Details

Time bar (total: 4.0s)

analyze96.0ms (2.4%)

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)

sample13.0ms (0.3%)

Algorithm
1×intervals
Results
7.0ms256×body128valid
Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify158.0ms (4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (151.0ms)

IterNodesCost
0493210
1493210

prune6.0ms (0.2%)

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 39 to 35 computations (10.3% 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 (0.4%)

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))

series35.0ms (0.9%)

Counts
1 → 3
Calls

1 calls:

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

simplify70.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
04855239
14855239

prune22.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New15217
Fresh101
Picked011
Done000
Total16319

Merged error: 0.0b

Counts
19 → 3
Compiler

Compiled 351 to 277 computations (21.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
0.6b
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite93.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Rules
63×*-un-lft-identity_binary64
43×cbrt-prod_binary64
33×cbrt-div_binary64
23×add-sqr-sqrt_binary64
16×distribute-lft-out_binary64
15×add-cube-cbrt_binary64
14×times-frac_binary64
11×flip3-+_binary64 pow1_binary64 frac-add_binary64 flip-+_binary64
10×swap-sqr_binary64
9×pow1/3_binary64 frac-times_binary64
8×associate-*r*_binary64 associate-*l*_binary64
6×add-exp-log_binary64
4×add-log-exp_binary64 add-cbrt-cube_binary64 unswap-sqr_binary64
3×associate-*r/_binary64 associate-*l/_binary64
2×pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64
1×cbrt-unprod_binary64 pow-plus_binary64 prod-exp_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 111
Calls

4 calls:

34.0ms
(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
17.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series736.0ms (18.6%)

Counts
4 → 12
Calls

4 calls:

199.0ms
(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
180.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
179.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
178.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify102.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
048822939
148822939

prune258.0ms (6.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1221123
Fresh011
Picked011
Done011
Total1224126

Merged error: 0b

Counts
126 → 4
Compiler

Compiled 4300 to 3382 computations (21.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite65.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
32×*-un-lft-identity_binary64
20×cbrt-prod_binary64
12×cbrt-div_binary64
8×distribute-lft-out_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 times-frac_binary64
4×flip3-+_binary64 add-log-exp_binary64 pow1_binary64 pow1/3_binary64 frac-add_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip-+_binary64
Counts
4 → 64
Calls

4 calls:

16.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
14.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
14.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
13.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series716.0ms (18.1%)

Counts
4 → 12
Calls

4 calls:

183.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
178.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
178.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
176.0ms
(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify56.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
050491640

prune196.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New76076
Fresh011
Picked011
Done022
Total76480

Merged error: 0b

Counts
80 → 4
Compiler

Compiled 3615 to 2861 computations (20.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 1/4 (*.f64 y y))
0.5b
(/.f64 1/4 (*.f64 x x))
2.1b
(-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x)))
30.3b
(/.f64 (-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite81.0ms (2.1%)

Algorithm
1×rewrite-expression-head
Rules
238×add-sqr-sqrt_binary64
194×times-frac_binary64
112×*-un-lft-identity_binary64
84×difference-of-squares_binary64
42×distribute-lft-out--_binary64
30×add-cube-cbrt_binary64
26×div-inv_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64
15×associate-/l*_binary64
11×associate-/r*_binary64
7×cancel-sign-sub-inv_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 → 185
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)))
14.0ms
(-.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))

series222.0ms (5.6%)

Counts
4 → 12
Calls

4 calls:

100.0ms
(/.f64 (-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
57.0ms
(-.f64 (/.f64 1/4 (*.f64 y y)) (/.f64 1/4 (*.f64 x x)))
33.0ms
(/.f64 1/4 (*.f64 x x))
32.0ms
(/.f64 1/4 (*.f64 y y))

simplify117.0ms (2.9%)

Algorithm
1×egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049036441
149036441

prune334.0ms (8.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1970197
Fresh000
Picked011
Done033
Total1974201

Merged error: 0b

Counts
201 → 4
Compiler

Compiled 5840 to 3860 computations (33.9% saved)

regimes27.0ms (0.7%)

Compiler

Compiled 186 to 162 computations (12.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0910
1910

end0.0ms (0%)

sample501.0ms (12.6%)

Algorithm
1×intervals
Results
229.0ms8000×body128valid
0.0ms1×body128invalid
Compiler

Compiled 115 to 101 computations (12.2% saved)

Profiling

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