Details

Time bar (total: 20.9s)

analyze2.6s (12.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
0.8%98.9%0.3%13
1.2%98.5%0.3%14
Compiler

Compiled 44 to 31 computations (29.5% saved)

sample1.9s (9.1%)

Results
1.7s8256×body128valid
203.0ms904×body128invalid
Compiler

Compiled 88 to 62 computations (29.5% saved)

preprocess47.0ms (0.2%)

Algorithm
egg-herbie
Rules
524×associate-+r+_binary64
524×associate-+l+_binary64
472×fma-def_binary64
435×associate-*l*_binary64
390×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0182656
1508656
21160624
33497624
066
Stop Event
saturated
node limit
Compiler

Compiled 43 to 30 computations (30.2% saved)

simplify32.0ms (0.2%)

Algorithm
egg-herbie
Rules
704×distribute-rgt-in_binary64
703×distribute-lft-in_binary64
676×fma-def_binary64
308×associate-*l*_binary64
236×associate-+l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03141
16341
213439
340239
4106739
5316439
6488939
Stop Event
node limit
Counts
1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
29.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
31.9b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
29.9b
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
Compiler

Compiled 228 to 150 computations (34.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000)
0.1b
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
0.1b
(fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t)
29.1b
(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))

series1.2s (5.9%)

Counts
4 → 156
Calls

39 calls:

75.0ms
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
t
inf
66.0ms
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
t
-inf
65.0ms
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
a
inf
65.0ms
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
b
-inf
64.0ms
(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
b
inf

rewrite52.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
243×add-sqr-sqrt_binary64
228×log1p-expm1-u_binary64
228×expm1-log1p-u_binary64
227×add-cbrt-cube_binary64
227×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02395
148595
Stop Event
node limit
Counts
4 → 80

simplify272.0ms (1.3%)

Algorithm
egg-herbie
Rules
520×associate-*l*_binary64
463×cancel-sign-sub-inv_binary64
313×fma-def_binary64
259×associate-+r+_binary64
219×+-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
024716263
178916138
2270013006
Stop Event
node limit
Counts
236 → 169

prune265.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1636169
Fresh101
Picked101
Done000
Total1656171
Error
0.0b
Counts
171 → 6
Alt Table
StatusErrorProgram
37.5b
(+.f64 (*.f64 (*.f64 1000000000000/607771387771 y) (+.f64 b (*.f64 z (*.f64 z t)))) (-.f64 (+.f64 (+.f64 x (*.f64 (*.f64 a y) (+.f64 (*.f64 (pow.f64 z 3) 123439798033292669987862100000000000000/224502278183706222041215714334315011) (*.f64 z 1000000000000/607771387771)))) (*.f64 y (*.f64 (*.f64 z z) (+.f64 (*.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 b) (*.f64 11166754126200/607771387771 z))))) (fma.f64 11940090572100000000000000/369386059793087248348441 (*.f64 y (*.f64 z (fma.f64 a z b))) (*.f64 y (*.f64 (pow.f64 z 3) (+.f64 (*.f64 1251144097444193138232650020820236307000000000000000/136446061169462227850157143060939731682147130481 b) (*.f64 11940090572100000000000000/369386059793087248348441 t)))))))
24.8b
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
47.6b
(+.f64 (*.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (+.f64 (*.f64 z (*.f64 z t)) b)) (*.f64 y (fma.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (fma.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (*.f64 (/.f64 a (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) z)))))
32.4b
(+.f64 (*.f64 55833770631/5000000000 (/.f64 (*.f64 y (pow.f64 z 3)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 y (*.f64 t (pow.f64 z 2))) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (/.f64 (*.f64 y b) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (*.f64 313060547623/100000000000 (/.f64 (*.f64 y (pow.f64 z 4)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) x)))))
24.9b
(fma.f64 y (+.f64 313060547623/100000000000 (+.f64 (/.f64 t (*.f64 z z)) (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 -3652704169880641883561/100000000000000000000 z)))) x)
29.9b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))) x)
Compiler

Compiled 8144 to 5325 computations (34.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)
0.7b
(*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000))
3.3b
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
9.3b
(/.f64 y (*.f64 z z))

series180.0ms (0.9%)

Counts
4 → 144
Calls

36 calls:

13.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
y
inf
13.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
y
-inf
11.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
x
0
10.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
t
inf
10.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (*.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
x
-inf

rewrite61.0ms (0.3%)

Algorithm
batch-egg-rewrite
Rules
192×add-sqr-sqrt_binary64
183×log1p-expm1-u_binary64
183×expm1-log1p-u_binary64
182×add-cbrt-cube_binary64
180×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01761
138259
Stop Event
node limit
Counts
4 → 144

simplify89.0ms (0.4%)

