Details

Time bar (total: 23.8s)

analyze2.0s (8.2%)

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
25%74.9%0.1%6
25%74.9%0.1%7
37.4%62.4%0.1%8
37.4%62.4%0.1%9
37.4%62.4%0.1%10
43.7%56.2%0.1%11
43.7%56.2%0.1%12
43.7%56.2%0.1%13
61.7%38.2%0.1%14
Compiler

Compiled 41 to 30 computations (26.8% saved)

sample37.0ms (0.2%)

Algorithm
intervals
Results
28.0ms256×body128valid
Compiler

Compiled 84 to 62 computations (26.2% saved)

simplify52.0ms (0.2%)

Algorithm
egg-herbie
Rules
753×associate-+l+_binary64
706×distribute-rgt-in_binary64
700×distribute-lft-in_binary64
667×associate-+r+_binary64
226×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03041
16441
215441
335741
4115741
5487641
6497641
7499241

prune6.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
27.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
27.5b
(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
27.5b
(/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))
Compiler

Compiled 216 to 150 computations (30.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)
0.1b
(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
0.3b
(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
26.5b
(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

series438.0ms (1.8%)

Counts
4 → 84
Calls

4 calls:

422.0ms
(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
12.0ms
(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
2.0ms
(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)
2.0ms
(fma.f64 x 104109730557/25000000000 393497462077/5000000000)

rewrite9.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
4 → 55
Calls

4 calls:

5.0ms
(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
0.0ms
(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
0.0ms
(fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000)
0.0ms
(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)

simplify300.0ms (1.3%)

Algorithm
egg-herbie
Rules
899×fma-def_binary64
565×distribute-rgt-in_binary64
296×times-frac_binary64
211×fma-neg_binary64
146×cancel-sign-sub-inv_binary64
Counts
139 → 125
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02368000
16137637
220097248
349907248
450327248

prune354.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1169125
Fresh101
Picked101
Done000
Total1189127
Error
0.2b
Counts
127 → 9
Alt Table
StatusErrorProgram
27.6b
(*.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
24.7b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))))
34.3b
(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (*.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 x x))))
24.0b
(*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
24.2b
(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
27.5b
(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 3)) 4297481763/31250000) y) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
38.2b
(/.f64 (*.f64 (-.f64 x 2) (fma.f64 x (*.f64 (*.f64 x x) (fma.f64 x 104109730557/25000000000 393497462077/5000000000)) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
26.7b
(-.f64 (fma.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x))))))) (fma.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x))))))) (fma.f64 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x))))))) x (/.f64 (*.f64 x (*.f64 x y)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x)))))))))) (fma.f64 2 (fma.f64 (/.f64 y (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x))))))) x (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x)))))))) (fma.f64 4297481763/15625000 (/.f64 (*.f64 x x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x))))))) (*.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (fma.f64 x 156699607947/500000000 (*.f64 (*.f64 x x) (+.f64 263505074721/1000000000 (*.f64 216700011257/5000000000 x)))))))))))
27.2b
(-.f64 (+.f64 (*.f64 1759267849271/25000000000 (/.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x))))))) (+.f64 (/.f64 (*.f64 y (pow.f64 x 2)) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x)))))) (+.f64 (*.f64 104109730557/25000000000 (/.f64 (pow.f64 x 5) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x))))))) (/.f64 (*.f64 z x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x))))))))) (+.f64 (*.f64 2 (/.f64 (*.f64 y x) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x))))))) (+.f64 (*.f64 2 (/.f64 z (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x))))))) (+.f64 (*.f64 4297481763/15625000 (/.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x))))))) (*.f64 49698921037/2500000000 (/.f64 (pow.f64 x 3) (+.f64 (pow.f64 x 4) (+.f64 23533438303/500000000 (+.f64 (*.f64 263505074721/1000000000 (pow.f64 x 2)) (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 3)) (*.f64 156699607947/500000000 x)))))))))))
Compiler

Compiled 6341 to 4334 computations (31.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
0.3b
(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
0.3b
(*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
23.2b
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

series1.5s (6.4%)

Counts
2 → 72
Calls

2 calls:

907.0ms
(*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
607.0ms
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

rewrite34.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
19×times-frac_binary64
18×add-cube-cbrt_binary64
13×associate-*r*_binary64
Counts
2 → 69
Calls

2 calls:

14.0ms
(*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
4.0ms
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

simplify348.0ms (1.5%)

Algorithm
egg-herbie
Rules
591×distribute-rgt-in_binary64
307×cancel-sign-sub-inv_binary64
233×fma-def_binary64
175×sub-neg_binary64
164×fma-neg_binary64
Counts
141 → 136
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029312965
180412552
2279312512
3500812512

prune275.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1724176
Fresh448
Picked101
Done000
Total1778185
Error
0.2b
Counts
185 → 8
Alt Table
StatusErrorProgram
24.0b
(/.f64 (*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4)) (+.f64 x 2))
27.6b
(*.f64 (*.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))
24.7b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x 2) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))))
34.3b
(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (*.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 x x))))
24.2b
(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
24.1b
(*.f64 (-.f64 x 2) (/.f64 1 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))))
24.6b
(*.f64 (*.f64 (-.f64 x 2) (*.f64 (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))) (cbrt.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
25.0b
(*.f64 (*.f64 (cbrt.f64 (-.f64 x 2)) (cbrt.f64 (-.f64 x 2))) (*.f64 (cbrt.f64 (-.f64 x 2)) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
Compiler

Compiled 8470 to 5695 computations (32.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4))
0.3b
(fma.f64 x 104109730557/25000000000 393497462077/5000000000)
13.4b
(/.f64 (*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4)) (+.f64 x 2))
23.2b
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

series1.6s (6.6%)

