Details

Time bar (total: 5.7s)

analyze31.0ms (0.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
75%25%0%5
87.5%12.5%0%6
93.7%6.2%0%7
96.8%3.1%0%8
98.4%1.6%0%9
99.2%0.8%0%10
99.6%0.4%0%11
99.8%0.2%0%12
99.9%0.1%0%13
99.9%0.1%0.1%14
Compiler

Compiled 17 to 14 computations (17.6% saved)

sample28.0ms (0.5%)

Algorithm
intervals
Results
7.0ms56×body512valid
6.0ms136×body128valid
6.0ms34×body1024valid
3.0ms30×body256valid
Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify15.0ms (0.3%)

Algorithm
egg-herbie
Rules
44×sub-neg_binary64
41×cancel-sign-sub-inv_binary64
28×distribute-rgt-in_binary64
28×unsub-neg_binary64
25×associate--r+_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
12222
23822
35922
410122
516522
619822
721722
821622
919222

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
9.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
9.6b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
Compiler

Compiled 48 to 39 computations (18.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 1 (+.f64 x 1))
0.0b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
1.9b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite149.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
9.4b
Rules
87×*-un-lft-identity_binary64
53×times-frac_binary64
43×add-sqr-sqrt_binary64
26×cancel-sign-sub-inv_binary64
26×add-cube-cbrt_binary64
Counts
3 → 112
Calls

3 calls:

29.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
13.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms
(/.f64 1 (+.f64 x 1))
Compiler

Compiled 2387 to 1928 computations (19.2% saved)

series32.0ms (0.6%)

Error
0.2b
Counts
3 → 22
Calls

3 calls:

9.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
7.0ms
(/.f64 1 (+.f64 x 1))
7.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
Compiler

Compiled 675 to 544 computations (19.4% saved)

simplify108.0ms (1.9%)

Algorithm
egg-herbie
Rules
428×associate-*l*_binary64
327×distribute-rgt-in_binary64
278×associate-/l*_binary64
278×distribute-lft-in_binary64
238×associate-*l/_binary64
Counts
134 → 107
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02032231
15252147
214982112
341962108
450042108

prune61.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9710107
Fresh000
Picked101
Done000
Total9810108
Error
9.4b
Counts
108 → 10
Alt Table
StatusErrorProgram
42.1b
(+.f64 (*.f64 (+.f64 (sqrt.f64 (/.f64 2 x)) (sqrt.f64 (/.f64 1 (+.f64 x 1)))) (-.f64 (sqrt.f64 (/.f64 1 (+.f64 x 1))) (sqrt.f64 (/.f64 2 x)))) (/.f64 1 (-.f64 x 1)))
28.2b
(/.f64 (+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
44.1b
(+.f64 (*.f64 (sqrt.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (sqrt.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))))) (/.f64 1 (-.f64 x 1)))
27.3b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))))) (cbrt.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))))) (/.f64 1 (-.f64 x 1)))
52.0b
(+.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) 3)) (/.f64 1 (-.f64 x 1)))
50.5b
(+.f64 (exp.f64 (log.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))))) (/.f64 1 (-.f64 x 1)))
27.7b
(+.f64 (-.f64 (*.f64 (/.f64 1 (+.f64 (*.f64 x x) -1)) (-.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
25.9b
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1))) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))
27.5b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
44.9b
(+.f64 (/.f64 (-.f64 (/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 x 1)) (/.f64 4 (*.f64 x x))) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))
Compiler

Compiled 1776 to 1401 computations (21.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1))
0.3b
(*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))))
6.2b
(-.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1)))
17.8b
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1))) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))

rewrite972.0ms (17%)

Algorithm
rewrite-expression-head
Error
9.4b
Rules
789×*-un-lft-identity_binary64
743×times-frac_binary64
462×add-sqr-sqrt_binary64
218×distribute-lft-out_binary64
177×add-cube-cbrt_binary64
Counts
4 → 545
Calls

4 calls:

81.0ms
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1))) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))
53.0ms
(-.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1)))
27.0ms
(*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))))
11.0ms
(/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1))
Compiler

Compiled 25091 to 20231 computations (19.4% saved)

series73.0ms (1.3%)

Error
2.2b
Counts
4 → 30
Calls

4 calls:

14.0ms
(-.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1)))
12.0ms
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1))) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))
11.0ms
(/.f64 (/.f64 1 (+.f64 x -1)) (+.f64 x -1))
11.0ms
(*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))))
Compiler

Compiled 2009 to 1653 computations (17.7% saved)

simplify549.0ms (9.6%)

