Details

Time bar (total: 5.1s)

analyze917.0ms (18.1%)

Algorithm
1×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
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample41.0ms (0.8%)

Algorithm
1×intervals
Results
8.0ms36×body2048valid
7.0ms160×body128valid
5.0ms16×body4096valid
4.0ms24×body1024valid
2.0ms14×body512valid
1.0ms21×body128nan
0.0ms6×body256valid
0.0ms10×body128invalid
Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify73.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
379×associate-/l*_binary64
363×div-sub_binary64
224×times-frac_binary64
196×distribute-rgt-in_binary64
168×cancel-sign-sub-inv_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01120
12218
23718
36118
49318
515118
622918
730818
843318
941218
1064918
1198918
1284318
1374518
1475318
1576118
1676318
1777118
1880718
1980918
2071418

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
36.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶36.7b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
Compiler

Compiled 45 to 27 computations (40% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
0.3b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
1.0b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
24.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite184.0ms (3.6%)

Algorithm
1×rewrite-expression-head
Error
36.5b
Rules
38×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
18×times-frac_binary64
17×add-cube-cbrt_binary64
10×difference-of-squares_binary64
Counts
4 → 86
Calls

4 calls:

17.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
6.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 1749 to 313 computations (82.1% saved)

series202.0ms (4%)

Error
5.8b
Counts
4 → 64
Calls

4 calls:

53.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
51.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
42.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
35.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 2200 to 1483 computations (32.6% saved)

simplify155.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
463×associate-*l*_binary64
442×associate-*r*_binary64
425×times-frac_binary64
300×associate-/l*_binary64
222×associate-/r*_binary64
Counts
150 → 72
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01812956
14372800
211282794
348192794
449862794
549552794

prune44.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New64872
Fresh000
Picked011
Done000
Total64973
Error
7.5b
Counts
73 → 9
Alt Table
StatusErrorProgram
37.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
47.7b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (+.f64 (*.f64 a c) (*.f64 b_2 b_2))) (+.f64 b_2 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) a)
44.6b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
✓36.7b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
42.2b
(+.f64 (*.f64 1/2 (/.f64 c b_2)) (*.f64 -2 (/.f64 b_2 a)))
42.1b
(/.f64 (*.f64 b_2 -2) a)
49.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
45.6b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b_2) -1/2) a)
▶36.9b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
Compiler

Compiled 1041 to 387 computations (62.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.0b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
24.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
24.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite56.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Error
7.5b
Rules
8×add-log-exp_binary64 add-sqr-sqrt_binary64
6×pow1_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 diff-log_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64
Counts
4 → 54
Calls

4 calls:

4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
Compiler

Compiled 1775 to 280 computations (84.2% saved)

series200.0ms (3.9%)

Error
7.5b
Counts
4 → 72
Calls

4 calls:

51.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
50.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
42.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
40.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 3995 to 2336 computations (41.5% saved)

simplify100.0ms (2%)

Algorithm
1×egg-herbie
Rules
492×cancel-sign-sub-inv_binary64
392×neg-mul-1_binary64
383×unswap-sqr_binary64
345×distribute-rgt-neg-in_binary64
342×distribute-lft-neg-in_binary64
Counts
126 → 74
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0751742
11761646
25331646
322741646
444621646
550121646

prune36.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New74074
Fresh077
Picked011
Done011
Total74983
Error
7.5b
Counts
83 → 9
Alt Table
StatusErrorProgram
▶37.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
47.7b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (+.f64 (*.f64 a c) (*.f64 b_2 b_2))) (+.f64 b_2 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) a)
44.6b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
✓36.7b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
42.2b
(+.f64 (*.f64 1/2 (/.f64 c b_2)) (*.f64 -2 (/.f64 b_2 a)))
42.1b
(/.f64 (*.f64 b_2 -2) a)
49.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
45.6b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b_2) -1/2) a)
✓36.9b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
Compiler

