Details

Time bar (total: 2.4s)

analyze149.0ms (6.3%)

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%62.4%12.6%6
25%46.8%28.2%7
31.2%35.9%32.9%8
39%25%36%9
42.9%18.7%38.3%10
47.2%12.9%39.9%11
49.4%9.6%41.1%12
51.6%6.5%41.9%13
52.7%4.8%42.4%14
Compiler

Compiled 16 to 10 computations (37.5% saved)

sample26.0ms (1.1%)

Algorithm
1×intervals
Results
8.0ms256×body128valid
0.0ms8×body128invalid
Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify11.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
8×*-commutative_binary64
7×+-commutative_binary64
3×associate-*l*_binary64 associate-*r*_binary64 associate-+l+_binary64 associate-+r+_binary64
2×distribute-rgt-out_binary64 distribute-lft-out_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01019
11816
23616
33816
43816

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.0b
(+.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x 2) y)) (*.f64 y y))
▶0.0b
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))
Compiler

Compiled 69 to 42 computations (39.1% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 x (+.f64 x (*.f64 2 y)))
0.0b
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))

rewrite58.0ms (2.5%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
6×add-sqr-sqrt_binary64
4×add-log-exp_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
3×associate-*l*_binary64 associate-*r*_binary64
2×flip3-+_binary64 flip-+_binary64 distribute-rgt-in_binary64 associate-+l+_binary64 distribute-lft-in_binary64 associate-*r/_binary64
1×sum-log_binary64 +-commutative_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
Counts
2 → 35
Calls

2 calls:

6.0ms
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))
5.0ms
(*.f64 x (+.f64 x (*.f64 2 y)))
Compiler

Compiled 670 to 354 computations (47.2% saved)

series73.0ms (3.1%)

Error
0.0b
Counts
2 → 30
Calls

2 calls:

38.0ms
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))
24.0ms
(*.f64 x (+.f64 x (*.f64 2 y)))
Compiler

Compiled 584 to 401 computations (31.3% saved)

simplify87.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
492×distribute-rgt-in_binary64
476×distribute-lft-in_binary64
459×sub-neg_binary64
310×+-commutative_binary64
209×*-commutative_binary64
Counts
65 → 59
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
074910
1233853
2796841
32526841
43876841
55056841

prune45.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New55459
Fresh101
Picked011
Done000
Total56561
Error
0b
Counts
61 → 5
Alt Table
StatusErrorProgram
✓0.0b
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))
▶0.0b
(*.f64 (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))))
1.3b
(+.f64 (*.f64 x x) (*.f64 y y))
0.0b
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
35.5b
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x (*.f64 y 2)) (+.f64 x (*.f64 y 2))))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x (*.f64 y 2))) (*.f64 y y)))
Compiler

Compiled 715 to 396 computations (44.6% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
0.0b
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
5.2b
(sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x)))
5.2b
(sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x)))

rewrite105.0ms (4.5%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
8×add-log-exp_binary64 add-sqr-sqrt_binary64
6×pow1_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 flip3-+_binary64 sqrt-div_binary64 flip-+_binary64 associate-+l+_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 sum-log_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 +-commutative_binary64
Counts
4 → 56
Calls

4 calls:

8.0ms
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
6.0ms
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
6.0ms
(sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x)))
5.0ms
(sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x)))
Compiler

Compiled 2004 to 1078 computations (46.2% saved)

series174.0ms (7.4%)

Error
0b
Counts
4 → 60
Calls

4 calls:

44.0ms
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
43.0ms
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
33.0ms
(sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x)))
31.0ms
(sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x)))
Compiler

Compiled 2266 to 1462 computations (35.5% saved)

simplify116.0ms (4.9%)

Algorithm
1×egg-herbie
Rules
422×cancel-sign-sub-inv_binary64
302×sub-neg_binary64
300×associate-*l*_binary64
289×distribute-rgt-out_binary64
281×distribute-rgt-in_binary64
Counts
116 → 86
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0641982
11611784
24651736
319731736
442481736
549511736

prune70.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New86086
Fresh033
Picked011
Done011
Total86591
Error
0b
Counts
91 → 5
Alt Table
StatusErrorProgram
✓0.0b
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))
✓0.0b
(*.f64 (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))))
1.3b
(+.f64 (*.f64 x x) (*.f64 y y))
▶0.0b
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
35.5b
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x (*.f64 y 2)) (+.f64 x (*.f64 y 2))))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x (*.f64 y 2))) (*.f64 y y)))
Compiler

