Details

Time bar (total: 5.6s)

analyze271.0ms (4.8%)

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)

sample45.0ms (0.8%)

Algorithm
1×intervals
Results
11.0ms280×pre128true
10.0ms106×body256valid
8.0ms52×body512valid
5.0ms98×body128valid
1.0ms24×body128nan
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify220.0ms (3.9%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
092724
192724

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 51.2b

Counts
2 → 1
Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
24.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite38.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64_98
13×*-un-lft-identity_binary64_77
9×add-exp-log_binary64_112 add-cbrt-cube_binary64_110
8×add-log-exp_binary64_113
7×add-cube-cbrt_binary64_109
6×sqrt-prod_binary64_92 times-frac_binary64_83 associate-/l*_binary64_24 difference-of-squares_binary64_46
5×pow1_binary64_135
4×flip--_binary64_52 flip3--_binary64_81
3×distribute-lft-out--_binary64_31
2×cbrt-undiv_binary64_108 sqrt-div_binary64_93 sub-neg_binary64_70 div-exp_binary64_125 diff-log_binary64_166 associate-/l/_binary64_26
1×associate-/r*_binary64_23 rem-sqrt-square_binary64_90 sqrt-pow1_binary64_94 cbrt-unprod_binary64_107 div-sub_binary64_82 prod-exp_binary64_123 pow1/2_binary64_154 clear-num_binary64_76 frac-2neg_binary64_88 div-inv_binary64_74
Counts
4 → 70
Calls

4 calls:

13.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
9.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series521.0ms (9.2%)

Counts
4 → 12
Calls

4 calls:

209.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
131.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
119.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
63.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify101.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
048841963
148841963

prune97.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.2b

Counts
83 → 3
Compiler

Compiled 1979 to 1173 computations (40.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite52.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
45×add-exp-log_binary64_112 add-cbrt-cube_binary64_110
22×times-frac_binary64_83
20×*-un-lft-identity_binary64_77
17×cbrt-undiv_binary64_108 div-exp_binary64_125
13×cbrt-unprod_binary64_107 prod-exp_binary64_123
11×associate-/l*_binary64_24
10×add-cube-cbrt_binary64_109 add-sqr-sqrt_binary64_98
8×add-log-exp_binary64_113
6×associate-/r/_binary64_25
5×associate-/r*_binary64_23 distribute-lft-out_binary64_30
4×flip-+_binary64_51 flip3-+_binary64_80 pow1_binary64_135 div-inv_binary64_74
2×clear-num_binary64_76 frac-2neg_binary64_88
1×sub-neg_binary64_70 flip--_binary64_52 +-commutative_binary64_9 flip3--_binary64_81 diff-log_binary64_166 associate-/l/_binary64_26 sum-log_binary64_165
Counts
4 → 98
Calls

4 calls:

16.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
13.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
7.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series884.0ms (15.7%)

Counts
4 → 12
Calls

4 calls:

381.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
309.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
125.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
69.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify74.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049233030
149233030

prune158.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1028110
Fresh202
Picked101
Done000
Total1058113

Merged error: 0.0b

Counts
113 → 8
Compiler

Compiled 3258 to 2011 computations (38.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
0.1b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

rewrite32.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_77
15×add-sqr-sqrt_binary64_98
14×add-cube-cbrt_binary64_109
12×times-frac_binary64_83
8×add-log-exp_binary64_113
6×add-exp-log_binary64_112 add-cbrt-cube_binary64_110
5×pow1_binary64_135 distribute-lft-out_binary64_30
4×associate-/r*_binary64_23
3×sqrt-prod_binary64_92 associate-/l*_binary64_24
2×flip-+_binary64_51 sqrt-div_binary64_93 flip3-+_binary64_80 flip--_binary64_52 associate-/r/_binary64_25 flip3--_binary64_81
1×rem-sqrt-square_binary64_90 sqrt-pow1_binary64_94 cbrt-undiv_binary64_108 sub-neg_binary64_70 +-commutative_binary64_9 div-exp_binary64_125 pow1/2_binary64_154 clear-num_binary64_76 diff-log_binary64_166 frac-2neg_binary64_88 sum-log_binary64_165 div-inv_binary64_74
Counts
4 → 71
Calls

4 calls:

9.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
7.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))

series675.0ms (12%)

Counts
4 → 12
Calls

4 calls:

351.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
128.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
127.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
68.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

simplify82.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049141962
149141962

prune113.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New80383
Fresh257
Picked101
Done000
Total83891

Merged error: 0b

Counts
91 → 8
Compiler

Compiled 2372 to 1486 computations (37.4% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b
(+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.2b
(*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))
0.3b
(*.f64 c (*.f64 (*.f64 c a) 16))
0.5b
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))

rewrite50.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
29×add-exp-log_binary64_112 add-cbrt-cube_binary64_110
27×pow1_binary64_135
16×pow-prod-down_binary64_145 cbrt-unprod_binary64_107 prod-exp_binary64_123
14×add-cube-cbrt_binary64_109 *-un-lft-identity_binary64_77 add-sqr-sqrt_binary64_98
9×times-frac_binary64_83
6×associate-*l*_binary64_20 add-log-exp_binary64_113
3×associate-/r*_binary64_23 associate-/l*_binary64_24
2×flip-+_binary64_51 flip3-+_binary64_80 associate-/r/_binary64_25 *-commutative_binary64_10 associate-/l/_binary64_26 associate-*r*_binary64_19
1×cbrt-undiv_binary64_108 div-sub_binary64_82 flip--_binary64_52 +-commutative_binary64_9 div-exp_binary64_125 clear-num_binary64_76 flip3--_binary64_81 frac-2neg_binary64_88 sum-log_binary64_165 div-inv_binary64_74
Counts
4 → 88
Calls

4 calls:

12.0ms
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
11.0ms
(*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))
10.0ms
(*.f64 c (*.f64 (*.f64 c a) 16))
5.0ms
(+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

series317.0ms (5.6%)

Counts
4 → 12
Calls

4 calls:

165.0ms
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
59.0ms
(+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
53.0ms
(*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))
39.0ms
(*.f64 c (*.f64 (*.f64 c a) 16))

simplify66.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
050072422

prune160.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1000100
Fresh077
Picked011
Done000
Total1008108

Merged error: 0b

Counts
108 → 8
Compiler

Compiled 3894 to 2310 computations (40.7% saved)

regimes70.0ms (1.2%)

Compiler

Compiled 771 to 579 computations (24.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09645
19645

end0.0ms (0%)

sample1.5s (27.3%)

Algorithm
1×intervals
Results
384.0ms3781×body256valid
281.0ms8887×pre128true
212.0ms1440×body512valid
144.0ms2779×body128valid
44.0ms887×body128nan
Compiler

Compiled 315 to 236 computations (25.1% saved)

Profiling

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