Details

Time bar (total: 4.5s)

analyze404.0ms (8.9%)

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
0%99.9%0.1%5
0%74.9%25.1%6
6.2%68.6%25.1%7
10.1%64.7%25.1%8
17.2%32.8%50.1%9
23%26.9%50.1%10
26.8%23.1%50.1%11
31.6%18.3%50.1%12
35.2%14.7%50.1%13
37.5%12.4%50.1%14
Compiler

Compiled 16 to 11 computations (31.3% saved)

sample26.0ms (0.6%)

Algorithm
intervals
Results
15.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify177.0ms (3.9%)

Algorithm
egg-herbie
Rules
772×sub-neg_binary64
624×unsub-neg_binary64
614×+-commutative_binary64
567×distribute-rgt-in_binary64
391×neg-sub0_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01118
12518
27318
322918
455618
5127818
6141218
7153118
8162218
9162118
10163818
11194818
12266418
13412418
14415918
15432318
16434718
17436818
18474218
19493218

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
Compiler

Compiled 45 to 30 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
0.0b
(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
0.1b
(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
0.2b
(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite139.0ms (3.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
20×add-log-exp_binary64 *-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
12×log-prod_binary64
11×add-cube-cbrt_binary64
pow1_binary64
Counts
4 → 83
Calls

4 calls:

8.0ms
(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
8.0ms
(*.f64 (+.f64 y 1/2) (log.f64 y))
6.0ms
(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
4.0ms
(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
Compiler

Compiled 1606 to 882 computations (45.1% saved)

series227.0ms (5%)

Error
0.1b
Counts
4 → 44
Calls

4 calls:

77.0ms
(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
51.0ms
(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
49.0ms
(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
16.0ms
(*.f64 (+.f64 y 1/2) (log.f64 y))
Compiler

Compiled 1511 to 976 computations (35.4% saved)

simplify177.0ms (3.9%)

Algorithm
egg-herbie
Rules
471×exp-sum_binary64
436×sub-neg_binary64
351×associate-+l+_binary64
305×exp-diff_binary64
295×associate-+r+_binary64
Counts
127 → 109
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01941994
15001921
214761880
334861880
444301876
549651876
649931876
748091876

prune112.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1018109
Fresh000
Picked101
Done000
Total1028110
Error
0b
Counts
110 → 8
Alt Table
StatusErrorProgram
0.1b
(-.f64 x (+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y)))
0.3b
(-.f64 (+.f64 (-.f64 x (*.f64 (sqrt.f64 (+.f64 y 1/2)) (*.f64 (log.f64 y) (sqrt.f64 (+.f64 1/2 y))))) y) z)
31.3b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (+.f64 1/2 y) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
31.4b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (sqrt.f64 (+.f64 1/2 y)) (sqrt.f64 (log.f64 y))) (*.f64 (sqrt.f64 (+.f64 1/2 y)) (sqrt.f64 (log.f64 y))))) y) z)
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x)) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) z)
0.6b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (+.f64 1/2 y) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y)))) y) z)
0.5b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 y) (+.f64 1/2 y))) (cbrt.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)))) (cbrt.f64 (*.f64 (log.f64 y) (+.f64 1/2 y))))) y) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
Compiler

Compiled 1644 to 917 computations (44.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 x (+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y)))
0.1b
(+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y))
0.2b
(*.f64 (log.f64 y) (+.f64 1/2 y))

rewrite113.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
17×add-log-exp_binary64
11×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-cube-cbrt_binary64
pow1_binary64 associate-*r/_binary64 cancel-sign-sub-inv_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 diff-log_binary64
Counts
3 → 67
Calls

3 calls:

10.0ms
(+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y))
10.0ms
(-.f64 x (+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y)))
7.0ms
(*.f64 (log.f64 y) (+.f64 1/2 y))
Compiler

Compiled 1427 to 699 computations (51% saved)

series167.0ms (3.7%)

Error
0b
Counts
3 → 33
Calls

3 calls:

79.0ms
(-.f64 x (+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y)))
48.0ms
(+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y))
18.0ms
(*.f64 (log.f64 y) (+.f64 1/2 y))
Compiler

Compiled 1142 to 741 computations (35.1% saved)

simplify101.0ms (2.2%)

Algorithm
egg-herbie
Rules
473×associate-+l+_binary64
457×associate-+r+_binary64
220×exp-diff_binary64
195×distribute-rgt-in_binary64
192×associate--r+_binary64
Counts
100 → 66
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01841797
15631752
219311707
347721707
451201707

prune64.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New66066
Fresh077
Picked011
Done000
Total66874
Error
0b
Counts
74 → 8
Alt Table
StatusErrorProgram
0.1b
(-.f64 x (+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y)))
0.3b
(-.f64 (+.f64 (-.f64 x (*.f64 (sqrt.f64 (+.f64 y 1/2)) (*.f64 (log.f64 y) (sqrt.f64 (+.f64 1/2 y))))) y) z)
31.3b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (+.f64 1/2 y) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
31.4b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (sqrt.f64 (+.f64 1/2 y)) (sqrt.f64 (log.f64 y))) (*.f64 (sqrt.f64 (+.f64 1/2 y)) (sqrt.f64 (log.f64 y))))) y) z)
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x)) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) z)
0.6b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (+.f64 1/2 y) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y)))) y) z)
0.5b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 y) (+.f64 1/2 y))) (cbrt.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)))) (cbrt.f64 (*.f64 (log.f64 y) (+.f64 1/2 y))))) y) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
Compiler

