Details

Time bar (total: 10.3s)

analyze462.0ms

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
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14

sample43.0ms

Algorithm
intervals
Results
10.0ms35×body2560valid
8.0ms161×body80valid
7.0ms28×body1280valid
2.0ms12×body640valid
2.0ms6×body5120valid
1.0ms10×body320valid
1.0ms29×body80nan
1.0ms15×body80invalid
0.0ms4×body160valid

simplify564.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (98.0ms)

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: 35.0b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a)
0.6b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
0.9b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
23.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_3412
15×add-sqr-sqrt_binary64_3397
14×add-cube-cbrt_binary64_3383
12×times-frac_binary64_3407
8×add-log-exp_binary64_3377
6×add-exp-log_binary64_3376 add-cbrt-cube_binary64_3384
5×distribute-lft-out_binary64_3456 pow1_binary64_3354
4×associate-/l*_binary64_3476
3×sqrt-prod_binary64_3391 associate-/r*_binary64_3475
2×flip--_binary64_3438 sqrt-div_binary64_3392 associate-/l/_binary64_3478 flip-+_binary64_3437 flip3--_binary64_3411 flip3-+_binary64_3410
1×cbrt-undiv_binary64_3382 diff-log_binary64_3323 clear-num_binary64_3415 frac-2neg_binary64_3405 pow1/2_binary64_3344 div-exp_binary64_3361 sum-log_binary64_3322 +-commutative_binary64_3479 rem-sqrt-square_binary64_3400 sub-neg_binary64_3416 div-inv_binary64_3413 sqrt-pow1_binary64_3393
Counts
4 → 71
Calls
4 calls:
11.0ms
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a)
6.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
8.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series1.5s

Counts
4 → 12
Calls
4 calls:
597.0ms
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) a)
297.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
313.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
298.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0683642
1683642
09873546
19873546
0683642
1683642
09873546
19873546
013
113
0713693
1713693
010703591
110703591
0713693
1713693
010703591
110703591
013
113
0653624
1653624
09853528
19853528
0653624
1653624
09853528
19853528
013
113
0853744
1853744
016523618
116523618
0853744
1853744
016523618
116523618
013
113

simplify145.0ms

Counts
83 → 83
Iterations

Useful iterations: 0 (116.0ms)

IterNodesCost
049381852
149381852

prune97.0ms

Filtered
60 candidates to 83 candidates (-38.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New75883
Fresh000
Picked101
Done000
Total76884

Merged error: 20.5b

Counts
84 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
4.1b
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
9.4b
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
23.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac_binary64_3407
57×add-sqr-sqrt_binary64_3397
42×*-un-lft-identity_binary64_3412
28×add-cube-cbrt_binary64_3383
27×add-exp-log_binary64_3376 add-cbrt-cube_binary64_3384
14×difference-of-squares_binary64_3441
13×associate-/l*_binary64_3476
10×sqrt-prod_binary64_3391 cbrt-undiv_binary64_3382 div-exp_binary64_3361 associate-/r/_binary64_3477
9×associate-/r*_binary64_3475
7×flip--_binary64_3438 flip3--_binary64_3411 distribute-lft-out--_binary64_3457
6×prod-exp_binary64_3359 cbrt-unprod_binary64_3381 div-inv_binary64_3413 add-log-exp_binary64_3377
5×pow1_binary64_3354
2×clear-num_binary64_3415 frac-2neg_binary64_3405 sqrt-div_binary64_3392
1×diff-log_binary64_3323 pow1/2_binary64_3344 associate-/l/_binary64_3478 rem-sqrt-square_binary64_3400 sub-neg_binary64_3416 sqrt-pow1_binary64_3393
Counts
4 → 130
Calls
4 calls:
9.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
19.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
16.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series1.3s

Counts
4 → 12
Calls
4 calls:
326.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
379.0ms
(/.f64 (/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))) a)
248.0ms
(/.f64 (*.f64 4 (*.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
304.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0683642
1683642
09873546
19873546
0683642
1683642
09873546
19873546
013
113
0833822
1833822
048833672
148833672
0833822
1833822
048833672
148833672
013
113
0973873
1973873
048073645
148073645
0973873
1973873
048073645
148073645
013
113
0713693
1713693
011133591
111133591
0713693
1713693
011133591
111133591
013
113

simplify88.0ms

Counts
142 → 142
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
052844672

prune164.0ms

Filtered
97 candidates to 142 candidates (-46.4%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1375142
Fresh257
Picked011
Done000
Total13911150

