Details

Time bar (total: 19.9s)

analyze1.3s (6.6%)

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)

sample1.5s (7.3%)

Results
1.4s8256×body128valid
1.0msbody128invalid
Compiler

Compiled 122 to 89 computations (27% saved)

simplify50.0ms (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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
24.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
24.9b
(/.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))
Compiler

Compiled 136 to 92 computations (32.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000)
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)
24.0b
(/.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))

series312.0ms (1.6%)

Counts
4 → 84
Calls

4 calls:

299.0ms
(/.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))
9.0ms
(fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
2.0ms
(fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000)
1.0ms
(fma.f64 x 104109730557/25000000000 393497462077/5000000000)

rewrite10.0ms (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 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y)
0.0ms
(fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000)

simplify238.0ms (1.2%)

Algorithm
egg-herbie
Rules
939×fma-def_binary64
547×distribute-rgt-in_binary64
296×times-frac_binary64
146×cancel-sign-sub-inv_binary64
122×+-commutative_binary64
Counts
139 → 120
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02408042
16267710
220557068
350007068

prune236.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1128120
Fresh000
Picked101
Done000
Total1138121
Error
0.2b
Counts
121 → 8
Alt Table
StatusErrorProgram
44.6b
(cbrt.f64 (pow.f64 (/.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)) 3))
33.0b
(/.f64 (*.f64 (+.f64 (*.f64 104109730557/25000000000 (pow.f64 x 4)) (+.f64 z (+.f64 (*.f64 4297481763/31250000 (pow.f64 x 2)) (*.f64 393497462077/5000000000 (pow.f64 x 3))))) (-.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))))))
24.1b
(/.f64 (*.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))) (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)))
35.1b
(-.f64 (+.f64 (/.f64 y (pow.f64 x 2)) (+.f64 (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)) (*.f64 104109730557/25000000000 x))) (+.f64 13764240537310136880149/125000000000000000000 (*.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (/.f64 1 (pow.f64 x 2)))))
31.3b
(-.f64 (+.f64 (*.f64 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (*.f64 z (pow.f64 x 3))) (+.f64 (*.f64 168466327098500000000/553822718361107519809 (*.f64 y (pow.f64 x 2))) (+.f64 (*.f64 106576606695487271009549/2769113591805537599045 (pow.f64 x 3)) (*.f64 168466327098500000000/553822718361107519809 (*.f64 z x))))) (+.f64 (*.f64 23298017199368982832548000000000/13033352773350869092174451844127 (*.f64 z (pow.f64 x 2))) (+.f64 (*.f64 1000000000/23533438303 z) (+.f64 (*.f64 137519416416/23533438303 (pow.f64 x 2)) (+.f64 (*.f64 23298017199368982832548000000000/13033352773350869092174451844127 (*.f64 y (pow.f64 x 3))) (*.f64 1000000000/23533438303 (*.f64 y x)))))))
24.9b
(/.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 (+.f64 156699607947/500000000 (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (*.f64 263505074721/1000000000 x) (pow.f64 x 3)))) 23533438303/500000000))
24.1b
(*.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))))
25.9b
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 2 2)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (*.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x 2)))
Compiler

Compiled 5349 to 3669 computations (31.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.9b
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
16.3b
(/.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)))
16.5b
(*.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))))
19.7b
(/.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)))

series523.0ms (2.6%)

Counts
4 → 96
Calls

4 calls:

293.0ms
(*.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))))
219.0ms
(/.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)))
6.0ms
(/.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)))
4.0ms
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

rewrite54.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt_binary64
108×times-frac_binary64
95×*-un-lft-identity_binary64
69×add-cube-cbrt_binary64
63×sqrt-prod_binary64
Counts
4 → 201
Calls

4 calls:

17.0ms
(*.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))))
5.0ms
(/.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)))
3.0ms
(/.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)))
1.0ms
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))

simplify433.0ms (2.2%)

