Details

Time bar (total: 8.2s)

analyze673.0ms (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%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 (27.9%)

Results
730.0ms5383×body128valid
579.0ms1110×body2048valid
334.0ms746×body1024valid
296.0ms468×body4096valid
181.0ms1111×body128invalid
124.0ms384×body512valid
38.0ms165×body256valid
Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess47.0ms (0.6%)

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)

simplify36.0ms (0.4%)

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%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
34.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
34.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
34.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
0.4b
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
1.3b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
24.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

series126.0ms (1.5%)

Counts
4 → 96
Calls

36 calls:

10.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
a
-inf
9.0ms
(/.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
8.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
c
inf
6.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
c
-inf

rewrite76.0ms (0.9%)

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

simplify50.0ms (0.6%)

Algorithm
egg-herbie
Rules
780×times-frac_binary64
488×associate-/l*_binary64
414×associate-/r*_binary64
400×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

prune190.0ms (2.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New22013233
Fresh011
Picked101
Done000
Total22114235
Error
7.8b
Counts
235 → 14
Alt Table
StatusErrorProgram
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (/.f64 1/3 a)))
45.8b
(/.f64 (*.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -3)))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
56.4b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
34.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
46.6b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
46.3b
(/.f64 -2/3 (/.f64 a b))
46.3b
(*.f64 -2/3 (/.f64 b a))
41.7b
(*.f64 (/.f64 -1/2 b) c)
41.6b
(*.f64 -1/2 (/.f64 c b))
34.2b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
46.7b
(/.f64 (fma.f64 b -2 (*.f64 3/2 (*.f64 (/.f64 a b) c))) (*.f64 3 a))
35.3b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) 3)) (*.f64 3 a))
45.7b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
45.7b
(/.f64 (*.f64 -3/2 (/.f64 (*.f64 c a) b)) (*.f64 3 a))
Compiler

Compiled 6332 to 3959 computations (37.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (*.f64 a -3))
0.5b
(fma.f64 b b (*.f64 c (*.f64 a -3)))
1.3b
(-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))
24.7b
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))

series79.0ms (1%)

Counts
4 → 88
Calls

30 calls:

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

rewrite72.0ms (0.9%)

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

simplify60.0ms (0.7%)

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

prune156.0ms (1.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1932195
Fresh11213
Picked011
Done000
Total19415209
Error
7.8b
Counts
209 → 15
Alt Table
StatusErrorProgram
33.5b
(*.f64 (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3) (/.f64 1 (*.f64 a -3)))
34.2b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (/.f64 1/3 a)))
45.8b
(/.f64 (*.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -3)))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
56.4b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
34.2b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 -1/3 a))
45.7b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
46.6b
(-.f64 (*.f64 1/2 (/.f64 c b)) (*.f64 2/3 (/.f64 b a)))
46.3b
(/.f64 -2/3 (/.f64 a b))
46.3b
(*.f64 -2/3 (/.f64 b a))
41.7b
(*.f64 (/.f64 -1/2 b) c)
41.6b
(*.f64 -1/2 (/.f64 c b))
46.7b
(/.f64 (fma.f64 b -2 (*.f64 3/2 (*.f64 (/.f64 a b) c))) (*.f64 3 a))
35.3b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) 3)) (*.f64 3 a))
45.7b
(/.f64 (*.f64 -3/2 (/.f64 (*.f64 c a) b)) (*.f64 3 a))
Compiler

Compiled 6264 to 4247 computations (32.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (*.f64 a -3))
0.4b
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3)
0.5b
(-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))
14.4b
(sqrt.f64 (*.f64 c (*.f64 a -3)))

series836.0ms (10.2%)

Counts
3 → 16
Calls

24 calls:

126.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3)
c
0
120.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3)
c
inf
103.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3)
c
-inf
101.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3)
a
0
92.0ms
(pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3)
a
-inf

rewrite68.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
566×prod-diff_binary64
216×expm1-udef_binary64
216×log1p-udef_binary64
140×egg-rr
124×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01339
127439
2316839
Stop Event
node limit
Counts
3 → 140

simplify41.0ms (0.5%)

