Details

Time bar (total: 5.2s)

analyze24.0ms (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)

sample29.0ms (0.6%)

Algorithm
intervals
Results
12.0ms77×body1024valid
5.0ms128×body128valid
4.0ms36×body512valid
1.0ms15×body256valid
Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify13.0ms (0.3%)

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

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
22.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
22.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b
(/.f64 1 (sqrt.f64 x))
2.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite313.0ms (6.1%)

Algorithm
rewrite-expression-head
Error
21.6b
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:

40.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 2573 to 1980 computations (23% saved)

series28.0ms (0.5%)

Error
22.1b
Counts
3 → 11
Calls

3 calls:

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

Compiled 309 to 248 computations (19.7% saved)

simplify187.0ms (3.6%)

Algorithm
egg-herbie
Rules
530×associate-/l*_binary64
320×div-sub_binary64
309×distribute-rgt-in_binary64
268×associate-/r*_binary64
263×distribute-lft-in_binary64
Counts
184 → 162
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01503088
13173006
26493001
316962995
443042926
549302926
648822926

prune113.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New14913162
Fresh000
Picked101
Done000
Total15013163
Error
21.6b
Counts
163 → 13
Alt Table
StatusErrorProgram
23.5b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
22.3b
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
27.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))))
26.2b
(-.f64 (/.f64 (/.f64 1 (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
28.9b
(-.f64 (/.f64 (/.f64 1 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
24.4b
(exp.f64 (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
27.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
22.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
28.6b
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 -1 (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))))
23.7b
(*.f64 (+.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (pow.f64 x 1/4))) (+.f64 (/.f64 1 (pow.f64 x 1/4)) (/.f64 -1 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))))
34.6b
(/.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)))))))
61.7b
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (neg.f64 (sqrt.f64 (+.f64 -1 x))) (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
22.2b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 1527 to 1198 computations (21.5% saved)

localize7.0ms (0.1%)

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))))
0.3b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.3b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite188.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
21.4b
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:

17.0ms
(/.f64 (-.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)))
9.0ms
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 1762 to 1111 computations (36.9% saved)

series49.0ms (0.9%)

Error
21.5b
Counts
3 → 12
Calls

3 calls:

15.0ms
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
13.0ms
(-.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)

simplify111.0ms (2.2%)

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

prune63.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New74276
Fresh11112
Picked101
Done000
Total86389
Error
0.3b
Counts
89 → 3
Alt Table
StatusErrorProgram
23.5b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
21.9b
(/.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (*.f64 (+.f64 1 x) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 1 x)))))
0.4b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 1085 to 708 computations (34.7% saved)

localize11.0ms (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))))
0.3b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite353.0ms (6.8%)

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:

19.0ms
(/.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))))
11.0ms
(*.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)

simplify182.0ms (3.5%)

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

prune186.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15010160
Fresh112
Picked101
Done000
Total15211163
Error
0.0b
Counts
163 → 11
Alt Table
StatusErrorProgram
23.5b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.7b
(*.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))))
0.7b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (*.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))))
0.5b
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
6.5b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (pow.f64 x 3/2) (pow.f64 (sqrt.f64 (+.f64 x 1)) 3))) (-.f64 (/.f64 (+.f64 x (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
0.3b
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.4b
(/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))
0.7b
(*.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)))))))
30.0b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (+.f64 x 1/2) (/.f64 1/8 x)))
0.6b
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) 3))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
1.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))) (cbrt.f64 (/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1))))))) (cbrt.f64 (/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))))
Compiler

Compiled 2671 to 1859 computations (30.4% saved)

localize11.0ms (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)))))
0.1b
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.3b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite460.0ms (8.9%)

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:

13.0ms
(/.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)

series64.0ms (1.2%)

Error
0.0b
Counts
4 → 21
Calls

4 calls:

14.0ms
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
11.0ms
(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
10.0ms
(*.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)

simplify326.0ms (6.3%)

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

prune184.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2235228
Fresh6410
Picked101
Done000
Total2309239
Error
0b
Counts
239 → 9
Alt Table
StatusErrorProgram
23.5b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
1.3b
(*.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))))))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))))
0.3b
(/.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
28.7b
(/.f64 (/.f64 1 (+.f64 1/2 (+.f64 x x))) (sqrt.f64 (+.f64 1 x)))
0.7b
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))))) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))))
0.4b
(/.f64 1 (+.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (*.f64 x (sqrt.f64 (+.f64 x 1)))))
0.7b
(*.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 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
0.6b
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))) 3))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 2916 to 2070 computations (29% saved)

regimes1.1s (22.2%)

Accuracy

Total 0.3b remaining (94.5%)

Threshold costs 0.3b (94.5%)

Compiler

Compiled 19877 to 15342 computations (22.8% 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)

sample1.1s (20.4%)

Algorithm
intervals
Results
335.0ms2240×body1024valid
168.0ms4283×body128valid
106.0ms977×body512valid
35.0ms500×body256valid
Compiler

Compiled 259 to 198 computations (23.6% saved)

Profiling

Loading profile data...