Details

Time bar (total: 7.0s)

analyze1.0s (14.8%)

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
0%99.9%0.1%6
18.7%81.2%0.1%7
32.8%67.1%0.1%8
38.2%61.7%0.1%9
41%58.9%0.1%10
43.9%56%0.1%11
45.4%54.5%0.1%12
46.9%53%0.1%13
47.6%52.3%0.1%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample83.0ms (1.2%)

Algorithm
intervals
Results
23.0ms30×body2048valid
21.0ms42×body1024valid
20.0ms143×body128valid
8.0ms28×body512valid
3.0ms13×body256valid
Compiler

Compiled 33 to 25 computations (24.2% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
associate-/r*_binary64
*-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0920
11220
21420
31420

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
33.2b
Counts
1 → 1
Alt Table
StatusErrorProgram
33.2b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

6.2b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
27.1b
(sin.f64 (/.f64 x (*.f64 y 2)))
27.4b
(tan.f64 (/.f64 x (*.f64 y 2)))

rewrite61.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
33.2b
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
3 → 43
Calls

3 calls:

6.0ms
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
1.0ms
(tan.f64 (/.f64 x (*.f64 y 2)))
1.0ms
(sin.f64 (/.f64 x (*.f64 y 2)))
Compiler

Compiled 1004 to 736 computations (26.7% saved)

series108.0ms (1.5%)

Error
24.8b
Counts
3 → 39
Calls

3 calls:

40.0ms
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
31.0ms
(tan.f64 (/.f64 x (*.f64 y 2)))
19.0ms
(sin.f64 (/.f64 x (*.f64 y 2)))
Compiler

Compiled 1444 to 1088 computations (24.7% saved)

simplify102.0ms (1.5%)

Algorithm
egg-herbie
Rules
640×unswap-sqr_binary64
619×associate-*l*_binary64
362×cancel-sign-sub-inv_binary64
353×associate-/l/_binary64
340×*-commutative_binary64
Counts
82 → 30
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01101996
12331876
25351831
318351822
441761822
555531822

prune24.0ms (0.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New22830
Fresh000
Picked101
Done000
Total23831
Error
26.6b
Counts
31 → 8
Alt Table
StatusErrorProgram
48.8b
(*.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
33.8b
(*.f64 (*.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
33.2b
(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) 3))
49.2b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 x (*.f64 y 2))) 3)))
48.8b
(/.f64 (cbrt.f64 (pow.f64 (tan.f64 (/.f64 x (*.f64 y 2))) 3)) (sin.f64 (/.f64 x (*.f64 y 2))))
30.1b
(+.f64 1 (*.f64 1/8 (*.f64 (/.f64 x y) (/.f64 x y))))
36.0b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (-.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 (pow.f64 (/.f64 x y) 3) 1/48)))
36.6b
(/.f64 (+.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 1/24 (pow.f64 (/.f64 x y) 3))) (sin.f64 (/.f64 x (*.f64 y 2))))
Compiler

Compiled 649 to 458 computations (29.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 1 (*.f64 1/8 (*.f64 (/.f64 x y) (/.f64 x y))))
0.2b
(*.f64 (/.f64 x y) (/.f64 x y))

rewrite93.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
26.6b
Rules
42×add-sqr-sqrt_binary64
40×times-frac_binary64
30×*-un-lft-identity_binary64
30×add-cube-cbrt_binary64
14×add-cbrt-cube_binary64
Counts
2 → 78
Calls

2 calls:

8.0ms
(*.f64 (/.f64 x y) (/.f64 x y))
3.0ms
(+.f64 1 (*.f64 1/8 (*.f64 (/.f64 x y) (/.f64 x y))))
Compiler

Compiled 1504 to 584 computations (61.2% saved)

series41.0ms (0.6%)

Error
26.6b
Counts
2 → 18
Calls

2 calls:

26.0ms
(+.f64 1 (*.f64 1/8 (*.f64 (/.f64 x y) (/.f64 x y))))
13.0ms
(*.f64 (/.f64 x y) (/.f64 x y))
Compiler

Compiled 377 to 319 computations (15.4% saved)

simplify84.0ms (1.2%)