Compiled 1173 to 619 computations (47.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2))
0.3b
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
0.6b
(cbrt.f64 y)
0.6b
(cbrt.f64 y)

rewrite155.0ms (3.4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
13×*-un-lft-identity_binary64
12×cbrt-prod_binary64 log-prod_binary64 associate-+r+_binary64
11×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
10×associate-*l/_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
Counts
4 → 71
Calls

4 calls:

12.0ms
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
8.0ms
(*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2))
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 2271 to 1260 computations (44.5% saved)

series134.0ms (3%)

Error
0b
Counts
4 → 16
Calls

4 calls:

42.0ms
(+.f64 (*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))
30.0ms
(*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2))
19.0ms
(cbrt.f64 y)
17.0ms
(cbrt.f64 y)
Compiler

Compiled 1113 to 819 computations (26.4% saved)

simplify113.0ms (2.5%)

Algorithm
egg-herbie
Rules
458×cancel-sign-sub-inv_binary64
220×associate-+l+_binary64
216×associate-*r*_binary64
204×associate-*l*_binary64
196×associate-+r+_binary64
Counts
87 → 67
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01601679
14501367
216061165
336251147
449611147
549711147

prune103.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New66167
Fresh246
Picked011
Done011
Total68775
Error
0b
Counts
75 → 7
Alt Table
StatusErrorProgram
0.1b
(-.f64 x (+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y)))
0.3b
(-.f64 (+.f64 (-.f64 x (*.f64 (sqrt.f64 (+.f64 y 1/2)) (*.f64 (log.f64 y) (sqrt.f64 (+.f64 1/2 y))))) y) z)
31.3b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (+.f64 1/2 y) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x)) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) z)
0.6b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (+.f64 1/2 y) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y)))) y) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 y 1/2) (+.f64 (*.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 y))) (+.f64 1/2 y)))) y) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
Compiler

Compiled 1634 to 966 computations (40.9% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b
(+.f64 (*.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))
0.4b
(*.f64 2/3 (log.f64 y))
0.5b
(cbrt.f64 (sqrt.f64 y))
0.5b
(cbrt.f64 (sqrt.f64 y))

rewrite162.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
21×log-prod_binary64
19×add-sqr-sqrt_binary64
18×cbrt-prod_binary64
17×add-cube-cbrt_binary64 *-un-lft-identity_binary64
sqrt-prod_binary64 associate-+r+_binary64
Counts
4 → 79
Calls

4 calls:

7.0ms
(+.f64 (*.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))
5.0ms
(*.f64 2/3 (log.f64 y))
2.0ms
(cbrt.f64 (sqrt.f64 y))
2.0ms
(cbrt.f64 (sqrt.f64 y))
Compiler

Compiled 2536 to 1215 computations (52.1% saved)

series85.0ms (1.9%)

Error
0b
Counts
4 → 12
Calls

4 calls:

25.0ms
(+.f64 (*.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))
16.0ms
(cbrt.f64 (sqrt.f64 y))
15.0ms
(*.f64 2/3 (log.f64 y))
15.0ms
(cbrt.f64 (sqrt.f64 y))
Compiler

Compiled 1022 to 726 computations (29% saved)

simplify90.0ms (2%)

Algorithm
egg-herbie
Rules
510×unsub-neg_binary64
490×distribute-rgt-in_binary64
394×distribute-lft-in_binary64
348×associate-*l*_binary64
307×distribute-neg-out_binary64
Counts
91 → 46
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01301117
12511045
25301031
310531001
43289979
54812979

prune67.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New45146
Fresh224
Picked011
Done022
Total47653
Error
0b
Counts
53 → 6
Alt Table
StatusErrorProgram
0.4b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 y 1/2) (+.f64 (*.f64 (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)) (*.f64 (log.f64 y) (cbrt.f64 2/3))) (log.f64 (cbrt.f64 (sqrt.f64 y))))) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 y))) (+.f64 1/2 y)))) y) z)
0.1b
(-.f64 x (+.f64 (*.f64 (log.f64 y) (+.f64 1/2 y)) (-.f64 z y)))
31.3b
(-.f64 (+.f64 (-.f64 x (*.f64 (*.f64 (+.f64 1/2 y) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
0.8b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x)) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) (cbrt.f64 (+.f64 (-.f64 y (*.f64 (log.f64 y) (+.f64 1/2 y))) x))) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 y 1/2) (+.f64 (*.f64 2/3 (log.f64 y)) (log.f64 (cbrt.f64 (sqrt.f64 y))))) (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 y))) (+.f64 1/2 y)))) y) z)
0.2b
(-.f64 (+.f64 (-.f64 x (+.f64 (*.f64 (+.f64 1/2 y) (*.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 1/2 y) (log.f64 (cbrt.f64 y))))) y) z)
Compiler

Compiled 1106 to 579 computations (47.6% saved)

regimes1000.0ms (22.1%)

Accuracy

Total 0.1b remaining (85.2%)

Threshold costs 0.1b (85.2%)

Compiler

Compiled 14530 to 9716 computations (33.1% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
27×cancel-sign-sub-inv_binary64
19×distribute-rgt-neg-in_binary64
18×distribute-lft-neg-in_binary64
14×neg-mul-1_binary64 neg-sub0_binary64 distribute-neg-in_binary64
13×sub-neg_binary64 +-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01425
13423
25723
39623
412623
514723
615523
714923

end1.0ms (0%)

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample836.0ms (18.5%)

Algorithm
intervals
Results
386.0ms7998×body128valid
2.0ms46×body128invalid
0.0msbody1024valid
Compiler

Compiled 207 to 136 computations (34.3% saved)

Profiling

Loading profile data...