Merged error: 17.5b

Counts
150 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
0.6b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.8b
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
23.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64_3397
26×*-un-lft-identity_binary64_3412
18×times-frac_binary64_3407
16×add-cube-cbrt_binary64_3383
10×difference-of-squares_binary64_3441
8×sqrt-prod_binary64_3391 add-log-exp_binary64_3377
6×add-exp-log_binary64_3376 add-cbrt-cube_binary64_3384 associate-/r*_binary64_3475
5×pow1_binary64_3354 distribute-lft-out--_binary64_3457
4×flip--_binary64_3438 flip3--_binary64_3411
3×associate-/l*_binary64_3476
2×diff-log_binary64_3323 sqrt-div_binary64_3392 associate-/r/_binary64_3477 sub-neg_binary64_3416
1×cbrt-undiv_binary64_3382 clear-num_binary64_3415 frac-2neg_binary64_3405 pow1/2_binary64_3344 div-exp_binary64_3361 rem-sqrt-square_binary64_3400 div-inv_binary64_3413 sqrt-pow1_binary64_3393
Counts
4 → 81
Calls
4 calls:
12.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
6.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
9.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series1.9s

Counts
4 → 12
Calls
4 calls:
953.0ms
(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))))
301.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
326.0ms
(-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
302.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0683642
1683642
09873546
19873546
0683642
1683642
09873546
19873546
013
113
0713693
1713693
011133591
111133591
0713693
1713693
011133591
111133591
013
113
0653624
1653624
09853528
19853528
0653624
1653624
09853528
19853528
013
113
0853744
1853744
019913636
119913636
0853744
1853744
019913636
119913636
013
113

simplify110.0ms

Counts
93 → 93
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
052042302

prune104.0ms

Filtered
65 candidates to 93 candidates (-43.1%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New88593
Fresh189
Picked011
Done011
Total8915104

Merged error: 17.1b

Counts
104 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

6.4b
(cbrt.f64 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
23.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
23.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
23.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64_3397
24×cbrt-prod_binary64_3379
23×*-un-lft-identity_binary64_3412
18×times-frac_binary64_3407
17×add-cube-cbrt_binary64_3383
12×sqrt-prod_binary64_3391
7×pow1_binary64_3354
6×difference-of-squares_binary64_3441 sqrt-div_binary64_3392
4×flip--_binary64_3438 add-exp-log_binary64_3376 add-cbrt-cube_binary64_3384 flip3--_binary64_3411 add-log-exp_binary64_3377
3×pow1/2_binary64_3344 rem-sqrt-square_binary64_3400 sqrt-pow1_binary64_3393 distribute-lft-out--_binary64_3457
2×associate-/r/_binary64_3477
1×pow1/3_binary64_3346 cbrt-div_binary64_3380 div-inv_binary64_3413
Counts
4 → 78
Calls
4 calls:
14.0ms
(cbrt.f64 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series1.9s

Counts
4 → 12
Calls
4 calls:
952.0ms
(cbrt.f64 (/.f64 c (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
300.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
301.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
299.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0683642
1683642
09873546
19873546
0683642
1683642
09873546
19873546
013
113
0683642
1683642
09873546
19873546
0683642
1683642
09873546
19873546
013
113
0683642
1683642
09873546
19873546
0683642
1683642
09873546
19873546
013
113
0773762
1773762
018143654
118143654
0773762
1773762
018143654
118143654
013
113

simplify107.0ms

Counts
90 → 90
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
049382354
149382354

prune158.0ms

Filtered
65 candidates to 90 candidates (-38.5%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New89190
Fresh01212
Picked101
Done022
Total9015105

Merged error: 17.1b

Counts
105 → 15

regimes164.0ms

Accuracy

89.7% (1.2b remaining)

Error of 18.4b against oracle of 17.1b and baseline of 29.0b

bsearch67.0ms

Steps
ItersRangePoint
10
6.4070354416359315e+153
1.6297035527649438e+164
1.3495206492131508e+154
10
1.6990986402510408e-159
6.665948400578647e-143
1.7297353395157233e-159

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
09073
19073

end0.0ms

sample1.3s

Algorithm
intervals
Results
330.0ms1095×body2560valid
271.0ms5127×body80valid
224.0ms916×body1280valid
82.0ms436×body640valid
41.0ms107×body5120valid
33.0ms675×body80nan
32.0ms223×body320valid
23.0ms402×body80invalid
9.0ms96×body160valid

Profiling

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