Details

Time bar (total: 8.9s)

analyze634.0ms (7.2%)

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
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)

sample2.6s (29.7%)

Results
808.0ms5429×body128valid
634.0ms1153×body2048valid
541.0ms715×body1024valid
251.0ms396×body4096valid
141.0ms1110×body128invalid
118.0ms371×body512valid
43.0ms192×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify257.0ms (2.9%)

Algorithm
egg-herbie
Rules
1743×fma-neg_binary64
1393×fma-def_binary64
800×div-sub_binary64
619×times-frac_binary64
473×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13322
26722
313822
420422
533822
655822
792422
8138822
9160422
10237522
11274222
12253322
13262122
14317122
15331322
16387322
17367922
18402922
19431722
20448522
21456122
22480522
23479322
24479722
25479722
26494822

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
33.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
33.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize13.0ms (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 (*.f64 4 a) c)))) (*.f64 2 a))
0.4b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series211.0ms (2.4%)

Counts
4 → 96
Calls

4 calls:

82.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
70.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
47.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
11.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite29.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
10×fma-def_binary64
10×add-cube-cbrt_binary64
10×add-log-exp_binary64
Counts
4 → 90
Calls

4 calls:

9.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
8.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
3.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify122.0ms (1.4%)

Algorithm
egg-herbie
Rules
701×fma-neg_binary64
334×cancel-sign-sub-inv_binary64
215×distribute-rgt-neg-in_binary64
159×associate-*r*_binary64
150×distribute-rgt-neg-out_binary64
Counts
186 → 207
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02434208
16953858
225123724
346943704
450313704

prune174.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New19611207
Fresh011
Picked101
Done000
Total19712209
Error
6.1b
Counts
209 → 12
Alt Table
StatusErrorProgram
37.0b
(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (*.f64 2 a))
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
37.4b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
45.4b
(-.f64 (/.f64 c b) (/.f64 b a))
57.0b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
32.0b
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) 2) a)
33.9b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))))) (*.f64 2 a))
45.1b
(/.f64 (neg.f64 b) a)
42.5b
(neg.f64 (/.f64 c b))
45.0b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (*.f64 (*.f64 2 a) (+.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))))
32.2b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
47.3b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2)) 3))
Compiler

Compiled 5807 to 3399 computations (41.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) 2) a)
0.7b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
12.1b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series409.0ms (4.6%)

Counts
3 → 24
Calls

3 calls:

236.0ms
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) 2) a)
150.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
23.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite27.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
117×times-frac_binary64
93×*-un-lft-identity_binary64
93×add-sqr-sqrt_binary64
67×add-cube-cbrt_binary64
19×associate-/l*_binary64
Counts
3 → 141
Calls

3 calls:

8.0ms
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) 2) a)
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
3.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

simplify151.0ms (1.7%)

Algorithm
egg-herbie
Rules
545×fma-def_binary64
329×cancel-sign-sub-inv_binary64
324×fma-neg_binary64
299×neg-mul-1_binary64
289×div-sub_binary64
Counts
165 → 263
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03435821
18115233
226505137
343385132
449895132

prune235.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2594263
Fresh4711
Picked101
Done000
Total26411275
Error
2.8b
Counts
275 → 11
Alt Table
StatusErrorProgram
37.4b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
57.0b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
32.2b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
32.3b
(*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b) (sqrt.f64 2)) a))
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
45.1b
(/.f64 (neg.f64 b) a)
58.8b
(log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) 2) a)))
42.5b
(neg.f64 (/.f64 c b))
33.9b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))))) (*.f64 2 a))
32.8b
(/.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b)) (cbrt.f64 2))))
45.7b
(/.f64 (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b) 2) a)
Compiler

Compiled 8214 to 5218 computations (36.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)
0.2b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
0.7b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
12.1b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series728.0ms (8.2%)

Counts
2 → 16
Calls

2 calls:

