Details

Time bar (total: 5.3s)

analyze29.0ms (0.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%0%50%2
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample30.0ms (0.6%)

Algorithm
intervals
Results
13.0ms74×body1024valid
6.0ms143×body128valid
3.0ms26×body512valid
1.0ms13×body256valid
Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify12.0ms (0.2%)

Algorithm
egg-herbie
Rules
15×sub-neg_binary64
14×cancel-sign-sub-inv_binary64
10×distribute-rgt-in_binary64
neg-mul-1_binary64
associate--r+_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11417
22017
32717
43417
55017
67217
78117
89317
99517
108917
117517

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
17.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
17.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b
(/.f64 1 (sqrt.f64 x))
2.9b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite341.0ms (6.4%)

Algorithm
rewrite-expression-head
Error
17.3b
Rules
124×add-sqr-sqrt_binary64
118×times-frac_binary64
113×*-un-lft-identity_binary64
72×sqrt-prod_binary64
54×add-cube-cbrt_binary64
Counts
3 → 173
Calls

3 calls:

38.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 2573 to 1980 computations (23% saved)

series26.0ms (0.5%)

Error
17.7b
Counts
3 → 10
Calls

3 calls:

9.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 270 to 217 computations (19.6% saved)

simplify182.0ms (3.4%)

Algorithm
egg-herbie
Rules
514×associate-/l*_binary64
328×unsub-neg_binary64 associate-*r/_binary64
309×distribute-rgt-in_binary64
268×associate-/r*_binary64
263×distribute-lft-in_binary64
Counts
183 → 161
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01463072
13082990
26312988
316442982
442132913
549562913
648822913

prune110.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New14813161
Fresh000
Picked101
Done000
Total14913162
Error
17.3b
Counts
162 → 13
Alt Table
StatusErrorProgram
18.1b
(*.f64 (+.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (-.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
25.8b
(-.f64 (/.f64 (/.f64 1 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0b
(exp.f64 (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
20.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
17.9b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
26.7b
(-.f64 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 x))) (/.f64 1 (sqrt.f64 (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
25.4b
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 -1 (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))))
28.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))
61.6b
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (neg.f64 (sqrt.f64 (+.f64 -1 x))) (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
17.8b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
18.3b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
23.8b
(-.f64 (*.f64 (/.f64 1 (pow.f64 x 1/4)) (/.f64 1 (pow.f64 x 1/4))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
27.0b
(/.f64 (+.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 -1 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))))
Compiler

Compiled 1531 to 1198 computations (21.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.9b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite185.0ms (3.5%)

Algorithm
rewrite-expression-head
Error
16.9b
Rules
45×add-sqr-sqrt_binary64
38×sqrt-prod_binary64
34×*-un-lft-identity_binary64
12×difference-of-squares_binary64
11×add-cube-cbrt_binary64
Counts
3 → 98
Calls

3 calls:

16.0ms
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 1762 to 1111 computations (36.9% saved)

series47.0ms (0.9%)

Error
17.2b
Counts
3 → 12
Calls

3 calls:

17.0ms
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
10.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
Compiler

Compiled 474 to 362 computations (23.6% saved)

simplify106.0ms (2%)

Algorithm
egg-herbie
Rules
917×times-frac_binary64
528×associate-/r*_binary64
482×div-sub_binary64
408×associate-/l*_binary64
183×distribute-rgt-in_binary64
Counts
110 → 76
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01442288
13591956
210771956
343761954
457531954

prune66.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New75176
Fresh11112
Picked011
Done000
Total86389
Error
0.2b
Counts
89 → 3
Alt Table
StatusErrorProgram
20.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
17.8b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 1041 to 679 computations (34.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite318.0ms (6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
118×*-un-lft-identity_binary64
78×times-frac_binary64
55×sqrt-prod_binary64
49×add-sqr-sqrt_binary64
45×distribute-lft-out_binary64
Counts
4 → 167
Calls

4 calls:

20.0ms
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 3644 to 2502 computations (31.3% saved)

series46.0ms (0.9%)

Error
0.1b
Counts
4 → 15
Calls

4 calls:

13.0ms
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
7.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 503 to 398 computations (20.9% saved)

simplify176.0ms (3.3%)

Algorithm
egg-herbie
Rules
468×associate-*l*_binary64
451×associate-/r*_binary64
439×associate-/l*_binary64
347×associate-/l/_binary64
297×associate-*r*_binary64
Counts
182 → 160
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01644199
13783566
210973550
338733546
445733536
550433536

prune169.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1537160
Fresh011
Picked101
Done101
Total1558163
Error
0.0b
Counts
163 → 8
Alt Table
StatusErrorProgram
0.9b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))) (sqrt.f64 (/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))))
0.6b
(/.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.4b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
20.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
1.1b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
0.3b
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.6b
(/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))
0.6b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 2521 to 1741 computations (30.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b
(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.2b
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite459.0ms (8.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
234×times-frac_binary64
159×*-un-lft-identity_binary64
158×add-sqr-sqrt_binary64
119×add-cube-cbrt_binary64
87×sqrt-prod_binary64
Counts
4 → 253
Calls

4 calls:

15.0ms
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
9.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms
(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms
(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 6301 to 4541 computations (27.9% saved)

series66.0ms (1.2%)

Error
0.0b
Counts
4 → 21
Calls

4 calls:

13.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
12.0ms
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
12.0ms
(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
9.0ms
(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 767 to 624 computations (18.6% saved)

simplify325.0ms (6.1%)

Algorithm
egg-herbie
Rules
686×div-sub_binary64
311×associate-/r*_binary64
234×*-commutative_binary64
229×cancel-sign-sub-inv_binary64
217×associate-/l*_binary64
Counts
274 → 228
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02469476
15709021
214348901
332728886
445548876
560268876

prune198.0ms (3.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2262228
Fresh167
Picked011
Done000
Total2279236
Error
0b
Counts
236 → 9
Alt Table
StatusErrorProgram
0.9b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))) (sqrt.f64 (/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))))
0.4b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
1.1b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (cbrt.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
20.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.4b
(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (cbrt.f64 (+.f64 x 1)))))
1.1b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
0.3b
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.6b
(/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))
0.6b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 2949 to 2090 computations (29.1% saved)

regimes1.2s (23.1%)

Accuracy

Total 0.3b remaining (92.2%)

Threshold costs 0.3b (92.2%)

Compiler

Compiled 19579 to 15066 computations (23.1% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64 *-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01125
11725
21625

end1.0ms (0%)

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample1.2s (21.9%)

Algorithm
intervals
Results
368.0ms2196×body1024valid
197.0ms4363×body128valid
126.0ms972×body512valid
43.0ms469×body256valid
Compiler

Compiled 292 to 218 computations (25.3% saved)

Profiling

Loading profile data...