Details

Time bar (total: 8.9s)

analyze259.0ms

Algorithm
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

sample36.0ms

Algorithm
intervals
Results
13.0ms146×body160valid
8.0ms278×pre80true
5.0ms110×body80valid
1.0ms22×body80nan

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (102.0ms)

IterNodesCost
092824
192824

prune4.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 28.2b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.2b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.2b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
28.1b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
9×add-exp-log_binary64 add-cbrt-cube_binary64
8×add-log-exp_binary64
7×add-cube-cbrt_binary64
6×difference-of-squares_binary64 associate-/l*_binary64 times-frac_binary64 sqrt-prod_binary64
5×pow1_binary64
4×flip3--_binary64 insert-posit16 flip--_binary64
3×distribute-lft-out--_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 div-exp_binary64 sqrt-div_binary64
1×associate-/r*_binary64 pow1/2_binary64 cbrt-unprod_binary64 sqrt-pow1_binary64 div-sub_binary64 rem-sqrt-square_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64
Counts
4 → 74
Calls
4 calls:
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
15.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
10.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

series2.0s

Counts
4 → 12
Calls
4 calls:
496.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
622.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
356.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
540.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
08641529
18641529
052391422
08641529
18641529
052391422
02211
12211
0735809
1735809
061184
161184
0735809
1735809
061184
161184
013
113
013492124
113492124
03661580
13661580
013492124
113492124
03661580
13661580
013
113
08131457
18131457
049451362
149451362
08131457
18131457
049451362
149451362
02211
12211

simplify162.0ms

Counts
86 → 86
Iterations

Useful iterations: 0 (133.0ms)

IterNodesCost
048951907
148951907

prune83.0ms

Filtered
64 candidates to 86 candidates (-34.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New83386
Fresh000
Picked101
Done000
Total84387

Merged error: 0.4b

Counts
87 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log_binary64 add-cbrt-cube_binary64
22×times-frac_binary64
20×*-un-lft-identity_binary64
17×cbrt-undiv_binary64 div-exp_binary64
13×cbrt-unprod_binary64 prod-exp_binary64
11×associate-/l*_binary64
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
8×add-log-exp_binary64
6×associate-/r/_binary64
5×associate-/r*_binary64 distribute-lft-out_binary64
4×flip3-+_binary64 pow1_binary64 div-inv_binary64 insert-posit16 flip-+_binary64
2×clear-num_binary64 frac-2neg_binary64
1×associate-/l/_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64
Counts
4 → 102
Calls
4 calls:
19.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 -4 c)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
6.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
8.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
15.0ms
(/.f64 (*.f64 a (*.f64 -4 c)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
758.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 -4 c)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
352.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
535.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
686.0ms
(/.f64 (*.f64 a (*.f64 -4 c)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
014352300
114352300
055941597
014352300
114352300
055941597
013
113
08641529
18641529
051201422
08641529
18641529
051201422
02211
12211
0735809
1735809
061184
161184
0735809
1735809
061184
161184
013
113
018862918
118862918
03551586
13551586
018862918
118862918
03551586
13551586
013
113

simplify80.0ms

Counts
114 → 114
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
052122973

prune132.0ms

Filtered
76 candidates to 114 candidates (-50.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1068114
Fresh202
Picked101
Done000
Total1098117

Merged error: 0b

Counts
117 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.2b
(*.f64 (*.f64 -4 c) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
0.2b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.3b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity_binary64
24×times-frac_binary64
21×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
18×associate-*r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
9×pow1_binary64
8×add-log-exp_binary64 distribute-lft-out_binary64
6×cbrt-unprod_binary64 prod-exp_binary64
4×associate-/r*_binary64 associate-/r/_binary64 insert-posit16
3×pow-prod-down_binary64 flip3-+_binary64 cbrt-undiv_binary64 associate-/l*_binary64 div-exp_binary64 flip-+_binary64
2×div-inv_binary64
1×sub-neg_binary64 flip3--_binary64 diff-log_binary64 associate-*r/_binary64 associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 98
Calls
4 calls:
10.0ms
(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
16.0ms
(*.f64 (*.f64 -4 c) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
8.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))

series2.8s

Counts
4 → 12
Calls
4 calls:
721.0ms
(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
932.0ms
(*.f64 (*.f64 -4 c) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
622.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
568.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
08601574
18601574
051511422
08601574
18601574
051511422
02211
12211
0731825
1731825
04921493
14921493
0731825
1731825
04921493
14921493
013
113
014552284
114552284
048021497
148021497
014552284
114552284
048021497
148021497
013
113
013082099
113082099
020108
120108
013082099
113082099
020108
120108
013
113

simplify98.0ms

Counts
110 → 110
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
053072544

prune120.0ms

Filtered
78 candidates to 110 candidates (-41.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1100110
Fresh077
Picked011
Done000
Total1108118

Merged error: 0b

Counts
118 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))) a)
0.2b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.3b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.3b
(*.f64 (/.f64 1 a) (*.f64 (*.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))) a))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log_binary64
45×add-cbrt-cube_binary64
41×prod-exp_binary64
23×cbrt-unprod_binary64
18×pow1_binary64
14×*-un-lft-identity_binary64 associate-*l*_binary64
13×div-exp_binary64
12×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
9×pow-prod-down_binary64 times-frac_binary64
8×add-log-exp_binary64
7×cbrt-undiv_binary64
4×associate-*r*_binary64 1-exp_binary64 associate-*r/_binary64 rec-exp_binary64 insert-posit16 associate-*l/_binary64
2×*-commutative_binary64
1×flip3-+_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 distribute-lft-out_binary64 div-inv_binary64 +-commutative_binary64 flip--_binary64 flip-+_binary64 frac-times_binary64 sum-log_binary64
Counts
4 → 100
Calls
4 calls:
16.0ms
(*.f64 (*.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))) a)
6.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
10.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
22.0ms
(*.f64 (/.f64 1 a) (*.f64 (*.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))) a))

series348.0ms

Iterations

Useful iterations: 0 (329.0ms)

IterNodesCost
018002620
118002620

Profiling

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