Algorithm
egg-herbie
Rules
846×fma-def_binary64
628×fma-neg_binary64
523×times-frac_binary64
178×associate-+l+_binary64
163×distribute-lft-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0622353
11792350
24362036
312121952
440711952
Stop Event
node limit
Counts
288 → 178

prune241.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1744178
Fresh145
Picked101
Done000
Total1768184
Error
0.0b
Counts
184 → 8
Alt Table
StatusErrorProgram
51.1b
(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y z) (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 y (pow.f64 z -2)) x))) 3))
32.4b
(+.f64 (*.f64 55833770631/5000000000 (/.f64 (*.f64 y (pow.f64 z 3)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 y (*.f64 t (pow.f64 z 2))) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (/.f64 (*.f64 y b) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (*.f64 313060547623/100000000000 (/.f64 (*.f64 y (pow.f64 z 4)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) x)))))
24.6b
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
43.6b
(/.f64 (-.f64 (pow.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 y (pow.f64 z -2)) x)) 2) (pow.f64 (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000)) 2)) (-.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 y (pow.f64 z -2)) x)) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
37.5b
(+.f64 (*.f64 (*.f64 1000000000000/607771387771 y) (+.f64 b (*.f64 z (*.f64 z t)))) (-.f64 (+.f64 (+.f64 x (*.f64 (*.f64 a y) (+.f64 (*.f64 (pow.f64 z 3) 123439798033292669987862100000000000000/224502278183706222041215714334315011) (*.f64 z 1000000000000/607771387771)))) (*.f64 y (*.f64 (*.f64 z z) (+.f64 (*.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 b) (*.f64 11166754126200/607771387771 z))))) (fma.f64 11940090572100000000000000/369386059793087248348441 (*.f64 y (*.f64 z (fma.f64 a z b))) (*.f64 y (*.f64 (pow.f64 z 3) (+.f64 (*.f64 1251144097444193138232650020820236307000000000000000/136446061169462227850157143060939731682147130481 b) (*.f64 11940090572100000000000000/369386059793087248348441 t)))))))
47.6b
(+.f64 (*.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (+.f64 (*.f64 z (*.f64 z t)) b)) (*.f64 y (fma.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (fma.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (*.f64 (/.f64 a (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) z)))))
29.9b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))) x)
43.8b
(*.f64 (cbrt.f64 (fma.f64 (/.f64 y z) (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 y (pow.f64 z -2)) x)))) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 y z) (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 y (pow.f64 z -2)) x))) 2)))
Compiler

Compiled 5918 to 3312 computations (44% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))
2.9b
(/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000)))
3.3b
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
9.3b
(/.f64 y (*.f64 z z))

series133.0ms (0.6%)

Counts
3 → 108
Calls

27 calls:

12.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
y
0
12.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
y
-inf
11.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
x
0
11.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
t
0
10.0ms
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
t
-inf

rewrite52.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
196×add-sqr-sqrt_binary64
187×log1p-expm1-u_binary64
187×expm1-log1p-u_binary64
186×add-cbrt-cube_binary64
184×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01753
138751
Stop Event
node limit
Counts
3 → 104

simplify80.0ms (0.4%)

Algorithm
egg-herbie
Rules
305×fma-neg_binary64
278×cancel-sign-sub-inv_binary64
252×fma-def_binary64
245×associate-/l/_binary64
231×associate-/r/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01052362
13022359
28112033
326571963
Stop Event
node limit
Counts
212 → 146

prune223.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1902192
Fresh257
Picked011
Done000
Total1928200
Error
0.0b
Counts
200 → 8
Alt Table
StatusErrorProgram
51.1b
(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) z) (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 (/.f64 y z) z) x))) 3))
32.4b
(+.f64 (*.f64 55833770631/5000000000 (/.f64 (*.f64 y (pow.f64 z 3)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 y (*.f64 t (pow.f64 z 2))) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (/.f64 (*.f64 y b) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (*.f64 313060547623/100000000000 (/.f64 (*.f64 y (pow.f64 z 4)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) x)))))
37.5b
(+.f64 (*.f64 (*.f64 1000000000000/607771387771 y) (+.f64 b (*.f64 z (*.f64 z t)))) (-.f64 (+.f64 (+.f64 x (*.f64 (*.f64 a y) (+.f64 (*.f64 (pow.f64 z 3) 123439798033292669987862100000000000000/224502278183706222041215714334315011) (*.f64 z 1000000000000/607771387771)))) (*.f64 y (*.f64 (*.f64 z z) (+.f64 (*.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 b) (*.f64 11166754126200/607771387771 z))))) (fma.f64 11940090572100000000000000/369386059793087248348441 (*.f64 y (*.f64 z (fma.f64 a z b))) (*.f64 y (*.f64 (pow.f64 z 3) (+.f64 (*.f64 1251144097444193138232650020820236307000000000000000/136446061169462227850157143060939731682147130481 b) (*.f64 11940090572100000000000000/369386059793087248348441 t)))))))
43.6b
(/.f64 (-.f64 (pow.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 (/.f64 y z) z) x)) 2) (pow.f64 (*.f64 y (/.f64 (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) z)) 2)) (-.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 (/.f64 y z) z) x)) (*.f64 y (/.f64 (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) z))))
47.6b
(+.f64 (*.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (+.f64 (*.f64 z (*.f64 z t)) b)) (*.f64 y (fma.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (fma.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (*.f64 (/.f64 a (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) z)))))
24.6b
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
29.9b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))) x)
43.8b
(*.f64 (cbrt.f64 (fma.f64 (/.f64 y z) (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 y (pow.f64 z -2)) x)))) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 y z) (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 y (pow.f64 z -2)) x))) 2)))
Compiler

