Details

Time bar (total: 8.3s)

analyze262.0ms (3.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 30 to 24 computations (20% saved)

sample38.0ms (0.5%)

Algorithm
1×intervals
Results
9.0ms293×pre128true
9.0ms89×body256valid
8.0ms167×body128valid
2.0ms37×body128nan
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify238.0ms (2.9%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
092724
192724

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 42.2b

Counts
2 → 1
Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
37.8b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite42.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_79
10×add-log-exp_binary64_118
9×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
8×add-sqr-sqrt_binary64_101
7×add-cube-cbrt_binary64_114
6×distribute-lft-out_binary64_30
5×times-frac_binary64_85 associate-/l*_binary64_24 pow1_binary64_140
3×sqrt-prod_binary64_95 distribute-rgt-neg-in_binary64_37
2×cbrt-undiv_binary64_113 div-exp_binary64_130 neg-sub0_binary64_74 flip-+_binary64_53 sum-log_binary64_170 associate-+l-_binary64_14 flip--_binary64_54 sqrt-div_binary64_96 flip3--_binary64_83 associate-/l/_binary64_26 flip3-+_binary64_82
1×associate-/r*_binary64_23 div-sub_binary64_84 div-inv_binary64_76 neg-log_binary64_172 +-commutative_binary64_9 cbrt-unprod_binary64_112 prod-exp_binary64_128 rem-sqrt-square_binary64_92 sqrt-pow1_binary64_97 diff-log_binary64_171 clear-num_binary64_78 pow1/2_binary64_159 cancel-sign-sub-inv_binary64_45 sub-neg_binary64_72 frac-2neg_binary64_90
Counts
4 → 70
Calls

4 calls:

14.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
10.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series554.0ms (6.7%)

Counts
4 → 12
Calls

4 calls:

223.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
137.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
129.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
66.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify56.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
052901826

prune131.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.3b

Counts
83 → 3
Compiler

Compiled 2536 to 1594 computations (37.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.2b
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.3b
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite66.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
45×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
34×times-frac_binary64_85
32×add-sqr-sqrt_binary64_101 *-un-lft-identity_binary64_79
17×cbrt-undiv_binary64_113 div-exp_binary64_130
14×associate-/l*_binary64_24
13×cbrt-unprod_binary64_112 prod-exp_binary64_128
12×add-cube-cbrt_binary64_114
10×distribute-lft-out--_binary64_31 difference-of-squares_binary64_48 add-log-exp_binary64_118
8×sqrt-prod_binary64_95 associate-/r*_binary64_23
7×cancel-sign-sub-inv_binary64_45
6×associate-/r/_binary64_25
5×flip--_binary64_54 distribute-rgt-neg-in_binary64_37 flip3--_binary64_83
4×div-inv_binary64_76 pow1_binary64_140
3×diff-log_binary64_171
2×clear-num_binary64_78 sub-neg_binary64_72 frac-2neg_binary64_90
1×associate--l-_binary64_17 neg-sub0_binary64_74 neg-log_binary64_172 associate-/l/_binary64_26
Counts
4 → 122
Calls

4 calls:

19.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
16.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series952.0ms (11.5%)

Counts
4 → 12
Calls

4 calls:

420.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
327.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
137.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
68.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify88.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049504144
149504144

prune525.0ms (6.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1259134
Fresh202
Picked101
Done000
Total1289137

Merged error: 0.0b

Counts
137 → 9
Compiler

Compiled 11500 to 7579 computations (34.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.2b
(/.f64 (*.f64 (*.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) (*.f64 2 a))
0.3b
(*.f64 (*.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))

rewrite88.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
61×add-sqr-sqrt_binary64_101 *-un-lft-identity_binary64_79
59×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
43×times-frac_binary64_85
29×add-cube-cbrt_binary64_114
27×associate-*r*_binary64_19
23×cbrt-unprod_binary64_112 prod-exp_binary64_128
17×cbrt-undiv_binary64_113 div-exp_binary64_130
16×distribute-lft-out--_binary64_31 difference-of-squares_binary64_48
11×sqrt-prod_binary64_95
9×pow1_binary64_140
8×associate-/r*_binary64_23 distribute-rgt-neg-in_binary64_37 add-log-exp_binary64_118
6×cancel-sign-sub-inv_binary64_45
4×associate-/l*_binary64_24 associate-/r/_binary64_25
3×div-inv_binary64_76 flip--_binary64_54 pow-prod-down_binary64_150 flip3--_binary64_83
2×associate-*r/_binary64_21 diff-log_binary64_171 clear-num_binary64_78 frac-2neg_binary64_90
1×associate-*l*_binary64_20 associate--l-_binary64_17 neg-sub0_binary64_74 neg-log_binary64_172 *-commutative_binary64_10 associate-/l/_binary64_26 sub-neg_binary64_72
Counts
4 → 149
Calls

4 calls:

20.0ms
(/.f64 (*.f64 (*.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) (*.f64 2 a))
20.0ms
(*.f64 (*.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
12.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))

series1.2s (14.8%)

Counts
4 → 12
Calls

4 calls:

408.0ms
(*.f64 (*.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
360.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
323.0ms
(/.f64 (*.f64 (*.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) (*.f64 2 a))
137.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))

simplify91.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049064609
149064609

prune354.0ms (4.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1592161
Fresh178
Picked011
Done000
Total16010170

Merged error: 0b

Counts
170 → 10
Compiler

Compiled 7863 to 4862 computations (38.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.2b
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a)
0.3b
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a))

rewrite129.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
330×times-frac_binary64_85
255×add-sqr-sqrt_binary64_101 *-un-lft-identity_binary64_79
151×add-cube-cbrt_binary64_114
85×associate-*r*_binary64_19
52×distribute-lft-out--_binary64_31 difference-of-squares_binary64_48
32×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
30×associate-/l*_binary64_24
29×sqrt-prod_binary64_95
26×distribute-rgt-neg-in_binary64_37
16×associate-/r/_binary64_25
10×associate-/r*_binary64_23 cbrt-undiv_binary64_113 div-exp_binary64_130 div-inv_binary64_76
9×flip--_binary64_54 cbrt-unprod_binary64_112 prod-exp_binary64_128 flip3--_binary64_83 pow1_binary64_140
8×add-log-exp_binary64_118
6×cancel-sign-sub-inv_binary64_45
3×pow-prod-down_binary64_150
2×diff-log_binary64_171 clear-num_binary64_78 frac-2neg_binary64_90
1×associate-*l*_binary64_20 associate--l-_binary64_17 neg-sub0_binary64_74 neg-log_binary64_172 associate-*r/_binary64_21 *-commutative_binary64_10 associate-/l/_binary64_26 sub-neg_binary64_72
Counts
4 → 303
Calls

4 calls:

34.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a))
22.0ms
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a)
12.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))

series1.3s (15.3%)

Counts
4 → 12
Calls

4 calls:

462.0ms
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a)
348.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
328.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a))
124.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))

simplify149.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
315 → 315
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0500011663

prune589.0ms (7.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3141315
Fresh358
Picked011
Done011
Total3178325

Merged error: 0b

Counts
325 → 8
Compiler

Compiled 13260 to 7097 computations (46.5% saved)

regimes65.0ms (0.8%)

Compiler

Compiled 639 to 492 computations (23% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08535
18535

end0.0ms (0%)

sample1.3s (15.7%)

Algorithm
1×intervals
Results
286.0ms2901×body256valid
274.0ms8922×pre128true
251.0ms5099×body128valid
42.0ms922×body128nan
Compiler

Compiled 264 to 203 computations (23.1% saved)

Profiling

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