Compiled 1407 to 422 computations (70% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
24.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
24.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
24.8b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

rewrite55.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Error
7.5b
Rules
10×add-sqr-sqrt_binary64
9×sqrt-prod_binary64
7×pow1_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
6×add-log-exp_binary64 sqrt-div_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 flip--_binary64
Counts
4 → 57
Calls

4 calls:

4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
4.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 2503 to 324 computations (87.1% saved)

series209.0ms (4.1%)

Error
7.5b
Counts
4 → 69
Calls

4 calls:

49.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
48.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
48.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
43.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
Compiler

Compiled 5686 to 2557 computations (55% saved)

simplify104.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
492×cancel-sign-sub-inv_binary64
392×neg-mul-1_binary64
383×unswap-sqr_binary64
345×distribute-rgt-neg-in_binary64
342×distribute-lft-neg-in_binary64
Counts
126 → 62
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0721832
11691748
25191748
322421676
444501676
550001676

prune33.0ms (0.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New62062
Fresh066
Picked011
Done022
Total62971
Error
7.5b
Counts
71 → 9
Alt Table
StatusErrorProgram
✓37.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
47.7b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (+.f64 (*.f64 a c) (*.f64 b_2 b_2))) (+.f64 b_2 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) a)
44.6b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
✓36.7b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
42.2b
(+.f64 (*.f64 1/2 (/.f64 c b_2)) (*.f64 -2 (/.f64 b_2 a)))
▶42.1b
(/.f64 (*.f64 b_2 -2) a)
49.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
45.6b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b_2) -1/2) a)
✓36.9b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
Compiler

Compiled 1789 to 435 computations (75.7% saved)

localize3.0ms (0.1%)

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Error
7.5b
Counts
0 → 0
Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error
7.5b
Counts
0 → 0
Compiler

Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune11.0ms (0.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New000
Fresh055
Picked011
Done033
Total099
Error
7.5b
Counts
9 → 9
Alt Table
StatusErrorProgram
37.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
47.7b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (+.f64 (*.f64 a c) (*.f64 b_2 b_2))) (+.f64 b_2 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))) a)
44.6b
(-.f64 (*.f64 -1/2 (/.f64 c b_2)) (*.f64 1/8 (/.f64 (*.f64 a (*.f64 c c)) (pow.f64 b_2 3))))
36.7b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
42.2b
(+.f64 (*.f64 1/2 (/.f64 c b_2)) (*.f64 -2 (/.f64 b_2 a)))
42.1b
(/.f64 (*.f64 b_2 -2) a)
49.1b
(/.f64 (-.f64 (sqrt.f64 (*.f64 b_2 b_2)) b_2) a)
45.6b
(/.f64 (*.f64 (/.f64 (*.f64 a c) b_2) -1/2) a)
36.9b
(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a))
Compiler

Compiled 175 to 89 computations (49.1% saved)

regimes1.3s (25.2%)

Accuracy

Total 2.5b remaining (25.9%)

Threshold costs 0b (0%)

Compiler

Compiled 8160 to 3974 computations (51.3% saved)

bsearch51.0ms (1%)

Steps
ItersRangePoint
6
5.0337545184383354e-55
6.238774800596405e-54
5.313037846592979e-55
10
-2.52965797221882e+87
-1.6013799237756217e+72
-2.0885454230623933e+87
Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
11×*-commutative_binary64
9×sub-neg_binary64 +-commutative_binary64
6×neg-mul-1_binary64 neg-sub0_binary64
4×cancel-sign-sub-inv_binary64 distribute-rgt-neg-in_binary64
3×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02853
14853
26653
37953
48753
58953
68753

end2.0ms (0%)

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample1.3s (24.8%)

Algorithm
1×intervals
Results
233.0ms1120×body2048valid
233.0ms5236×body128valid
114.0ms705×body1024valid
103.0ms399×body4096valid
41.0ms346×body512valid
35.0ms815×body128nan
15.0ms194×body256valid
11.0ms259×body128invalid
Compiler

Compiled 234 to 127 computations (45.7% saved)

Profiling

Loading profile data...