Details

Time bar (total: 8.4s)

analyze1.1s (12.6%)

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
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.4s (29.2%)

Results
744.0ms5425×body128valid
625.0ms1146×body2048valid
325.0ms747×body1024valid
267.0ms402×body4096valid
154.0ms1081×body128invalid
115.0ms351×body512valid
43.0ms185×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify145.0ms (1.7%)

Algorithm
egg-herbie
Rules
2079×fma-neg_binary64
1006×fma-def_binary64
919×div-sub_binary64
626×distribute-rgt-in_binary64
435×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01526
13824
29524
322722
435722
561422
6110322
7137322
8163622
9233022
10318722
11288022
12282722
13289622
14292222
15379722
16482422
17524022

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
33.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
33.2b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
Compiler

Compiled 75 to 50 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
1.2b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
25.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series189.0ms (2.3%)

Counts
4 → 96
Calls

4 calls:

79.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
55.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
42.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
13.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))

rewrite43.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt_binary64
62×*-un-lft-identity_binary64
61×prod-diff_binary64
50×add-cube-cbrt_binary64
39×sqrt-prod_binary64
Counts
4 → 162
Calls

4 calls:

11.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
10.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
3.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
3.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))

simplify194.0ms (2.3%)

Algorithm
egg-herbie
Rules
855×fma-neg_binary64
335×cancel-sign-sub-inv_binary64
185×associate-*r*_binary64
176×unswap-sqr_binary64
170×sub-neg_binary64
Counts
258 → 277
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03158609
18106489
229855417
348245409
451965409

prune272.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New26413277
Fresh000
Picked101
Done000
Total26513278
Error
7.5b
Counts
278 → 13
Alt Table
StatusErrorProgram
41.5b
(neg.f64 (/.f64 c b))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
33.3b
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
52.9b
(/.f64 (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 -4 (/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5)))) (*.f64 2 a))
38.5b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a))
57.5b
(/.f64 (-.f64 (neg.f64 b) (neg.f64 b)) (*.f64 2 a))
33.8b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (/.f64 (*.f64 2 a) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))))
33.3b
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (/.f64 1/2 a))
40.9b
(/.f64 (-.f64 (neg.f64 b) (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))) (*.f64 2 a))
39.4b
(/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (*.f64 2 a))
43.7b
(/.f64 (neg.f64 b) a)
44.3b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 -16 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 4)) (fma.f64 4 (*.f64 c a) (*.f64 b b))))) (*.f64 2 a))
35.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) 2) (/.f64 (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) a))
Compiler

Compiled 10400 to 5561 computations (46.5% saved)

localize11.0ms (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 4 (*.f64 a c))))) (/.f64 1/2 a))
1.2b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
25.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series77.0ms (0.9%)

Counts
1 → 20
Calls

1 calls:

77.0ms
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (/.f64 1/2 a))

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
13×associate-*r*_binary64
13×*-un-lft-identity_binary64
10×times-frac_binary64
add-cube-cbrt_binary64
Counts
1 → 42
Calls

1 calls:

13.0ms
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (/.f64 1/2 a))

simplify119.0ms (1.4%)

Algorithm
egg-herbie
Rules
694×times-frac_binary64
404×fma-neg_binary64
347×fma-def_binary64
286×distribute-rgt-in_binary64
124×distribute-rgt-neg-out_binary64
Counts
62 → 91
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01601900
14371745
216101658
345751656
449941656
549991656
649261656

prune230.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2943297
Fresh5712
Picked011
Done000
Total29911310
Error
7.4b
Counts
310 → 11
Alt Table
StatusErrorProgram
36.7b
(/.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
33.3b
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (/.f64 1/2 a))
41.5b
(neg.f64 (/.f64 c b))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
33.3b
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
35.5b
(*.f64 (*.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
38.5b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a))
57.5b
(/.f64 (-.f64 (neg.f64 b) (neg.f64 b)) (*.f64 2 a))
39.4b
(/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (*.f64 2 a))
43.7b
(/.f64 (neg.f64 b) a)
35.2b
(*.f64 (*.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
Compiler

