32 ux uy))
(fma.f32 ux uy (-.f32 1 ux))
(-.f32 (fma.f32 ux uy 1) ux)
Compiler

Compiled 10 to 7 computations (30% saved)

simplify14.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
199×fma-def_binary32
155×fma-neg_binary32
47×cancel-sign-sub-inv_binary32
34×sub-neg_binary32
26×unsub-neg_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0710
1158
2358
3728
41678
53618
66188
77658
87978
98028
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
Outputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 ux))
(-.f32 (fma.f32 ux maxCos 1) ux)

prune3.0ms (0.1%)

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
0.1b
(-.f32 (fma.f32 ux maxCos 1) ux)
▶0.0b
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
Compiler

Compiled 54 to 36 computations (33.3% saved)

localize16.0ms (0.9%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(*.f32 ux maxCos)
✓0.0b
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

series5.0ms (0.3%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
ux
@inf
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
1.0ms
ux
@-inf
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
0.0ms
ux
@0
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
0.0ms
ux
@0
(*.f32 ux maxCos)
0.0ms
maxCos
@inf
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

rewrite42.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
836×log1p-expm1-u_binary32
836×expm1-log1p-u_binary32
81×add-sqr-sqrt_binary32
79×*-un-lft-identity_binary32
79×pow1_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0714
115412
2220812
Stop Event
1×node limit
Counts
2 → 54
Calls
Call 1
Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(*.f32 ux maxCos)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 1 (-.f32 ux (*.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) (-.f32 1 (+.f32 ux (*.f32 ux maxCos)))) (/.f32 (pow.f32 (*.f32 ux maxCos) 2) (-.f32 1 (+.f32 ux (*.f32 ux maxCos)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 ux maxCos) 1) ux)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 ux maxCos (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2) (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3)) (/.f32 1 (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2)) (/.f32 1 (-.f32 1 (+.f32 ux (*.f32 ux maxCos)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux)))) (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 1 (+.f32 ux (*.f32 ux maxCos))) (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3)) (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3)) (+.f32 (pow.f32 (*.f32 ux maxCos) 2) (-.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 (-.f32 1 ux) ux) maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2)) (-.f32 1 (+.f32 ux (*.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (*.f32 ux maxCos) 3))) (neg.f32 (+.f32 (pow.f32 (-.f32 1 ux) 2) (*.f32 (*.f32 ux maxCos) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 1 ux) 2) (pow.f32 (*.f32 ux maxCos) 2))) (neg.f32 (-.f32 1 (+.f32 ux (*.f32 ux maxCos)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (-.f32 ux (*.f32 ux maxCos)) 3)) (+.f32 1 (+.f32 (*.f32 (-.f32 ux (*.f32 ux maxCos)) (-.f32 ux (*.f32 ux maxCos))) (-.f32 ux (*.f32 ux maxCos)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (*.f32 (-.f32 ux (*.f32 ux maxCos)) (-.f32 ux (*.f32 ux maxCos)))) (+.f32 1 (-.f32 ux (*.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (*.f32 ux maxCos) 2) (pow.f32 (-.f32 1 ux) 2)) (-.f32 (*.f32 ux maxCos) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 ux maxCos (-.f32 1 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (-.f32 1 ux) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (*.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 ux maxCos (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 maxCos ux (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (*.f32 ux maxCos)) 2) (cbrt.f32 (*.f32 ux maxCos)) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (*.f32 ux maxCos)) (sqrt.f32 (*.f32 ux maxCos)) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (-.f32 1 ux)) (sqrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 ux maxCos (-.f32 1 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 ux maxCos))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 ux maxCos) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 ux maxCos)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 ux maxCos)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 ux maxCos) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 ux maxCos) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 ux maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 ux maxCos) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 ux maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 ux maxCos)) 1))))))

simplify23.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
185×fma-def_binary32
158×fma-neg_binary32
31×sub-neg_binary32
25×unsub-neg_binary32
22×cancel-sign-sub-inv_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
017303
145267
2107267
3227267
4461267
5662267
6762267
7780267
Stop Event
1×saturated
Counts
102 → 64
Calls
Call 1
Inputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(+.f32 1 (*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
Outputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 -1 (*.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)
(*.f32 maxCos ux)

prune37.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New63164
Fresh101
Picked011
Done000
Total64266
Error
0b
Counts
66 → 2
Alt Table
StatusErrorProgram
✓0.0b
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
▶0.0b
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
Compiler

Compiled 825 to 478 computations (42.1% saved)

localize16.0ms (0.9%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
✓0.1b
(*.f32 (-.f32 maxCos 1) ux)

series5.0ms (0.3%)

Counts
2 → 27
Calls

12 calls:

TimeVariablePointExpression
1.0ms
ux
@-inf
(*.f32 (-.f32 maxCos 1) ux)
0.0ms
maxCos
@inf
(*.f32 (-.f32 maxCos 1) ux)
0.0ms
ux
@inf
(*.f32 (-.f32 maxCos 1) ux)
0.0ms
maxCos
@0
(*.f32 (-.f32 maxCos 1) ux)
0.0ms
ux
@0
(*.f32 (-.f32 maxCos 1) ux)

rewrite39.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
799×pow1_binary32
742×log1p-expm1-u_binary32
742×expm1-log1p-u_binary32
79×add-sqr-sqrt_binary32
76×*-un-lft-identity_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0717
115215
2204215
Stop Event
1×node limit
Counts
2 → 53
Calls
Call 1
Inputs
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 maxCos ux) (*.f32 -1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (*.f32 ux -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 maxCos 3) -1) ux) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (fma.f32 maxCos maxCos -1) ux) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (+.f32 (pow.f32 maxCos 3) -1)) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (fma.f32 maxCos maxCos -1)) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) (+.f32 maxCos -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (+.f32 maxCos -1) ux)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 (+.f32 maxCos -1) ux 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 1 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))) (/.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 (+.f32 maxCos -1) ux 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2) (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (/.f32 1 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (/.f32 1 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))) (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)) (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))) (neg.f32 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))) (neg.f32 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) 1) (-.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 (+.f32 maxCos -1) ux 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (+.f32 maxCos -1) ux 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 ux (+.f32 maxCos -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 2) (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 1))))))

simplify25.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
186×fma-def_binary32
186×fma-neg_binary32
59×cancel-sign-sub-inv_binary32
32×sub-neg_binary32
31×associate--r+_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
013201
131173
246173
364173
496173
5155173
6311173
7522173
8733173
9822173
10846173
11847173
Stop Event
1×saturated
Counts
80 → 65
Calls
Call 1
Inputs
(*.f32 -1 ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
1
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
Outputs
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) (*.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (*.f32 -1 ux) (+.f32 1 (*.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
1
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)

prune37.0ms (1.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New65065
Fresh000
Picked011
Done011
Total65267
Error
0b
Counts
67 → 2
Alt Table
StatusErrorProgram
✓0.0b
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
✓0.0b
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
Compiler

Compiled 765 to 571 computations (25.4% saved)

regimes41.0ms (2.2%)

Accuracy

Total 0.0b remaining (29.7%)

Threshold costs 0.0b (29.7%)

Counts
15 → 1
Compiler

Compiled 113 to 74 computations (34.5% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary32
1×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
Stop Event
1×saturated
Calls
Call 1
Inputs
(fma.f32 ux (+.f32 maxCos -1) 1)
Outputs
(fma.f32 ux (+.f32 maxCos -1) 1)

end35.0ms (1.8%)

Stop Event
1×done
Compiler

Compiled 38 to 29 computations (23.7% saved)

Profiling

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