490.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)
238.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))

rewrite48.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt_binary64
84×times-frac_binary64
69×*-un-lft-identity_binary64
56×sqrt-prod_binary64
49×add-cube-cbrt_binary64
Counts
2 → 138
Calls

2 calls:

21.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
7.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)

simplify178.0ms (2%)

Algorithm
egg-herbie
Rules
719×times-frac_binary64
381×associate-/l/_binary64
367×fma-neg_binary64
276×fma-def_binary64
186×associate-*r/_binary64
Counts
154 → 230
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02706206
17055899
220765685
346365491
449855491
549445491

prune361.0ms (4.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3960396
Fresh01010
Picked011
Done000
Total39611407
Error
2.8b
Counts
407 → 11
Alt Table
StatusErrorProgram
37.4b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
57.0b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
32.2b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
32.3b
(*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b) (sqrt.f64 2)) a))
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
45.1b
(/.f64 (neg.f64 b) a)
58.8b
(log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) 2) a)))
42.5b
(neg.f64 (/.f64 c b))
33.9b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))))) (*.f64 2 a))
32.8b
(/.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b)) (cbrt.f64 2))))
45.7b
(/.f64 (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b) 2) a)
Compiler

Compiled 16405 to 10648 computations (35.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b) (sqrt.f64 2))
0.7b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b)
1.0b
(/.f64 1 (sqrt.f64 2))
12.1b
(sqrt.f64 (*.f64 -4 (*.f64 c a)))

series357.0ms (4%)

Counts
4 → 24
Calls

4 calls:

190.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b) (sqrt.f64 2))
147.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b)
20.0ms
(sqrt.f64 (*.f64 -4 (*.f64 c a)))
0.0ms
(/.f64 1 (sqrt.f64 2))

rewrite25.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity_binary64
62×add-sqr-sqrt_binary64
48×times-frac_binary64
46×add-cube-cbrt_binary64
31×sqrt-prod_binary64
Counts
4 → 149
Calls

4 calls:

6.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b) (sqrt.f64 2))
4.0ms
(sqrt.f64 (*.f64 -4 (*.f64 c a)))
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b)
3.0ms
(/.f64 1 (sqrt.f64 2))

simplify126.0ms (1.4%)

Algorithm
egg-herbie
Rules
531×fma-def_binary64
427×fma-neg_binary64
365×associate-*l/_binary64
287×associate-/r/_binary64
274×cancel-sign-sub-inv_binary64
Counts
173 → 200
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02564592
15743985
218963899
346953895
448823895

prune168.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2000200
Fresh099
Picked011
Done011
Total20011211
Error
2.8b
Counts
211 → 11
Alt Table
StatusErrorProgram
37.4b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
57.0b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
32.2b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
32.3b
(*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b) (sqrt.f64 2)) a))
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
45.1b
(/.f64 (neg.f64 b) a)
58.8b
(log.f64 (exp.f64 (/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) 2) a)))
42.5b
(neg.f64 (/.f64 c b))
33.9b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 (*.f64 c a) -4 (*.f64 b b)))))) (*.f64 2 a))
32.8b
(/.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) b) b)) (cbrt.f64 2))))
45.7b
(/.f64 (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b) 2) a)
Compiler

Compiled 6762 to 4758 computations (29.6% saved)

regimes1.7s (18.9%)

Accuracy

Total 7.4b remaining (72.5%)

Threshold costs 0b (0%)

Counts
162 → 3
Compiler

Compiled 15461 to 11069 computations (28.4% saved)

bsearch89.0ms (1%)

Steps
ItersRangePoint
9
3.2067924523174545e-41
2.4190282902010186e-35
9.407427085893267e-41
8
-3.0054071990655414e+53
-7.973999190487984e+48
-2.9485189597382724e+53
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
02654
14452
26952
38152
48752
58852
68752

end168.0ms (1.9%)

Compiler

Compiled 313 to 214 computations (31.6% saved)

Profiling

Loading profile data...