Algorithm
egg-herbie
Rules
871×fma-neg_binary64
327×associate-*r*_binary64
289×times-frac_binary64
286×associate-*l*_binary64
218×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
086735
1247678
2773631
34102622
Stop Event
node limit
Counts
156 → 117

prune128.0ms (1.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1394143
Fresh31013
Picked101
Done011
Total14315158
Error
4.3b
Counts
158 → 15
Alt Table
StatusErrorProgram
54.9b
(*.f64 (pow.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (pow.f64 (sqrt.f64 (*.f64 -3 (*.f64 c a))) 2) b))) 3) (/.f64 1 (*.f64 a -3)))
34.2b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
56.4b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
33.6b
(*.f64 (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (/.f64 1/3 a)))
45.8b
(/.f64 (*.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -3)))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
34.2b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 -1/3 a))
45.7b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
46.6b
(*.f64 (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 a -3)) (sqrt.f64 c))))) 3) (/.f64 1 (*.f64 a -3)))
46.3b
(*.f64 -2/3 (/.f64 b a))
41.7b
(*.f64 (/.f64 -1/2 b) c)
41.6b
(*.f64 -1/2 (/.f64 c b))
45.9b
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 c a) 3/2) b)) 3) (/.f64 1 (*.f64 a -3)))
46.7b
(/.f64 (fma.f64 b -2 (*.f64 3/2 (*.f64 (/.f64 a b) c))) (*.f64 3 a))
35.3b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) 3)) (*.f64 3 a))
Compiler

Compiled 4987 to 3622 computations (27.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series70.0ms (0.9%)

Counts
2 → 0
Calls

6 calls:

21.0ms
(pow.f64 (cbrt.f64 (*.f64 a -3)) 2)
a
inf
18.0ms
(pow.f64 (cbrt.f64 (*.f64 a -3)) 2)
a
0
14.0ms
(cbrt.f64 (*.f64 a -3))
a
inf
7.0ms
(cbrt.f64 (*.f64 a -3))
a
0
6.0ms
(pow.f64 (cbrt.f64 (*.f64 a -3)) 2)
a
-inf

rewrite51.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
509×log1p-expm1-u_binary64
509×expm1-log1p-u_binary64
379×unpow-prod-down_binary64
259×log-prod_binary64
151×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
114215
2148415
Stop Event
node limit
Counts
2 → 106

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
106 → 106

prune263.0ms (3.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New2603263
Fresh11213
Picked101
Done011
Total26216278
Error
4.3b
Counts
278 → 16
Alt Table
StatusErrorProgram
54.9b
(*.f64 (pow.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (pow.f64 (sqrt.f64 (*.f64 -3 (*.f64 c a))) 2) b))) 3) (/.f64 1 (*.f64 a -3)))
34.2b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 1 (*.f64 a -3)))
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (/.f64 1/3 a)))
45.8b
(/.f64 (*.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -3)))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
56.4b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
45.9b
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 c a) 3/2) b)) 3) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
46.7b
(/.f64 (fma.f64 b -2 (*.f64 3/2 (*.f64 (/.f64 a b) c))) (*.f64 3 a))
46.7b
(*.f64 (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -3)))))) 3) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a -3)) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
35.3b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) 3)) (*.f64 3 a))
34.2b
(*.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (/.f64 -1/3 a))
34.3b
(*.f64 (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) 3) (*.f64 (pow.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 a -3)))) 2) 3) (cbrt.f64 (cbrt.f64 (*.f64 a -3)))) 2) -1) (pow.f64 (cbrt.f64 (*.f64 a -3)) -1)))
45.7b
(/.f64 (*.f64 (*.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
46.6b
(*.f64 (pow.f64 (cbrt.f64 (-.f64 b (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 a -3)) (sqrt.f64 c))))) 3) (/.f64 1 (*.f64 a -3)))
46.3b
(*.f64 -2/3 (/.f64 b a))
41.7b
(*.f64 (/.f64 -1/2 b) c)
41.6b
(*.f64 -1/2 (/.f64 c b))
Compiler

Compiled 10437 to 8215 computations (21.3% saved)

regimes2.5s (30.6%)

Accuracy

Total 7.4b remaining (70.5%)

Threshold costs 0b (0%)

Counts
125 → 3
Compiler

Compiled 14095 to 10376 computations (26.4% saved)

bsearch77.0ms (0.9%)

Algorithm
binary-search
Calls

2 calls:

41.0ms
b
31.0ms
b
Steps
ItersPointRange
2.0725894999449674e-109
∈ [
5.922553449532183e-117
,
7.490172743962604e-109
]
-6.043449617406464e+148
∈ [
-1.3891652471045586e+155
,
-3.291227721434158e+144
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (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
02648
13348
23848
34048
44148
Stop Event
saturated

end246.0ms (3%)

Stop Event
fuel
Compiler

Compiled 416 to 306 computations (26.4% saved)

Profiling

Loading profile data...