Algorithm
egg-herbie
Rules
743×associate-/l*_binary64
420×times-frac_binary64
354×associate-/l/_binary64
301×unswap-sqr_binary64
277×*-commutative_binary64
Counts
96 → 85
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01331619
13981345
212531149
338251078
449501078

prune63.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New80585
Fresh077
Picked101
Done000
Total811293
Error
26.6b
Counts
93 → 12
Alt Table
StatusErrorProgram
31.2b
(+.f64 1 (*.f64 1/8 (*.f64 x (/.f64 x (*.f64 y y)))))
49.2b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 x (*.f64 y 2))) 3)))
43.7b
(+.f64 1 (*.f64 1/8 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y))))))
36.6b
(/.f64 (+.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 1/24 (pow.f64 (/.f64 x y) 3))) (sin.f64 (/.f64 x (*.f64 y 2))))
43.7b
(exp.f64 (log.f64 (+.f64 1 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x y)) 4) 1/8))))
49.0b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (/.f64 (cbrt.f64 x) (/.f64 (pow.f64 y 3/2) x)) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (sqrt.f64 y)))))
30.1b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) 4) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
48.8b
(*.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
33.8b
(*.f64 (*.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
33.2b
(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) 3))
48.8b
(/.f64 (cbrt.f64 (pow.f64 (tan.f64 (/.f64 x (*.f64 y 2))) 3)) (sin.f64 (/.f64 x (*.f64 y 2))))
36.0b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (-.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 (pow.f64 (/.f64 x y) 3) 1/48)))
Compiler

Compiled 1331 to 800 computations (39.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)
0.6b
(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) 4)

rewrite140.0ms (2%)

Algorithm
rewrite-expression-head
Error
26.4b
Rules
45×cbrt-prod_binary64
40×unpow-prod-down_binary64
36×times-frac_binary64
33×*-un-lft-identity_binary64
33×add-sqr-sqrt_binary64
Counts
4 → 88
Calls

4 calls:

6.0ms
(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) 4)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
Compiler

Compiled 2718 to 1036 computations (61.9% saved)

series110.0ms (1.6%)

Error
26.6b
Counts
4 → 15
Calls

4 calls:

62.0ms
(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) 4)
13.0ms
(cbrt.f64 x)
11.0ms
(cbrt.f64 x)
11.0ms
(cbrt.f64 x)
Compiler

Compiled 1195 to 770 computations (35.6% saved)

simplify113.0ms (1.6%)

Algorithm
egg-herbie
Rules
543×unswap-sqr_binary64
439×times-frac_binary64
403×log-prod_binary64
252×sqr-pow_binary64
149×associate-*l*_binary64
Counts
103 → 66
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01691714
13381634
27091593
319971546
448031546
553571546

prune70.0ms (1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New61566
Fresh2911
Picked101
Done000
Total641478
Error
26.6b
Counts
78 → 14
Alt Table
StatusErrorProgram
48.8b
(*.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
46.6b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 x 1/6) (*.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y)))) 4) (pow.f64 (/.f64 (pow.f64 x 1/6) (cbrt.f64 (cbrt.f64 y))) 4)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
31.2b
(+.f64 1 (*.f64 1/8 (*.f64 x (/.f64 x (*.f64 y y)))))
49.2b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 x (*.f64 y 2))) 3)))
43.7b
(+.f64 1 (*.f64 1/8 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y))))))
36.6b
(/.f64 (+.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 1/24 (pow.f64 (/.f64 x y) 3))) (sin.f64 (/.f64 x (*.f64 y 2))))
46.7b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (exp.f64 (*.f64 4 (log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y))))) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
47.9b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (*.f64 (pow.f64 x 4/3) (pow.f64 (/.f64 1 (cbrt.f64 y)) 4)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
33.8b
(*.f64 (*.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
33.2b
(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) 3))
48.8b
(/.f64 (cbrt.f64 (pow.f64 (tan.f64 (/.f64 x (*.f64 y 2))) 3)) (sin.f64 (/.f64 x (*.f64 y 2))))
44.1b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (*.f64 (*.f64 -1 (cbrt.f64 -1)) (pow.f64 (/.f64 (/.f64 1 y) (/.f64 -1 x)) 4/3)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
43.7b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (/.f64 x y) 4/3) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
36.0b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (-.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 (pow.f64 (/.f64 x y) 3) 1/48)))
Compiler

Compiled 1874 to 1001 computations (46.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 1 (*.f64 1/8 (*.f64 x (/.f64 x (*.f64 y y)))))
3.4b
(*.f64 x (/.f64 x (*.f64 y y)))
7.2b
(/.f64 x (*.f64 y y))

rewrite78.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
26.4b
Rules
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
3 → 60
Calls

