Details

Time bar (total: 8.7s)

analyze680.0ms (7.8%)

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)

sample51.0ms (0.6%)

Algorithm
intervals
Results
11.0ms33×body2048valid
10.0ms161×body128valid
7.0ms28×body1024valid
6.0ms16×body4096valid
2.0ms11×body512valid
1.0ms23×body128nan
1.0msbody256valid
1.0msbody128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify367.0ms (4.2%)

Algorithm
egg-herbie
Rules
1968×fma-neg_binary64
1363×fma-def_binary64
898×div-sub_binary64
743×associate-/l*_binary64
567×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01326
13022
26422
313522
420122
533522
655422
792922
8147722
9211522
10259922
11255422
12260222
13267122
14311722
15232722
16237522
17238322
18238922
19239522
20239722
21239722
22258522
23268522
24261922
25263122
26266122
27267722
28270722
29270722
30275122
31285122
32282722
33282722
34263822

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
36.3b
Counts
2 → 2
Alt Table
StatusErrorProgram
36.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
36.4b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
Compiler

Compiled 94 to 64 computations (31.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
0.7b
(*.f64 (*.f64 3 a) c)
26.6b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))

rewrite137.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
36.1b
Rules
13×*-un-lft-identity_binary64
10×fma-def_binary64
10×add-sqr-sqrt_binary64
10×add-log-exp_binary64
10×pow1_binary64
Counts
4 → 80
Calls

4 calls:

8.0ms
(*.f64 (*.f64 3 a) c)
7.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
3.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
Compiler

Compiled 1857 to 1037 computations (44.2% saved)

series131.0ms (1.5%)

Error
12.1b
Counts
4 → 57
Calls

4 calls:

33.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))))
33.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))
29.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c))
20.0ms
(*.f64 (*.f64 3 a) c)
Compiler

Compiled 2366 to 1697 computations (28.3% saved)

simplify106.0ms (1.2%)

Algorithm
egg-herbie
Rules
723×fma-neg_binary64
679×times-frac_binary64
562×fma-def_binary64
281×cancel-sign-sub-inv_binary64
246×div-sub_binary64
Counts
137 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02032502
15002286
217922098
345702098
448222098

prune53.0ms (0.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1029111
Fresh011
Picked011
Done000
Total10211113
Error
5.4b
Counts
113 → 11
Alt Table
StatusErrorProgram
33.6b
(/.f64 (/.f64 (*.f64 3 (*.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 3 a))
39.0b
(*.f64 -1/2 (*.f64 1 (/.f64 c b)))
36.6b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b)) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
55.2b
0
36.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
36.7b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))) (*.f64 3 a))
36.4b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
50.6b
(/.f64 (fma.f64 b -2 (fma.f64 3/2 (/.f64 (*.f64 c a) b) (*.f64 9/8 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))))) (*.f64 3 a))
45.3b
(fma.f64 1/2 (*.f64 1 (/.f64 c b)) (*.f64 -2/3 (/.f64 b a)))
45.2b
(*.f64 -2/3 (/.f64 b a))
38.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
Compiler

Compiled 1571 to 959 computations (39% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b
(fma.f64 b b (*.f64 c (*.f64 a -3)))
4.6b
(/.f64 (/.f64 (*.f64 3 (*.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 3 a))
10.3b
(/.f64 (*.f64 3 (*.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))
26.6b
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))

rewrite109.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
5.3b
Rules
45×add-cbrt-cube_binary64
45×add-exp-log_binary64
34×times-frac_binary64
28×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
Counts
4 → 116
Calls

4 calls:

11.0ms
(/.f64 (/.f64 (*.f64 3 (*.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 3 a))
9.0ms
(/.f64 (*.f64 3 (*.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))
1.0ms
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))
0.0ms
(fma.f64 b b (*.f64 c (*.f64 a -3)))
Compiler

Compiled 3801 to 2152 computations (43.4% saved)

series196.0ms (2.3%)

Error
5.3b
Counts
4 → 66
Calls

4 calls:

