Details

Time bar (total: 4.5s)

analyze177.0ms (3.9%)

Algorithm
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
0%99.9%0.1%5
25%74.9%0.1%6
93.7%6.2%0.1%7
96.8%3.1%0.1%8
99.5%0.4%0.1%9
99.7%0.2%0.1%10
99.8%0.1%0.1%11
99.9%0%0.1%12
99.9%0%0.1%13
99.9%0%0.1%14
Compiler

Compiled 22 to 13 computations (40.9% saved)

sample18.0ms (0.4%)

Algorithm
intervals
Results
10.0ms256×body128valid
Compiler

Compiled 45 to 27 computations (40% saved)

simplify111.0ms (2.5%)

Algorithm
egg-herbie
Rules
494×sub-neg_binary64
455×cancel-sign-sub-inv_binary64
430×times-frac_binary64 distribute-rgt-neg-in_binary64
410×unswap-sqr_binary64
364×div-sub_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01028
12128
24828
39428
417628
527428
633928
744828
868728
9204628
10337928
11372728
12406528
13428628
14478728

prune204.0ms (4.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
29.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
29.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))
Compiler

Compiled 63 to 36 computations (42.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))
4.8b
(-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))
28.9b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))

rewrite121.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
29.4b
Rules
11×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
times-frac_binary64
add-log-exp_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64 associate-/l*_binary64 associate-/r*_binary64
Counts
3 → 55
Calls

3 calls:

9.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))
4.0ms
(+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))
4.0ms
(-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))
Compiler

Compiled 1848 to 956 computations (48.3% saved)

series114.0ms (2.5%)

Error
0.4b
Counts
3 → 42
Calls

3 calls:

42.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))
30.0ms
(-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))
30.0ms
(+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y))
Compiler

Compiled 1201 to 892 computations (25.7% saved)

simplify162.0ms (3.6%)

Algorithm
egg-herbie
Rules
457×associate-*l*_binary64
382×associate-*r*_binary64
253×times-frac_binary64
235×associate-/l*_binary64
224×div-sub_binary64
Counts
97 → 84
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01152459
13102283
29552260
340232260
447642242
549842242
649312242

prune53.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New81384
Fresh000
Picked011
Done000
Total81485
Error
8.5b
Counts
85 → 4
Alt Table
StatusErrorProgram
29.4b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3))
29.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))
37.4b
(-.f64 1 (*.f64 8 (/.f64 (*.f64 y y) (*.f64 x x))))
34.6b
(+.f64 -1 (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 y y))))
Compiler

Compiled 1639 to 781 computations (52.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3))
0.0b
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3)
4.8b
(+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4))
28.9b
(/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4)))

rewrite177.0ms (3.9%)

Algorithm
rewrite-expression-head
Error
8.5b
Rules
45×times-frac_binary64
42×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
36×cbrt-prod_binary64
30×unpow-prod-down_binary64 cube-prod_binary64
10×associate-/r/_binary64
Counts
4 → 138
Calls

4 calls:

12.0ms
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3)
10.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3))
9.0ms
(/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4)))
4.0ms
(+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4))
Compiler

Compiled 4268 to 2053 computations (51.9% saved)

series202.0ms (4.5%)

Error
0.4b
Counts
4 → 66
Calls

4 calls:

57.0ms
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3)
46.0ms
(/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4)))
44.0ms
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3))
31.0ms
(+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4))
Compiler

Compiled 1795 to 1469 computations (18.2% saved)

simplify227.0ms (5.1%)

Algorithm
egg-herbie
Rules
435×unswap-sqr_binary64
301×distribute-rgt-in_binary64
260×cancel-sign-sub-inv_binary64
254×log-prod_binary64
179×exp-prod_binary64
Counts
204 → 146
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02107518
15876927
219586694
342326694
449356694

prune74.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1460146
Fresh022
Picked011
Done011
Total1464150
Error
8.5b
Counts
150 → 4
Alt Table
StatusErrorProgram
29.4b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3))
29.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))
37.4b
(-.f64 1 (*.f64 8 (/.f64 (*.f64 y y) (*.f64 x x))))
34.6b
(+.f64 -1 (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 y y))))
Compiler

Compiled 2100 to 1064 computations (49.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 -1 (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 y y))))
15.8b
(/.f64 (*.f64 x x) (*.f64 y y))

rewrite42.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
3.0b
Rules
14×add-exp-log_binary64 add-cbrt-cube_binary64
prod-exp_binary64 div-exp_binary64 add-log-exp_binary64 cbrt-undiv_binary64 cbrt-unprod_binary64
pow1_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
frac-2neg_binary64 times-frac_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 associate-/r*_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64
Counts
2 → 32
Calls

2 calls:

6.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
3.0ms
(+.f64 -1 (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 y y))))
Compiler