Algorithm
egg-herbie
Rules
342×fma-def_binary64
223×associate-/l*_binary64
206×associate-*r/_binary64
201×associate-*l/_binary64
198×fma-neg_binary64
Counts
297 → 319
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049722462
1143420376
2480220372
3494020372

prune593.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3464350
Fresh437
Picked101
Done000
Total3517358
Error
0.2b
Counts
358 → 7
Alt Table
StatusErrorProgram
24.1b
(*.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 1 (/.f64 (sqrt.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))))
24.5b
(*.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 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (/.f64 (cbrt.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)))))
24.9b
(/.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 (+.f64 156699607947/500000000 (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (*.f64 263505074721/1000000000 x) (pow.f64 x 3)))) 23533438303/500000000))
31.3b
(-.f64 (fma.f64 (*.f64 z (pow.f64 x 3)) 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (+.f64 (*.f64 168466327098500000000/553822718361107519809 (fma.f64 z x (*.f64 y (*.f64 x x)))) (*.f64 (pow.f64 x 3) 106576606695487271009549/2769113591805537599045))) (fma.f64 (*.f64 z (*.f64 x x)) 23298017199368982832548000000000/13033352773350869092174451844127 (+.f64 (fma.f64 (*.f64 x x) 137519416416/23533438303 (*.f64 (*.f64 y (pow.f64 x 3)) 23298017199368982832548000000000/13033352773350869092174451844127)) (*.f64 1000000000/23533438303 (fma.f64 y x z)))))
35.1b
(-.f64 (+.f64 (/.f64 y (pow.f64 x 2)) (+.f64 (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)) (*.f64 104109730557/25000000000 x))) (+.f64 13764240537310136880149/125000000000000000000 (*.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (/.f64 1 (pow.f64 x 2)))))
44.4b
(cbrt.f64 (*.f64 (*.f64 (*.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)))) (*.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))))) (*.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))))))
25.9b
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 2 2)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (*.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x 2)))
Compiler

Compiled 22522 to 15606 computations (30.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.9b
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))
16.3b
(/.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)))
16.5b
(*.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 1 (/.f64 (sqrt.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))))
22.9b
(/.f64 (sqrt.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))

series591.0ms (3%)

Counts
2 → 72
Calls

2 calls:

302.0ms
(*.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 1 (/.f64 (sqrt.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))))
289.0ms
(/.f64 (sqrt.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))

rewrite101.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
212×times-frac_binary64
185×add-sqr-sqrt_binary64
117×*-un-lft-identity_binary64
96×add-cube-cbrt_binary64
71×associate-*r*_binary64
Counts
2 → 202
Calls

2 calls:

38.0ms
(*.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 1 (/.f64 (sqrt.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))))
3.0ms
(/.f64 (sqrt.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))

simplify468.0ms (2.4%)

Algorithm
egg-herbie
Rules
811×fma-def_binary64
510×times-frac_binary64
258×*-commutative_binary64
168×+-commutative_binary64
132×associate-+r+_binary64
Counts
274 → 337
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
080331467
1253527577
2495027577

prune1.0s (5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4720472
Fresh066
Picked011
Done000
Total4727479
Error
0.2b
Counts
479 → 7
Alt Table
StatusErrorProgram
24.1b
(*.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 1 (/.f64 (sqrt.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))))
24.5b
(*.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 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (/.f64 (cbrt.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)))))
24.9b
(/.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 (+.f64 156699607947/500000000 (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (*.f64 263505074721/1000000000 x) (pow.f64 x 3)))) 23533438303/500000000))
31.3b
(-.f64 (fma.f64 (*.f64 z (pow.f64 x 3)) 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (+.f64 (*.f64 168466327098500000000/553822718361107519809 (fma.f64 z x (*.f64 y (*.f64 x x)))) (*.f64 (pow.f64 x 3) 106576606695487271009549/2769113591805537599045))) (fma.f64 (*.f64 z (*.f64 x x)) 23298017199368982832548000000000/13033352773350869092174451844127 (+.f64 (fma.f64 (*.f64 x x) 137519416416/23533438303 (*.f64 (*.f64 y (pow.f64 x 3)) 23298017199368982832548000000000/13033352773350869092174451844127)) (*.f64 1000000000/23533438303 (fma.f64 y x z)))))
35.1b
(-.f64 (+.f64 (/.f64 y (pow.f64 x 2)) (+.f64 (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)) (*.f64 104109730557/25000000000 x))) (+.f64 13764240537310136880149/125000000000000000000 (*.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (/.f64 1 (pow.f64 x 2)))))
44.4b
(cbrt.f64 (*.f64 (*.f64 (*.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)))) (*.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))))) (*.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))))))
25.9b
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 2 2)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (*.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x 2)))
Compiler