Counts
2 → 72
Calls

2 calls:

790.0ms
(*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4))
771.0ms
(/.f64 (*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4)) (+.f64 x 2))

rewrite38.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
14×times-frac_binary64
Counts
2 → 66
Calls

2 calls:

13.0ms
(/.f64 (*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4)) (+.f64 x 2))
10.0ms
(*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4))

simplify819.0ms (3.4%)

Algorithm
egg-herbie
Rules
345×fma-neg_binary64
318×cancel-sign-sub-inv_binary64
248×fma-def_binary64
223×sub-neg_binary64
201×associate-/l*_binary64
Counts
138 → 154
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033117610
197416854
2354416854
3483216854
4494016854

prune653.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2204224
Fresh527
Picked011
Done000
Total2257232
Error
0.2b
Counts
232 → 7
Alt Table
StatusErrorProgram
24.0b
(/.f64 (*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4)) (+.f64 x 2))
34.3b
(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (*.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 x x))))
24.2b
(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
24.0b
(*.f64 (*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4)) (+.f64 (*.f64 x x) (-.f64 (*.f64 2 2) (*.f64 x 2))))
24.1b
(/.f64 (*.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (*.f64 (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4))) (+.f64 x 2))
48.2b
(/.f64 (-.f64 (+.f64 (fma.f64 (*.f64 x x) 104109730557/25000000000 2146807885506674472887084159837293/625000000000000000000000000000) (/.f64 y x)) (fma.f64 x 12723143231740136880149/125000000000000000000 (/.f64 386460204902400897220924677061312055388407301/3125000000000000000000000000000000000000 x))) (+.f64 x 2))
41.6b
(/.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (*.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x x -4))) (+.f64 x 2))
Compiler

Compiled 12049 to 8050 computations (33.2% saved)

localize63.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8))
13.4b
(*.f64 (*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4)) (+.f64 (*.f64 x x) (-.f64 (*.f64 2 2) (*.f64 x 2))))
19.5b
(*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4))
23.2b
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

series3.4s (14.1%)

Counts
3 → 108
Calls

3 calls:

1.5s
(*.f64 (*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4)) (+.f64 (*.f64 x x) (-.f64 (*.f64 2 2) (*.f64 x 2))))
1.0s
(*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4))
807.0ms
(/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8))

rewrite84.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
188×times-frac_binary64
150×*-un-lft-identity_binary64
105×add-sqr-sqrt_binary64
96×add-cube-cbrt_binary64
59×associate-*l*_binary64
Counts
3 → 203
Calls

3 calls:

19.0ms
(*.f64 (*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4)) (+.f64 (*.f64 x x) (-.f64 (*.f64 2 2) (*.f64 x 2))))
14.0ms
(*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4))
8.0ms
(/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8))

simplify812.0ms (3.4%)

Algorithm
egg-herbie
Rules
455×fma-def_binary64
283×distribute-rgt-in_binary64
272×associate-/l*_binary64
269×distribute-lft-in_binary64
238×associate-/r*_binary64
Counts
311 → 354
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
060140048
1186638480
2498938480

prune1.7s (7.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4091410
Fresh055
Picked011
Done011
Total4098417
Error
0.1b
Counts
417 → 8
Alt Table
StatusErrorProgram
24.1b
(/.f64 (*.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (*.f64 (/.f64 1 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4))) (+.f64 x 2))
50.8b
(*.f64 (-.f64 (*.f64 104109730557/25000000000 (/.f64 1 x)) (*.f64 12723143231740136880149/125000000000000000000 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 2 2) (*.f64 x 2))))
24.0b
(/.f64 (*.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (fma.f64 x x -4)) (+.f64 x 2))
34.3b
(-.f64 (+.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 y (*.f64 x x))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 x x))))
24.2b
(*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))
24.0b
(*.f64 (*.f64 (/.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)) (+.f64 (pow.f64 x 3) 8)) (fma.f64 x x -4)) (+.f64 (*.f64 x x) (-.f64 (*.f64 2 2) (*.f64 x 2))))
48.2b
(/.f64 (-.f64 (+.f64 (fma.f64 (*.f64 x x) 104109730557/25000000000 2146807885506674472887084159837293/625000000000000000000000000000) (/.f64 y x)) (fma.f64 x 12723143231740136880149/125000000000000000000 (/.f64 386460204902400897220924677061312055388407301/3125000000000000000000000000000000000000 x))) (+.f64 x 2))
41.6b
(/.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (*.f64 (sqrt.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (fma.f64 x x -4))) (+.f64 x 2))
Compiler

Compiled 32014 to 21970 computations (31.4% saved)

regimes7.8s (32.6%)

Accuracy

Total 0.6b remaining (72.4%)

Threshold costs 0.6b (72.4%)

Counts
303 → 3
Compiler

Compiled 49636 to 34908 computations (29.7% saved)

bsearch126.0ms (0.5%)

Steps
ItersRangePoint
9
4.784160272867505e+54
8.548425137380954e+63
5.857838753793935e+60
9
-4.414525483178021e+47
-3.279239897567955e+41
-3.272620141963037e+47
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
04491
15391
26391
37191
47491
57591
67391

end1.0ms (0%)

Compiler

Compiled 67 to 44 computations (34.3% saved)

sample1.4s (5.9%)

Algorithm
intervals
Results
922.0ms8000×body128valid
1.0msbody128invalid
Compiler

Compiled 431 to 297 computations (31.1% saved)

Profiling

Loading profile data...