Algorithm
egg-herbie
Rules
556×distribute-rgt-in_binary64
533×distribute-lft-in_binary64
146×sub-neg_binary64
130×*-commutative_binary64
119×neg-mul-1_binary64
Counts
575 → 485
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054928563
1180926957
2489026921
3495426921

prune242.0ms (4.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4841485
Fresh729
Picked101
Done000
Total4923495
Error
2.2b
Counts
495 → 3
Alt Table
StatusErrorProgram
33.1b
(/.f64 (+.f64 (/.f64 -4 (pow.f64 x 4)) (/.f64 -4 (pow.f64 x 5))) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))
27.5b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
28.2b
(/.f64 (+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
Compiler

Compiled 11518 to 9083 computations (21.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))
0.2b
(+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))
7.5b
(+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)
14.4b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))

rewrite223.0ms (3.9%)

Algorithm
rewrite-expression-head
Error
2.2b
Rules
28×*-un-lft-identity_binary64
17×flip-+_binary64
17×flip3-+_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
Counts
4 → 88
Calls

4 calls:

54.0ms
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
25.0ms
(+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)
16.0ms
(+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))
14.0ms
(+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))
Compiler

Compiled 5014 to 4017 computations (19.9% saved)

series62.0ms (1.1%)

Error
0.0b
Counts
4 → 26
Calls

4 calls:

14.0ms
(+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)
9.0ms
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
8.0ms
(+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))
8.0ms
(+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))
Compiler

Compiled 1718 to 1384 computations (19.4% saved)

simplify125.0ms (2.2%)

Algorithm
egg-herbie
Rules
327×distribute-rgt-in_binary64
310×distribute-lft-in_binary64
265×associate-/l/_binary64
243×associate-*l*_binary64
237×times-frac_binary64
Counts
114 → 77
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01814666
16913893
232723121
347743121
449573121

prune85.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New76177
Fresh022
Picked011
Done000
Total76480
Error
0.0b
Counts
80 → 4
Alt Table
StatusErrorProgram
28.2b
(/.f64 (+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
31.1b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 (pow.f64 x 3)))) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
33.1b
(/.f64 (+.f64 (/.f64 -4 (pow.f64 x 4)) (/.f64 -4 (pow.f64 x 5))) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))
27.5b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
Compiler

Compiled 3404 to 2671 computations (21.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 x (+.f64 2 (*.f64 x 2)))
0.0b
(*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2))))
0.0b
(/.f64 (+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
20.0b
(+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x)))

rewrite231.0ms (4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
60×add-sqr-sqrt_binary64
48×*-un-lft-identity_binary64
33×flip-+_binary64
33×flip3-+_binary64
32×frac-add_binary64
Counts
4 → 174
Calls

4 calls:

17.0ms
(/.f64 (+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
15.0ms
(*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2))))
12.0ms
(+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x)))
4.0ms
(-.f64 x (+.f64 2 (*.f64 x 2)))
Compiler

Compiled 8004 to 4586 computations (42.7% saved)

series39.0ms (0.7%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

14.0ms
(*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2))))
7.0ms
(/.f64 (+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
7.0ms
(-.f64 x (+.f64 2 (*.f64 x 2)))
4.0ms
(+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x)))
Compiler

Compiled 757 to 510 computations (32.6% saved)

simplify216.0ms (3.8%)

Algorithm
egg-herbie
Rules
555×distribute-rgt-in_binary64
522×distribute-lft-in_binary64
455×associate-*l*_binary64
424×associate-*r*_binary64
112×*-commutative_binary64
Counts
198 → 178
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03497971
110757417
247487389
349867389
449527389

prune142.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1780178
Fresh022
Picked011
Done011
Total1784182
Error
0.0b
Counts
182 → 4
Alt Table
StatusErrorProgram
28.2b
(/.f64 (+.f64 (*.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (*.f64 x 2)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
31.1b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (-.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 (pow.f64 x 3)))) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
33.1b
(/.f64 (+.f64 (/.f64 -4 (pow.f64 x 4)) (/.f64 -4 (pow.f64 x 5))) (-.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))
27.5b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
Compiler

Compiled 6160 to 3629 computations (41.1% saved)

regimes1.2s (21.4%)

Accuracy

Total 0.2b remaining (70%)

Threshold costs 0.2b (70%)

Compiler

Compiled 32625 to 26113 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
1910
21410
31610
41710
51710

end1.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.1s (18.4%)

Algorithm
intervals
Results
270.0ms4485×body128valid
226.0ms1309×body1024valid
209.0ms1506×body512valid
61.0ms700×body256valid
Compiler

Compiled 154 to 120 computations (22.1% saved)

Profiling

Loading profile data...