3 calls:

6.0ms
(*.f64 x (/.f64 x (*.f64 y y)))
3.0ms
(/.f64 x (*.f64 y y))
2.0ms
(+.f64 1 (*.f64 1/8 (*.f64 x (/.f64 x (*.f64 y y)))))
Compiler

Compiled 1065 to 440 computations (58.7% saved)

series54.0ms (0.8%)

Error
26.6b
Counts
3 → 24
Calls

3 calls:

21.0ms
(+.f64 1 (*.f64 1/8 (*.f64 x (/.f64 x (*.f64 y y)))))
14.0ms
(*.f64 x (/.f64 x (*.f64 y y)))
11.0ms
(/.f64 x (*.f64 y y))
Compiler

Compiled 544 to 447 computations (17.8% saved)

simplify90.0ms (1.3%)

Algorithm
egg-herbie
Rules
672×times-frac_binary64
460×associate-*l/_binary64
456×associate-*r/_binary64
316×associate-/l*_binary64
251×distribute-neg-frac_binary64
Counts
84 → 57
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0961155
1248981
2858951
33296923
44984923
54977923

prune47.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New55257
Fresh01313
Picked101
Done000
Total561571
Error
26.4b
Counts
71 → 15
Alt Table
StatusErrorProgram
48.8b
(*.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
46.6b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 x 1/6) (*.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y)))) 4) (pow.f64 (/.f64 (pow.f64 x 1/6) (cbrt.f64 (cbrt.f64 y))) 4)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
48.8b
(/.f64 (cbrt.f64 (pow.f64 (tan.f64 (/.f64 x (*.f64 y 2))) 3)) (sin.f64 (/.f64 x (*.f64 y 2))))
31.2b
(exp.f64 (log.f64 (+.f64 1 (*.f64 (*.f64 x (/.f64 x (*.f64 y y))) 1/8))))
43.7b
(+.f64 1 (*.f64 1/8 (exp.f64 (*.f64 2 (log.f64 (/.f64 x y))))))
36.6b
(/.f64 (+.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 1/24 (pow.f64 (/.f64 x y) 3))) (sin.f64 (/.f64 x (*.f64 y 2))))
33.5b
(+.f64 1 (*.f64 1/8 (log.f64 (pow.f64 (exp.f64 (/.f64 x (*.f64 y y))) x))))
46.7b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (exp.f64 (*.f64 4 (log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y))))) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
47.9b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (*.f64 (pow.f64 x 4/3) (pow.f64 (/.f64 1 (cbrt.f64 y)) 4)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
33.8b
(*.f64 (*.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (*.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2)))))
33.2b
(cbrt.f64 (pow.f64 (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) 3))
49.2b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 x (*.f64 y 2))) 3)))
44.1b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (*.f64 (*.f64 -1 (cbrt.f64 -1)) (pow.f64 (/.f64 (/.f64 1 y) (/.f64 -1 x)) 4/3)) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
43.7b
(+.f64 1 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (/.f64 x y) 4/3) (/.f64 (cbrt.f64 x) (cbrt.f64 y))) (/.f64 (cbrt.f64 x) (cbrt.f64 y)))))
36.0b
(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (-.f64 (*.f64 1/2 (/.f64 x y)) (*.f64 (pow.f64 (/.f64 x y) 3) 1/48)))
Compiler

Compiled 733 to 436 computations (40.5% saved)

regimes1.1s (15.5%)

Accuracy

Total 0.6b remaining (2.2%)

Threshold costs 0.6b (2.2%)

Compiler

Compiled 20029 to 13752 computations (31.3% saved)

bsearch15.0ms (0.2%)

Steps
ItersRangePoint
11
12.194807360576258
#hash((type . real) (value . NaN))
#hash((type . real) (value . NaN))
Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01546
11946
21846

end1.0ms (0%)

Compiler

Compiled 32 to 24 computations (25% saved)

sample3.5s (49.5%)

Algorithm
intervals
Results
1.2s1100×body2048valid
660.0ms1317×body1024valid
507.0ms4276×body128valid
310.0ms823×body512valid
97.0ms480×body256valid
10.0msbody4096valid
Compiler

Compiled 398 to 279 computations (29.9% saved)

Profiling

Loading profile data...