Details

Time bar (total: 8.1s)

analyze111.0ms (1.4%)

Algorithm
1×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
25%74.9%0.1%5
25%74.9%0.1%6
56.2%43.7%0.1%7
56.2%43.7%0.1%8
76.5%23.4%0.1%9
76.5%23.4%0.1%10
87.8%12.1%0.1%11
87.8%12.1%0.1%12
93.8%6.1%0.1%13
93.8%6.1%0.1%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample14.0ms (0.2%)

Algorithm
1×intervals
Results
8.0ms256×body128valid
Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify147.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (140.0ms)

IterNodesCost
0553310

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 2
Compiler

Compiled 23 to 21 computations (8.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite15.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
7×*-un-lft-identity_binary64
3×add-log-exp_binary64
2×distribute-lft-out_binary64 times-frac_binary64
1×flip3-+_binary64 pow1_binary64 frac-add_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-sqr-sqrt_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
1 → 14
Calls

1 calls:

14.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series37.0ms (0.4%)

Counts
1 → 3
Calls

1 calls:

37.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify62.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
04936239
14936239

prune18.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New16117
Fresh101
Picked011
Done000
Total17219

Merged error: 0.0b

Counts
19 → 2
Compiler

Compiled 222 to 168 computations (24.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 1/4 (*.f64 y y))
0.6b
(/.f64 1/4 (*.f64 x x))
4.0b
(-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x)))
26.7b
(/.f64 (-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite80.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
236×add-sqr-sqrt_binary64
191×times-frac_binary64
110×*-un-lft-identity_binary64
84×difference-of-squares_binary64
42×distribute-lft-out--_binary64
28×add-cube-cbrt_binary64
25×div-inv_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64
15×associate-/l*_binary64
11×associate-/r*_binary64
6×add-log-exp_binary64
5×cbrt-undiv_binary64 div-exp_binary64
4×pow1_binary64
3×associate-/l/_binary64 flip3--_binary64 associate-/r/_binary64 clear-num_binary64 frac-2neg_binary64 flip--_binary64 frac-sub_binary64
2×cbrt-unprod_binary64 prod-exp_binary64
1×sub-neg_binary64 diff-log_binary64 div-sub_binary64
Counts
4 → 178
Calls

4 calls:

30.0ms
(/.f64 (-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
10.0ms
(-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x)))
5.0ms
(/.f64 1/4 (*.f64 x x))
5.0ms
(/.f64 1/4 (*.f64 y y))

series215.0ms (2.6%)

Counts
4 → 12
Calls

4 calls:

97.0ms
(/.f64 (-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
50.0ms
(-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x)))
35.0ms
(/.f64 1/4 (*.f64 x x))
33.0ms
(/.f64 1/4 (*.f64 y y))

simplify96.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049026365
149026365

prune321.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1891190
Fresh000
Picked011
Done011
Total1893192

Merged error: 0.0b

Counts
192 → 3
Compiler

Compiled 5604 to 3693 computations (34.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (/.f64 (sqrt.f64 1/4) y) (/.f64 (sqrt.f64 1/4) x))
0.0b
(/.f64 (+.f64 (/.f64 (sqrt.f64 1/4) y) (/.f64 (sqrt.f64 1/4) x)) (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
0.0b
(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.0b
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

rewrite441.0ms (5.4%)

Algorithm
1×rewrite-expression-head
Rules
2945×times-frac_binary64
2749×*-un-lft-identity_binary64
1627×add-sqr-sqrt_binary64
814×distribute-lft-out_binary64
499×add-cube-cbrt_binary64
432×sqrt-prod_binary64
304×difference-of-squares_binary64
152×distribute-lft-out--_binary64
124×div-inv_binary64
57×associate-/r*_binary64
46×associate-/r/_binary64
22×associate-/l*_binary64
18×flip3-+_binary64 frac-add_binary64 flip-+_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
8×add-log-exp_binary64
6×associate-/l/_binary64
4×pow1_binary64 cbrt-undiv_binary64 div-exp_binary64
2×clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 sum-log_binary64
1×flip3--_binary64 div-sub_binary64 flip--_binary64 frac-sub_binary64
Counts
4 → 873
Calls

4 calls:

85.0ms
(/.f64 (+.f64 (/.f64 (sqrt.f64 1/4) y) (/.f64 (sqrt.f64 1/4) x)) (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
34.0ms
(+.f64 (/.f64 (sqrt.f64 1/4) y) (/.f64 (sqrt.f64 1/4) x))
31.0ms
(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
15.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series240.0ms (2.9%)

Counts
4 → 12
Calls

4 calls:

117.0ms
(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
47.0ms
(/.f64 (+.f64 (/.f64 (sqrt.f64 1/4) y) (/.f64 (sqrt.f64 1/4) x)) (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
39.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
37.0ms
(+.f64 (/.f64 (sqrt.f64 1/4) y) (/.f64 (sqrt.f64 1/4) x))

simplify429.0ms (5.3%)

Algorithm
1×egg-herbie
Counts
885 → 885
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
0548449853

prune4.1s (50%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New8832885
Fresh000
Picked101
Done022
Total8844888

Merged error: 0b

Counts
888 → 4
Compiler

Compiled 36145 to 27604 computations (23.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
0.0b
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
0.2b
(/.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.2b
(/.f64 (/.f64 1/2 y) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite112.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
298×times-frac_binary64
296×*-un-lft-identity_binary64
116×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
60×distribute-lft-out_binary64
26×associate-/l*_binary64
14×add-exp-log_binary64 add-cbrt-cube_binary64 div-inv_binary64
10×associate-/r*_binary64
8×add-log-exp_binary64
6×cbrt-undiv_binary64 associate-/r/_binary64 div-exp_binary64
4×flip3-+_binary64 pow1_binary64 frac-add_binary64 flip-+_binary64
2×associate-/l/_binary64 clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 230
Calls

4 calls:

21.0ms
(/.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
21.0ms
(/.f64 (/.f64 1/2 y) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
15.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
14.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series231.0ms (2.8%)

Counts
4 → 12
Calls

4 calls:

80.0ms
(/.f64 (/.f64 -1/2 x) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
74.0ms
(/.f64 (/.f64 1/2 y) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
42.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
35.0ms
(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify102.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
056826334

prune805.0ms (9.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2420242
Fresh011
Picked011
Done022
Total2424246

Merged error: 0b

Counts
246 → 4
Compiler

Compiled 10250 to 7733 computations (24.6% saved)

regimes25.0ms (0.3%)

Compiler

Compiled 188 to 160 computations (14.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0910
1910

end0.0ms (0%)

sample517.0ms (6.4%)

Algorithm
1×intervals
Results
238.0ms8000×body128valid
Compiler

Compiled 116 to 100 computations (13.8% saved)

Profiling

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