59.0ms
(/.f64 (*.f64 3 (*.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))))
52.0ms
(/.f64 (/.f64 (*.f64 3 (*.f64 c a)) (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))))) (*.f64 3 a))
35.0ms
(sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3))))
33.0ms
(fma.f64 b b (*.f64 c (*.f64 a -3)))
Compiler

Compiled 3383 to 2315 computations (31.6% saved)

simplify145.0ms (1.7%)

Algorithm
egg-herbie
Rules
439×fma-def_binary64
370×associate-/l*_binary64
341×div-sub_binary64
294×times-frac_binary64
287×fma-neg_binary64
Counts
182 → 167
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03106185
18635064
236744925
349444925

prune74.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1625167
Fresh369
Picked101
Done011
Total16612178
Error
5.3b
Counts
178 → 12
Alt Table
StatusErrorProgram
50.6b
(/.f64 (fma.f64 b -2 (fma.f64 3/2 (/.f64 (*.f64 c a) b) (*.f64 9/8 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))))) (*.f64 3 a))
45.3b
(fma.f64 -2/3 (/.f64 b a) (*.f64 1/2 (/.f64 c b)))
45.2b
(*.f64 -2/3 (/.f64 b a))
46.0b
(/.f64 (-.f64 (/.f64 b -3/2) (/.f64 (/.f64 (*.f64 c a) b) -2)) a)
38.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
38.8b
(*.f64 (*.f64 1 (*.f64 c a)) (/.f64 (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) a))
36.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
39.0b
(*.f64 (*.f64 (cbrt.f64 (*.f64 1 (/.f64 (/.f64 (*.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) a))) (cbrt.f64 (*.f64 1 (/.f64 (/.f64 (*.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) a)))) (cbrt.f64 (*.f64 1 (/.f64 (/.f64 (*.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) a))))
36.4b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
46.5b
(/.f64 (neg.f64 c) (sqrt.f64 (*.f64 c (*.f64 a -3))))
39.0b
(*.f64 -1/2 (*.f64 1 (/.f64 c b)))
36.6b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b)) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
Compiler

Compiled 3052 to 1767 computations (42.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
0.4b
(/.f64 1/3 a)
0.5b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
26.6b
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))

rewrite98.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
5.3b
Rules
50×add-sqr-sqrt_binary64
40×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
19×times-frac_binary64
18×prod-diff_binary64
Counts
4 → 128
Calls

4 calls:

8.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
6.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
2.0ms
(/.f64 1/3 a)
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))
Compiler

Compiled 3177 to 1695 computations (46.6% saved)

series130.0ms (1.5%)

Error
5.3b
Counts
4 → 51
Calls

4 calls:

44.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
34.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))
32.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
6.0ms
(/.f64 1/3 a)
Compiler

Compiled 2293 to 1641 computations (28.4% saved)

simplify197.0ms (2.3%)

Algorithm
egg-herbie
Rules
546×fma-neg_binary64
355×distribute-rgt-in_binary64
334×distribute-lft-in_binary64
228×cancel-sign-sub-inv_binary64
149×distribute-rgt-neg-in_binary64
Counts
179 → 116
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02614289
16203342
221263309
346093309
449903309
549953309
648733309

prune51.0ms (0.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1142116
Fresh2810
Picked101
Done011
Total11711128
Error
5.3b
Counts
128 → 11
Alt Table
StatusErrorProgram
45.2b
(*.f64 -2/3 (/.f64 b a))
46.0b
(/.f64 (-.f64 (/.f64 b -3/2) (/.f64 (/.f64 (*.f64 c a) b) -2)) a)
38.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
38.8b
(*.f64 (*.f64 1 (*.f64 c a)) (/.f64 (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -3)))))) a))
46.0b
(*.f64 (/.f64 1/3 a) (fma.f64 3/2 (/.f64 (*.f64 a c) b) (*.f64 b -2)))
36.4b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
45.3b
(fma.f64 -2/3 (/.f64 b a) (*.f64 1/2 (/.f64 c b)))
46.5b
(/.f64 (neg.f64 c) (sqrt.f64 (*.f64 c (*.f64 a -3))))
39.0b
(*.f64 -1/2 (*.f64 1 (/.f64 c b)))
36.6b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b)) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
35.3b
(/.f64 (*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0)) (*.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))))
Compiler