Compiled 40896 to 29161 computations (28.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
13.9b
(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))
16.3b
(/.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)))
16.5b
(*.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 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (/.f64 (cbrt.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)))))
17.2b
(/.f64 (cbrt.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)))

series893.0ms (4.5%)

Counts
3 → 108
Calls

3 calls:

419.0ms
(/.f64 (cbrt.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)))
311.0ms
(*.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 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (/.f64 (cbrt.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)))))
162.0ms
(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))

rewrite54.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
66×times-frac_binary64
61×*-un-lft-identity_binary64
61×add-sqr-sqrt_binary64
49×add-cube-cbrt_binary64
46×add-exp-log_binary64
Counts
3 → 146
Calls

3 calls:

18.0ms
(*.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 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (/.f64 (cbrt.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)))))
3.0ms
(/.f64 (cbrt.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)))
1.0ms
(cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))

simplify662.0ms (3.3%)

Algorithm
egg-herbie
Rules
698×*-commutative_binary64
417×fma-def_binary64
371×associate-+r+_binary64
324×associate-*r*_binary64
150×associate-/l*_binary64
Counts
254 → 347
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0170637893
1499637893
2499437893

prune2.1s (10.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New5811582
Fresh145
Picked011
Done011
Total5827589
Error
0.2b
Counts
589 → 7
Alt Table
StatusErrorProgram
35.1b
(-.f64 (+.f64 (/.f64 y (*.f64 x x)) (+.f64 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x) (*.f64 x 104109730557/25000000000))) (+.f64 13764240537310136880149/125000000000000000000 (/.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 x x))))
24.1b
(*.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 1 (/.f64 (sqrt.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))))
24.5b
(*.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 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (cbrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z))) (/.f64 (cbrt.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)))))
24.9b
(/.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 (+.f64 156699607947/500000000 (+.f64 (*.f64 216700011257/5000000000 (pow.f64 x 2)) (+.f64 (*.f64 263505074721/1000000000 x) (pow.f64 x 3)))) 23533438303/500000000))
31.3b
(-.f64 (fma.f64 (*.f64 z (pow.f64 x 3)) 3140446455626174059100348970313144550000000/306719603372886620352117082586607327396481 (+.f64 (*.f64 168466327098500000000/553822718361107519809 (fma.f64 z x (*.f64 y (*.f64 x x)))) (*.f64 (pow.f64 x 3) 106576606695487271009549/2769113591805537599045))) (fma.f64 (*.f64 z (*.f64 x x)) 23298017199368982832548000000000/13033352773350869092174451844127 (+.f64 (fma.f64 (*.f64 x x) 137519416416/23533438303 (*.f64 (*.f64 y (pow.f64 x 3)) 23298017199368982832548000000000/13033352773350869092174451844127)) (*.f64 1000000000/23533438303 (fma.f64 y x z)))))
44.4b
(cbrt.f64 (*.f64 (*.f64 (*.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)))) (*.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))))) (*.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))))))
25.9b
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 2 2)) (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z)) (*.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x 2)))
Compiler

Compiled 93132 to 65431 computations (29.7% saved)

regimes8.3s (42%)

Accuracy

Total 1.1b remaining (80.3%)

Threshold costs 0b (0%)

Counts
425 → 2
Compiler

Compiled 97028 to 68784 computations (29.1% saved)

bsearch40.0ms (0.2%)

Compiler

Compiled 40 to 29 computations (27.5% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
054132
179132
290132
398132
4101132
5102132
699132

end269.0ms (1.4%)

Compiler

Compiled 615 to 416 computations (32.4% saved)

Profiling

Loading profile data...