Compiled 10676 to 5738 computations (46.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
1.2b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
25.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series77.0ms (0.9%)

Counts
1 → 20
Calls

1 calls:

77.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
67×times-frac_binary64
39×*-un-lft-identity_binary64
39×add-sqr-sqrt_binary64
23×add-cube-cbrt_binary64
22×add-exp-log_binary64
Counts
1 → 82
Calls

1 calls:

12.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))

simplify152.0ms (1.8%)

Algorithm
egg-herbie
Rules
655×associate-/l*_binary64
318×fma-def_binary64
303×fma-neg_binary64
268×associate-/r/_binary64
191×distribute-rgt-in_binary64
Counts
102 → 123
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01743540
14343295
215323091
346893085
449973085
549973085
649233085

prune261.0ms (3.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3263329
Fresh279
Picked011
Done011
Total32812340
Error
7.4b
Counts
340 → 12
Alt Table
StatusErrorProgram
38.5b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a))
47.8b
(cbrt.f64 (pow.f64 (*.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) (/.f64 1/2 a)) 3))
36.7b
(/.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
33.3b
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (/.f64 1/2 a))
41.5b
(neg.f64 (/.f64 c b))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
33.3b
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
35.5b
(*.f64 (*.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
57.5b
(/.f64 (-.f64 (neg.f64 b) (neg.f64 b)) (*.f64 2 a))
39.4b
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))))))
43.7b
(/.f64 (neg.f64 b) a)
43.8b
(/.f64 1 (/.f64 (*.f64 2 a) (*.f64 b -2)))
Compiler

Compiled 12530 to 7013 computations (44% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 a)
0.7b
(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))
1.0b
(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
13.8b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series211.0ms (2.5%)

Counts
4 → 26
Calls

4 calls:

155.0ms
(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))
35.0ms
(cbrt.f64 a)
20.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))
0.0ms
(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
40×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
30×prod-diff_binary64
19×cbrt-prod_binary64
Counts
4 → 130
Calls

4 calls:

5.0ms
(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))
4.0ms
(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
3.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))
1.0ms
(cbrt.f64 a)

simplify143.0ms (1.7%)

Algorithm
egg-herbie
Rules
759×fma-neg_binary64
356×associate-/l*_binary64
352×fma-def_binary64
283×associate-/r*_binary64
248×*-commutative_binary64
Counts
156 → 188
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02213676
14292633
212962187
341312178
449712178
549792178
648722178

prune194.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2213224
Fresh369
Picked101
Done022
Total22511236
Error
3.7b
Counts
236 → 11
Alt Table
StatusErrorProgram
38.5b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a))
47.8b
(cbrt.f64 (pow.f64 (*.f64 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) (/.f64 1/2 a)) 3))
36.7b
(/.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
33.3b
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (/.f64 1/2 a))
41.5b
(neg.f64 (/.f64 c b))
44.0b
(-.f64 (/.f64 c b) (/.f64 b a))
33.3b
(/.f64 1 (/.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
35.6b
(*.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (cbrt.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
49.0b
(*.f64 (*.f64 (-.f64 (neg.f64 b) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
44.3b
(*.f64 (*.f64 (*.f64 -2 b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
43.8b
(/.f64 1 (/.f64 (*.f64 2 a) (*.f64 b -2)))
Compiler

Compiled 9528 to 5925 computations (37.8% saved)

regimes2.1s (25.5%)

Accuracy

Total 6.7b remaining (69.4%)

Threshold costs 0b (0%)

Counts
170 → 4
Compiler

Compiled 16817 to 11690 computations (30.5% saved)

bsearch121.0ms (1.5%)

Steps
ItersRangePoint
9
4130001314661275600.0
2.823573165476186e+24
2.4148286761692006e+24
7
-3.79665096160999e-118
-2.2357728299447292e-119
-2.2556714692887474e-119
6
-2.5493285277707463e+134
-2.0170402562964358e+133
-2.049220194580872e+133
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
04093
16289
28489
310289
411489
512089
612289
711989

end177.0ms (2.1%)

Compiler

Compiled 381 to 257 computations (32.5% saved)

Profiling

Loading profile data...