Details

Time bar (total: 6.7s)

analyze648.0ms (9.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%74.9%0.1%6
25%68.6%6.4%7
31.2%62.4%6.4%8
36.7%54.6%8.7%9
38.2%48.4%13.4%10
42.7%42.3%15%11
47.8%34.1%18.1%12
49.1%30.3%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.3s (34.6%)

Results
774.0ms5406×body128valid
633.0ms1197×body2048valid
323.0ms732×body1024valid
262.0ms403×body4096valid
145.0ms1129×body128invalid
116.0ms349×body512valid
37.0ms169×body256valid
Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess47.0ms (0.7%)

Algorithm
egg-herbie
Rules
795×fma-def_binary64
731×div-sub_binary64
295×fma-neg_binary64
212×associate-/l*_binary64
209×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034104
19288
221388
344088
475888
5125188
6222188
7445788
033
Stop Event
saturated
node limit
Compiler

Compiled 20 to 14 computations (30% saved)

simplify33.0ms (0.5%)

Algorithm
egg-herbie
Rules
1220×fma-neg_binary64
367×fma-def_binary64
351×times-frac_binary64
266×associate-/l*_binary64
254×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01326
13022
26922
316022
426422
543322
674422
7134122
8276922
9470222
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
34.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
34.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
34.4b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
0.6b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
1.2b
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
25.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

series128.0ms (1.9%)

Counts
4 → 96
Calls

36 calls:

11.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
a
-inf
10.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
a
inf
8.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
c
-inf
7.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
c
inf
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
a
inf

rewrite80.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
248×expm1-udef_binary64
248×log1p-udef_binary64
158×egg-rr
150×add-sqr-sqrt_binary64
145×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01374
130262
2445162
Stop Event
node limit
Counts
4 → 158

simplify52.0ms (0.8%)

Algorithm
egg-herbie
Rules
780×times-frac_binary64
488×associate-/l*_binary64
414×associate-/r*_binary64
402×fma-def_binary64
142×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01372325
14292249
214712208
Stop Event
node limit
Counts
254 → 233

prune172.0ms (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New22211233
Fresh101
Picked011
Done000
Total22312235
Error
7.0b
Counts
235 → 12
Alt Table
StatusErrorProgram
34.4b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
45.1b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
46.5b
(*.f64 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) 1/3) (/.f64 1 a))
44.9b
(*.f64 (/.f64 -2/3 a) b)
34.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
41.5b
(*.f64 -1/2 (/.f64 c b))
55.9b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
44.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (neg.f64 (*.f64 3 (*.f64 c a)))) a))
44.9b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
47.3b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
34.7b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))) 1/4) 2)) (*.f64 3 a))
35.4b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
Compiler

Compiled 6240 to 3905 computations (37.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (*.f64 a -3))
0.6b
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
1.5b
(fma.f64 b b (*.f64 c (*.f64 a -3)))
25.7b
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))

series77.0ms (1.2%)

Counts
4 → 88
Calls

30 calls:

7.0ms
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
c
-inf
6.0ms
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))
c
-inf
6.0ms
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
c
inf
5.0ms
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
a
-inf
5.0ms
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
a
inf

rewrite70.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
630×prod-diff_binary64
218×expm1-udef_binary64
218×log1p-udef_binary64
141×egg-rr
124×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01247
125342
2319642
Stop Event
node limit
Counts
4 → 141

simplify56.0ms (0.8%)

Algorithm
egg-herbie
Rules
455×times-frac_binary64
407×fma-neg_binary64
274×associate-/l*_binary64
268×associate-*r*_binary64
252×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0851684
12571618
28131604
344381602
Stop Event
node limit
Counts
229 → 195

prune154.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1914195
Fresh2810
Picked101
Done011
Total19413207
Error
7.0b
Counts
207 → 13
Alt Table
StatusErrorProgram
44.9b
(*.f64 (/.f64 -2/3 a) b)
32.5b
(*.f64 (*.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)) (/.f64 1 (*.f64 a -3)))
35.4b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
34.4b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (/.f64 1 a) -1/3))
45.1b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
34.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
41.5b
(*.f64 -1/2 (/.f64 c b))
36.1b
(*.f64 (-.f64 b (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3))))) 3)) (/.f64 1 (*.f64 a -3)))
55.9b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
44.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (neg.f64 (*.f64 3 (*.f64 c a)))) a))
44.9b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
47.3b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
34.8b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
Compiler

