Details

Time bar (total: 7.8s)

analyze709.0ms (9.1%)

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
0%99.9%0.1%5
18.7%81.1%0.1%6
26.5%67.1%6.4%7
35.1%58.5%6.4%8
41.3%49.9%8.7%9
46.4%40.2%13.4%10
50.8%34.2%15%11
55.2%26.7%18.1%12
57.4%22%20.6%13
59.8%17.9%22.3%14
Compiler

Compiled 42 to 27 computations (35.7% saved)

sample1.8s (22.9%)

Results
1.5s8256×body128valid
181.0ms1070×body128invalid
Compiler

Compiled 125 to 80 computations (36% saved)

simplify155.0ms (2%)

Algorithm
egg-herbie
Rules
1753×fma-neg_binary64
1288×fma-def_binary64
631×div-sub_binary64
512×times-frac_binary64
430×associate-/l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02258
14752
211852
326950
442950
574350
6131550
7173850
8217650
9285350
10406650
11352350
12357550
13354350
14355750
15451050
16462250
17476150

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
18.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
18.0b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
18.3b
(if (>=.f64 b 0) (*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)) (/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
Compiler

Compiled 231 to 143 computations (38.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.8b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
2.7b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series175.0ms (2.2%)

Counts
4 → 96
Calls

4 calls:

59.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
58.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
11.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite39.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
61×prod-diff_binary64
59×*-un-lft-identity_binary64
56×add-sqr-sqrt_binary64
51×add-cube-cbrt_binary64
37×sqrt-prod_binary64
Counts
4 → 155
Calls

4 calls:

9.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
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))

simplify208.0ms (2.7%)

Algorithm
egg-herbie
Rules
413×fma-neg_binary64
345×cancel-sign-sub-inv_binary64
235×exp-prod_binary64
216×distribute-rgt-neg-in_binary64
177×distribute-lft-neg-in_binary64
Counts
251 → 246
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02498106
16136063
221194942
344064869
448704869
548254869

prune495.0ms (6.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3216327
Fresh101
Picked101
Done000
Total3236329
Error
5.7b
Counts
329 → 6
Alt Table
StatusErrorProgram
35.7b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))))
27.6b
(if (>=.f64 b 0) (/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
18.1b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
20.6b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
18.6b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
20.0b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
Compiler

Compiled 18215 to 10508 computations (42.3% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.8b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
14.4b
(-.f64 (neg.f64 b) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
24.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series63.0ms (0.8%)

Counts
1 → 20
Calls

1 calls:

62.0ms
(-.f64 (neg.f64 b) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

rewrite7.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×fma-neg_binary64
10×prod-diff_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
1 → 37
Calls

1 calls:

4.0ms
(-.f64 (neg.f64 b) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify84.0ms (1.1%)

Algorithm
egg-herbie
Rules
753×times-frac_binary64
598×fma-neg_binary64
365×fma-def_binary64
347×associate-*l*_binary64
299×associate-/l*_binary64
Counts
57 → 80
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01271859
13641481
210831264
350001262
453921262

prune591.0ms (7.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3640364
Fresh055
Picked011
Done000
Total3646370
Error
5.7b
Counts
370 → 6
Alt Table
StatusErrorProgram
35.7b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))))
27.6b
(if (>=.f64 b 0) (/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
18.1b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
20.6b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
18.6b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
20.0b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) b) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
Compiler

Compiled 21892 to 12798 computations (41.5% saved)

localize21.0ms (0.3%)

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))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.7b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series81.0ms (1%)

Counts
1 → 20
Calls

1 calls:

81.0ms
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
associate-/l*_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
1 → 34
Calls

1 calls:

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

simplify74.0ms (0.9%)

Algorithm
egg-herbie
Rules
791×times-frac_binary64
461×associate-/l*_binary64
352×fma-neg_binary64
324×fma-def_binary64
167×distribute-rgt-in_binary64
Counts
54 → 71
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01371675
13951518
213491451
348901449
450891449

prune393.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2733276
Fresh224
Picked101
Done011
Total2766282
Error
5.7b
Counts
282 → 6
Alt Table
StatusErrorProgram
35.7b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))))
27.6b
(if (>=.f64 b 0) (/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
20.6b
(if (>=.f64 b 0) (-.f64 (/.f64 c b) (/.f64 b a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
20.6b
(if (>=.f64 b 0) (*.f64 -1 (/.f64 b a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
18.7b
(if (>=.f64 b 0) (*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (/.f64 1/2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
18.1b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
Compiler

Compiled 13961 to 8336 computations (40.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (/.f64 1/2 a))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.7b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series92.0ms (1.2%)

Counts
1 → 20
Calls

1 calls:

92.0ms
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (/.f64 1/2 a))

rewrite15.0ms (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:

11.0ms
(*.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (/.f64 1/2 a))

simplify83.0ms (1.1%)

Algorithm
egg-herbie
Rules
694×times-frac_binary64
396×fma-neg_binary64
350×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
14421745
216151658
345831656
449261656

prune602.0ms (7.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2951296
Fresh134
Picked101
Done011
Total2975302
Error
5.7b
Counts
302 → 5
Alt Table
StatusErrorProgram
28.2b
(if (>=.f64 b 0) (*.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) (/.f64 1/2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
20.6b
(if (>=.f64 b 0) (-.f64 (/.f64 c b) (/.f64 b a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
35.7b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))))
20.6b
(if (>=.f64 b 0) (*.f64 -1 (/.f64 b a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (*.f64 -1 b))))
18.1b
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
Compiler

Compiled 14592 to 8711 computations (40.3% saved)

regimes1.8s (23.4%)

Accuracy

Total 0.9b remaining (14.9%)

Threshold costs 0.9b (14.9%)

Counts
162 → 5
Compiler

Compiled 24290 to 16698 computations (31.3% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify15.0ms (0.2%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
046466
163448
291448
3107448
4121448
5127448
6128448
7125448

end193.0ms (2.5%)

Compiler

Compiled 778 to 466 computations (40.1% saved)

Profiling

Loading profile data...