Compiled 1770 to 991 computations (44% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 y (+.f64 y (*.f64 2 x)))
0.0b
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))

rewrite50.0ms (2.1%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
6×add-sqr-sqrt_binary64
4×add-log-exp_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
3×associate-*l*_binary64 associate-*r*_binary64
2×flip3-+_binary64 flip-+_binary64 distribute-rgt-in_binary64 associate-+l+_binary64 distribute-lft-in_binary64 associate-*r/_binary64
1×sum-log_binary64 +-commutative_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
Counts
2 → 35
Calls

2 calls:

6.0ms
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
5.0ms
(*.f64 y (+.f64 y (*.f64 2 x)))
Compiler

Compiled 670 to 354 computations (47.2% saved)

series68.0ms (2.9%)

Error
0b
Counts
2 → 30
Calls

2 calls:

37.0ms
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
23.0ms
(*.f64 y (+.f64 y (*.f64 2 x)))
Compiler

Compiled 584 to 401 computations (31.3% saved)

simplify111.0ms (4.7%)

Algorithm
1×egg-herbie
Rules
459×sub-neg_binary64
414×distribute-rgt-in_binary64
400×distribute-lft-in_binary64
297×+-commutative_binary64
211×*-commutative_binary64
Counts
65 → 56
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
074928
1230853
2768841
32383841
43724841
54980841
64936841

prune35.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New56056
Fresh022
Picked011
Done022
Total56561
Error
0b
Counts
61 → 5
Alt Table
StatusErrorProgram
✓0.0b
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))
✓0.0b
(*.f64 (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))))
▶1.3b
(+.f64 (*.f64 x x) (*.f64 y y))
✓0.0b
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
35.5b
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x (*.f64 y 2)) (+.f64 x (*.f64 y 2))))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x (*.f64 y 2))) (*.f64 y y)))
Compiler

Compiled 666 to 369 computations (44.6% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 (*.f64 x x) (*.f64 y y))

rewrite13.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
3×add-log-exp_binary64
1×sum-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 *-un-lft-identity_binary64 flip-+_binary64 +-commutative_binary64
Counts
1 → 11
Calls

1 calls:

4.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 180 to 40 computations (77.8% saved)

series24.0ms (1%)

Error
0b
Counts
1 → 12
Calls

1 calls:

22.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 153 to 119 computations (22.2% saved)

simplify94.0ms (4%)

Algorithm
1×egg-herbie
Rules
836×unswap-sqr_binary64
336×cancel-sign-sub-inv_binary64
248×distribute-rgt-out_binary64
245×distribute-rgt-in_binary64
222×*-commutative_binary64
Counts
23 → 20
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
031292
1108247
2273247
3812247
41976247
54695247
64994247
74927247

prune13.0ms (0.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New20020
Fresh011
Picked011
Done033
Total20525
Error
0b
Counts
25 → 5
Alt Table
StatusErrorProgram
0.0b
(+.f64 (*.f64 x (+.f64 x (*.f64 2 y))) (*.f64 y y))
0.0b
(*.f64 (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))))
1.3b
(+.f64 (*.f64 x x) (*.f64 y y))
0.0b
(+.f64 (*.f64 y (+.f64 y (*.f64 2 x))) (*.f64 x x))
35.5b
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 (+.f64 x (*.f64 y 2)) (+.f64 x (*.f64 y 2))))) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x (*.f64 y 2))) (*.f64 y y)))
Compiler

Compiled 219 to 95 computations (56.6% saved)

regimes162.0ms (6.8%)

Accuracy

Total 0.0b remaining (70.9%)

Threshold costs 0.0b (70.9%)

Compiler

Compiled 2031 to 1292 computations (36.4% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64 +-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
11316
21316

end6.0ms (0.3%)

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample834.0ms (35.2%)

Algorithm
1×intervals
Results
294.0ms8000×body128valid
6.0ms185×body128invalid
Compiler

Compiled 126 to 78 computations (38.1% saved)

Profiling

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