Compiled 6236 to 4237 computations (32.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (*.f64 a -3))
0.3b
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)
0.3b
(cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3))))))
14.4b
(sqrt.f64 (*.f64 c (*.f64 a -3)))

series983.0ms (14.8%)

Counts
3 → 8
Calls

24 calls:

109.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)
c
inf
93.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)
c
-inf
83.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)
a
-inf
80.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)
c
0
70.0ms
(cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3))))))
c
inf

rewrite51.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
566×prod-diff_binary64
228×expm1-udef_binary64
228×log1p-udef_binary64
132×add-sqr-sqrt_binary64
127×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01346
127646
2330046
Stop Event
node limit
Counts
3 → 70

simplify29.0ms (0.4%)

Algorithm
egg-herbie
Rules
754×associate-*l*_binary64
734×associate-*r*_binary64
424×fma-def_binary64
286×cancel-sign-sub-inv_binary64
186×unswap-sqr_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0112990
1323940
21135915
Stop Event
node limit
Counts
78 → 86

prune190.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1711172
Fresh11011
Picked101
Done011
Total17312185
Error
7.0b
Counts
185 → 12
Alt Table
StatusErrorProgram
32.6b
(*.f64 (*.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
36.1b
(*.f64 (-.f64 b (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3))))) 3)) (/.f64 1 (*.f64 a -3)))
35.4b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
34.4b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (/.f64 1 a) -1/3))
45.1b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
34.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
41.5b
(*.f64 -1/2 (/.f64 c b))
55.9b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
44.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (neg.f64 (*.f64 3 (*.f64 c a)))) a))
44.9b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
47.3b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
34.8b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
Compiler

Compiled 7962 to 5933 computations (25.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1))
0.5b
(pow.f64 (cbrt.f64 (*.f64 a -3)) 2)
0.6b
(cbrt.f64 (*.f64 a -3))
14.4b
(sqrt.f64 (*.f64 c (*.f64 a -3)))

series223.0ms (3.4%)

Counts
3 → 12
Calls

9 calls:

74.0ms
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1))
a
inf
64.0ms
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1))
a
0
20.0ms
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1))
a
-inf
20.0ms
(pow.f64 (cbrt.f64 (*.f64 a -3)) 2)
a
inf
18.0ms
(pow.f64 (cbrt.f64 (*.f64 a -3)) 2)
a
0

rewrite40.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
795×log1p-expm1-u_binary64
795×expm1-log1p-u_binary64
98×add-sqr-sqrt_binary64
97×add-cbrt-cube_binary64
95×add-cube-cbrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
123222
2248022
Stop Event
node limit
Counts
3 → 65

simplify13.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
Stop Event
saturated
Counts
77 → 66

prune153.0ms (2.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1441145
Fresh01010
Picked011
Done011
Total14413157
Error
7.0b
Counts
157 → 13
Alt Table
StatusErrorProgram
32.6b
(*.f64 (*.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
36.1b
(*.f64 (-.f64 b (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3))))) 3)) (/.f64 1 (*.f64 a -3)))
44.9b
(/.f64 (*.f64 -2 b) (*.f64 3 a))
32.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 2)) (*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 a -3))) 3) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
35.4b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
34.4b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (/.f64 1 a) -1/3))
45.1b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
34.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
41.5b
(*.f64 -1/2 (/.f64 c b))
55.9b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
44.0b
(*.f64 1/3 (/.f64 (sqrt.f64 (neg.f64 (*.f64 3 (*.f64 c a)))) a))
47.3b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
34.8b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
Compiler

Compiled 6569 to 5010 computations (23.7% saved)

regimes817.0ms (12.3%)

Accuracy

Total 4.4b remaining (44%)

Threshold costs 0b (0%)

Counts
70 → 3
Compiler

Compiled 7662 to 5550 computations (27.6% saved)

bsearch63.0ms (0.9%)

Algorithm
binary-search
Calls

2 calls:

42.0ms
b
18.0ms
b
Steps
ItersPointRange
1.7454011737234576e-87
∈ [
1.5759469908447728e-87
,
1.1141340710173169e-85
]
-6.492330097195095e+142
∈ [
-3.1727397311388303e+143
,
-2.2082337871231996e+142
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02956
13456
Stop Event
saturated

end220.0ms (3.3%)

Stop Event
fuel
Compiler

Compiled 368 to 266 computations (27.7% saved)

Profiling

Loading profile data...