Details

Time bar (total: 3.5s)

analyze14.0ms (0.4%)

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

Compiled 9 to 8 computations (11.1% saved)

sample230.0ms (6.6%)

Algorithm
1×intervals
Results
218.0ms256×body128valid
Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify221.0ms (6.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (115.0ms)

IterNodesCost
049759
149759

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
29.4b
Counts
2 → 1
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 2 (*.f64 x x))
28.3b
(sqrt.f64 (*.f64 2 (*.f64 x x)))

rewrite50.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Error
29.3b
Rules
13×pow1_binary64
7×add-exp-log_binary64 add-cbrt-cube_binary64
6×pow-prod-down_binary64
4×add-sqr-sqrt_binary64
3×add-cube-cbrt_binary64 sqrt-pow1_binary64 *-un-lft-identity_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
2×add-log-exp_binary64
1×pow1/2_binary64 sqrt-prod_binary64 unswap-sqr_binary64 associate-*r*_binary64 *-commutative_binary64
Counts
2 → 31
Calls

2 calls:

6.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
6.0ms
(*.f64 2 (*.f64 x x))
Compiler

Compiled 344 to 213 computations (38.1% saved)

series69.0ms (2%)

Error
0.2b
Counts
2 → 6
Calls

2 calls:

38.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
25.0ms
(*.f64 2 (*.f64 x x))
Compiler

Compiled 96 to 91 computations (5.2% saved)

simplify55.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04932300
14932300

prune27.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New33437
Fresh000
Picked011
Done000
Total33538
Error
0.2b
Counts
38 → 5
Compiler

Compiled 349 to 233 computations (33.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))
0.5b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))
28.3b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
28.3b
(sqrt.f64 (*.f64 2 (*.f64 x x)))

rewrite189.0ms (5.5%)

Algorithm
1×rewrite-expression-head
Error
0.2b
Rules
158×pow1_binary64
154×sqrt-pow1_binary64
82×pow-prod-down_binary64
33×sqrt-prod_binary64
28×add-sqr-sqrt_binary64
24×pow1/2_binary64
21×pow-prod-up_binary64
13×add-cube-cbrt_binary64 *-un-lft-identity_binary64 pow-sqr_binary64
9×swap-sqr_binary64
7×associate-*l*_binary64 associate-*r*_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64 unswap-sqr_binary64
3×rem-sqrt-square_binary64
1×pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 sqrt-unprod_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 *-commutative_binary64
Counts
4 → 131
Calls

4 calls:

19.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))
8.0ms
(sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))
4.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
4.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Compiler

Compiled 2665 to 1778 computations (33.3% saved)

series125.0ms (3.6%)

Error
0.2b
Counts
4 → 12
Calls

4 calls:

30.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
30.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))
30.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
26.0ms
(sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))
Compiler

Compiled 437 to 362 computations (17.2% saved)

simplify75.0ms (2.2%)

Algorithm
1×egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
051881158

prune110.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1421143
Fresh123
Picked101
Done011
Total1444148
Error
0.2b
Counts
148 → 4
Compiler

Compiled 1900 to 1245 computations (34.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 3))
0.8b
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 3)
28.3b
(sqrt.f64 (*.f64 2 (*.f64 x x)))
28.3b
(sqrt.f64 (*.f64 2 (*.f64 x x)))

rewrite303.0ms (8.8%)

Algorithm
1×rewrite-expression-head
Error
0.2b
Rules
104×sqrt-prod_binary64
66×add-sqr-sqrt_binary64
29×unpow-prod-down_binary64 cube-prod_binary64
26×pow1_binary64 associate-*r*_binary64
24×unswap-sqr_binary64
21×add-cube-cbrt_binary64 sqrt-pow1_binary64 *-un-lft-identity_binary64
10×add-exp-log_binary64 associate-*l*_binary64
9×pow-prod-down_binary64 pow-pow_binary64
7×add-cbrt-cube_binary64
5×pow1/2_binary64 sqr-pow_binary64
4×add-log-exp_binary64
3×pow-unpow_binary64 prod-exp_binary64
2×pow-to-exp_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64
1×rem-cube-cbrt_binary64 sqrt-pow2_binary64 pow-prod-up_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 143
Calls

4 calls:

28.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 3))
9.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 3)
5.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
5.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
Compiler

Compiled 4448 to 3170 computations (28.7% saved)

series262.0ms (7.6%)

Error
0.2b
Counts
4 → 12
Calls

4 calls:

155.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 3)
33.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
31.0ms
(sqrt.f64 (*.f64 2 (*.f64 x x)))
31.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 3))
Compiler

Compiled 552 to 479 computations (13.2% saved)

simplify115.0ms (3.3%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
048822529
148822529

prune183.0ms (5.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1550155
Fresh022
Picked011
Done011
Total1554159
Error
0.2b
Counts
159 → 4
Compiler

Compiled 3203 to 2220 computations (30.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.4b
(*.f64 x (sqrt.f64 2))

rewrite26.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
8×add-sqr-sqrt_binary64
6×associate-*r*_binary64
4×add-cube-cbrt_binary64 *-un-lft-identity_binary64 sqrt-prod_binary64
3×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64
2×unswap-sqr_binary64
1×pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
1 → 22
Calls

1 calls:

5.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 206 to 166 computations (19.4% saved)

series32.0ms (0.9%)

Error
0.2b
Counts
1 → 3
Calls

1 calls:

31.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 36 to 34 computations (5.6% saved)

simplify45.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05010211

prune19.0ms (0.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New23225
Fresh011
Picked011
Done022
Total23629
Error
0.1b
Counts
29 → 6
Compiler

Compiled 193 to 154 computations (20.2% saved)

regimes250.0ms (7.2%)

Accuracy

Total 0.3b remaining (74%)

Threshold costs 0.3b (74%)

Compiler

Compiled 1470 to 1186 computations (19.3% saved)

bsearch21.0ms (0.6%)

Steps
ItersRangePoint
10
-6.611580846772381e-302
2.1885311794389874e-302
2.6083400758351e-310
Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03929
13929

end0.0ms (0%)

sample1.0s (29.1%)

Algorithm
1×intervals
Results
356.0ms8000×body128valid
Compiler

Compiled 385 to 313 computations (18.7% saved)

Profiling

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