Compiled 1573 to 940 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0))
0.7b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))
15.1b
(/.f64 (*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0)) (*.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))))
26.6b
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))

rewrite88.0ms (1%)

Algorithm
rewrite-expression-head
Error
5.3b
Rules
18×add-cbrt-cube_binary64
18×add-exp-log_binary64
11×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
4 → 83
Calls

4 calls:

11.0ms
(/.f64 (*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0)) (*.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))))
7.0ms
(*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0))
3.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))
Compiler

Compiled 2733 to 1726 computations (36.8% saved)

series156.0ms (1.8%)

Error
5.3b
Counts
4 → 57
Calls

4 calls:

48.0ms
(/.f64 (*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0)) (*.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))))
42.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))
38.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))
12.0ms
(*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0))
Compiler

Compiled 3170 to 2235 computations (29.5% saved)

simplify126.0ms (1.5%)

Algorithm
egg-herbie
Rules
890×fma-def_binary64
491×times-frac_binary64
273×associate-/l*_binary64
233×div-sub_binary64
208×associate-/r*_binary64
Counts
140 → 121
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02513640
17332902
233642832
349972832
449152832

prune57.0ms (0.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1192121
Fresh189
Picked011
Done011
Total12012132
Error
5.3b
Counts
132 → 12
Alt Table
StatusErrorProgram
39.0b
(expm1.f64 (log1p.f64 (*.f64 (/.f64 a a) (/.f64 (neg.f64 c) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))))))))
46.0b
(/.f64 (-.f64 (/.f64 b -3/2) (/.f64 (/.f64 (*.f64 c a) b) -2)) a)
45.2b
(*.f64 -2/3 (/.f64 b a))
39.0b
(*.f64 -1/2 (*.f64 1 (/.f64 c b)))
34.0b
(*.f64 (/.f64 a a) (/.f64 (neg.f64 c) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -3)))))))
46.0b
(*.f64 (/.f64 1/3 a) (fma.f64 3/2 (/.f64 (*.f64 a c) b) (*.f64 b -2)))
36.4b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
45.3b
(fma.f64 -2/3 (/.f64 b a) (*.f64 1/2 (/.f64 c b)))
46.5b
(/.f64 (neg.f64 c) (sqrt.f64 (*.f64 c (*.f64 a -3))))
36.6b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b)) (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
35.3b
(/.f64 (*.f64 1/3 (+.f64 (*.f64 a (*.f64 c -3)) 0)) (*.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))))
38.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -3)))) b))) (*.f64 3 a))
Compiler

Compiled 2047 to 1206 computations (41.1% saved)

regimes3.9s (44.3%)

Accuracy

Total 2.6b remaining (31.7%)

Threshold costs 0b (0%)

Compiler

Compiled 19016 to 12957 computations (31.9% saved)

bsearch109.0ms (1.2%)

Steps
ItersRangePoint
9
3.141714220724109e-33
8.777455439125919e-27
8.64278930394556e-27
10
-1.9869470002003814e-261
-3.0257799085203566e-279
-4.0088356050405405e-270
7
-2.2955636927496068e+144
-1.2381088262704627e+143
-1.0187968088253477e+144
Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
04189
15987
27087
37887
48587
59087
69387
79487
89487

end1.0ms (0%)

Compiler

Compiled 62 to 39 computations (37.1% saved)

sample1.7s (19.8%)

Algorithm
intervals
Results
372.0ms1137×body2048valid
358.0ms5128×body128valid
186.0ms747×body1024valid
151.0ms398×body4096valid
74.0ms404×body512valid
54.0ms709×body128nan
28.0ms443×body128invalid
22.0ms186×body256valid
Compiler

Compiled 302 to 207 computations (31.5% saved)

Profiling

Loading profile data...