Compiled 6268 to 3414 computations (45.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))
9.6b
(sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))
18.6b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))))
25.3b
(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))

series783.0ms (3.8%)

Counts
4 → 120
Calls

30 calls:

49.0ms
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))))
t
inf
49.0ms
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))))
b
inf
47.0ms
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))))
t
-inf
47.0ms
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))))
a
inf
47.0ms
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))))
a
-inf

rewrite59.0ms (0.3%)

Algorithm
batch-egg-rewrite
Rules
246×add-sqr-sqrt_binary64
231×add-cbrt-cube_binary64
231×log1p-expm1-u_binary64
231×expm1-log1p-u_binary64
230×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
024111
1508109
Stop Event
node limit
Counts
4 → 110

simplify211.0ms (1%)

Algorithm
egg-herbie
Rules
456×times-frac_binary64
415×cancel-sign-sub-inv_binary64
395×fma-def_binary64
237×associate-+r+_binary64
235×+-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029911300
198410254
2356610250
Stop Event
node limit
Counts
230 → 201

prune970.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2361237
Fresh156
Picked011
Done011
Total2378245
Error
0.0b
Counts
245 → 8
Alt Table
StatusErrorProgram
51.1b
(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) z) (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 (/.f64 y z) z) x))) 3))
32.4b
(+.f64 (*.f64 55833770631/5000000000 (/.f64 (*.f64 y (pow.f64 z 3)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 y (*.f64 t (pow.f64 z 2))) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (/.f64 (*.f64 y b) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) (+.f64 (*.f64 313060547623/100000000000 (/.f64 (*.f64 y (pow.f64 z 4)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z))))))) (+.f64 (/.f64 (*.f64 a (*.f64 y z)) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (*.f64 15234687407/1000000000 (pow.f64 z 3)) (*.f64 119400905721/10000000000 z)))))) x)))))
37.5b
(+.f64 (*.f64 (*.f64 1000000000000/607771387771 y) (+.f64 b (*.f64 z (*.f64 z t)))) (-.f64 (+.f64 (+.f64 x (*.f64 (*.f64 a y) (+.f64 (*.f64 (pow.f64 z 3) 123439798033292669987862100000000000000/224502278183706222041215714334315011) (*.f64 z 1000000000000/607771387771)))) (*.f64 y (*.f64 (*.f64 z z) (+.f64 (*.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 b) (*.f64 11166754126200/607771387771 z))))) (fma.f64 11940090572100000000000000/369386059793087248348441 (*.f64 y (*.f64 z (fma.f64 a z b))) (*.f64 y (*.f64 (pow.f64 z 3) (+.f64 (*.f64 1251144097444193138232650020820236307000000000000000/136446061169462227850157143060939731682147130481 b) (*.f64 11940090572100000000000000/369386059793087248348441 t)))))))
43.6b
(/.f64 (-.f64 (pow.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 (/.f64 y z) z) x)) 2) (pow.f64 (*.f64 y (/.f64 (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) z)) 2)) (-.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 (/.f64 y z) z) x)) (*.f64 y (/.f64 (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000) z))))
30.1b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))) 3)) x)
47.6b
(+.f64 (*.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (+.f64 (*.f64 z (*.f64 z t)) b)) (*.f64 y (fma.f64 55833770631/5000000000 (/.f64 (pow.f64 z 3) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (fma.f64 313060547623/100000000000 (/.f64 (pow.f64 z 4) (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) (*.f64 (/.f64 a (+.f64 607771387771/1000000000000 (+.f64 (*.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (*.f64 z (fma.f64 z 314690115749/10000000000 119400905721/10000000000))))) z)))))
24.6b
(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (*.f64 z z)) x)) (/.f64 y (/.f64 z (+.f64 (/.f64 t z) -3652704169880641883561/100000000000000000000))))
29.9b
(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (sqrt.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)))) x)
Compiler

Compiled 12663 to 8508 computations (32.8% saved)

regimes11.0s (52.5%)

Accuracy

Total 0.3b remaining (70.9%)

Threshold costs 0.3b (70.9%)

Counts
410 → 3
Compiler

Compiled 133536 to 91980 computations (31.1% saved)

bsearch80.0ms (0.4%)

Algorithm
binary-search
Calls

2 calls:

36.0ms
z
18.0ms
z
Steps
ItersPointRange
6.208949676433419e+36
∈ [
1.2677179260844055e+36
,
2.282765266991728e+41
]
-9.83449241470277e+39
∈ [
-1.558605165253961e+40
,
-9.48245262687842e+39
]
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
052168
162168
270168
381168
486168
588168
Stop Event
saturated

end323.0ms (1.5%)

Stop Event
fuel
Compiler

Compiled 783 to 539 computations (31.2% saved)

Profiling

Loading profile data...