Compiled 639 to 265 computations (58.5% saved)

series62.0ms (1.4%)

Error
8.5b
Counts
2 → 18
Calls

2 calls:

37.0ms
(+.f64 -1 (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 y y))))
21.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 388 to 328 computations (15.5% saved)

simplify75.0ms (1.7%)

Algorithm
egg-herbie
Rules
561×times-frac_binary64
485×associate-*l/_binary64
418×associate-*r/_binary64
408×associate-*l*_binary64
398×unswap-sqr_binary64
Counts
50 → 37
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
074864
1203682
2707636
33977622
45222622

prune23.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New34337
Fresh011
Picked101
Done022
Total35641
Error
3.0b
Counts
41 → 6
Alt Table
StatusErrorProgram
29.4b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3))
29.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))
37.4b
(-.f64 1 (*.f64 8 (/.f64 (*.f64 y y) (*.f64 x x))))
28.9b
(+.f64 -1 (*.f64 1/2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
28.9b
(+.f64 -1 (*.f64 1/2 (/.f64 x (/.f64 y (/.f64 x y)))))
43.6b
(+.f64 -1 (*.f64 1/2 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y))))))
Compiler

Compiled 406 to 230 computations (43.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite158.0ms (3.5%)

Algorithm
rewrite-expression-head
Error
3.0b
Rules
116×add-sqr-sqrt_binary64
72×fabs-mul_binary64
60×times-frac_binary64
34×add-cube-cbrt_binary64 *-un-lft-identity_binary64
28×fabs-sqr_binary64
Counts
2 → 110
Calls

2 calls:

16.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
3.0ms
(+.f64 -1 (*.f64 1/2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
Compiler

Compiled 2435 to 802 computations (67.1% saved)

series41.0ms (0.9%)

Error
3.0b
Counts
2 → 12
Calls

2 calls:

21.0ms
(+.f64 -1 (*.f64 1/2 (*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
17.0ms
(*.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))
Compiler

Compiled 310 to 256 computations (17.4% saved)

simplify102.0ms (2.3%)

Algorithm
egg-herbie
Rules
596×associate-/r/_binary64
372×*-commutative_binary64
277×associate-/l*_binary64
207×distribute-rgt-neg-in_binary64
203×unswap-sqr_binary64
Counts
122 → 114
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01792472
13571883
211681782
322971674
450411674

prune87.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1095114
Fresh033
Picked101
Done022
Total11010120
Error
3.0b
Counts
120 → 10
Alt Table
StatusErrorProgram
29.4b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) -4)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y y) 4))) 3))
28.9b
(+.f64 -1 (*.f64 1/2 (*.f64 (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) 4) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))))))
29.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y 4) y)))
37.4b
(-.f64 1 (*.f64 8 (/.f64 (*.f64 y y) (*.f64 x x))))
28.9b
(+.f64 -1 (*.f64 1/2 (*.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 4) (*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))))))
28.9b
(+.f64 -1 (*.f64 1/2 (/.f64 x (/.f64 y (/.f64 x y)))))
28.9b
(+.f64 -1 (*.f64 1/2 (*.f64 (/.f64 (/.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 y)))))
28.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/2) 1)) (cbrt.f64 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/2) 1))) (cbrt.f64 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/2) 1)))
63.3b
(exp.f64 (log.f64 (-.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/2) 1)))
43.6b
(+.f64 -1 (*.f64 1/2 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y))))))
Compiler

Compiled 1401 to 689 computations (50.8% saved)

regimes1.4s (30.1%)

Accuracy

Total 8.7b remaining (69.2%)

Threshold costs 0b (0%)

Compiler

Compiled 16122 to 9447 computations (41.4% saved)

bsearch66.0ms (1.5%)

Steps
ItersRangePoint
7
9.149815947076835e+77
7.234835594360878e+79
7.090214672623547e+79
8
9.03016989431881e-142
2.6685145719873674e-138
1.5065991278181313e-140
10
-1.0445487681739017e-98
-2.5607176706663901e-110
-2.0471170134376602e-106
11
-1.312751001694106e+151
-4.0820874523168483e+129
-6.782623048135753e+135
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0.2%)

Algorithm
egg-herbie
Rules
11×*-commutative_binary64
+-commutative_binary64
fabs-mul_binary64
sub-neg_binary64 distribute-rgt-neg-in_binary64
fabs-div_binary64 sqr-abs_binary64 neg-mul-1_binary64 neg-sub0_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058210
190210
2103210
3113210
4115210
5116210
6114210

end2.0ms (0.1%)

Compiler

Compiled 138 to 69 computations (50% saved)

sample793.0ms (17.7%)

Algorithm
intervals
Results
334.0ms8000×body128valid
Compiler

Compiled 367 to 215 computations (41.4% saved)

Profiling

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