Details

Time bar (total: 6.6s)

analyze268.0ms (4.1%)

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
12.5%87.4%0.1%4
12.5%87.4%0.1%5
15.6%84.3%0.1%6
32.8%67.1%0.1%7
38.2%61.6%0.1%8
46%53.8%0.1%9
62.6%37.3%0.1%10
67.2%32.7%0.1%11
71.1%28.8%0.1%12
81.6%18.2%0.1%13
84.1%15.7%0.1%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample149.0ms (2.3%)

Algorithm
intervals
Results
9.0ms256×body128valid
Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify229.0ms (3.5%)

Algorithm
egg-herbie
Rules
2674×fma-neg_binary64
2270×div-sub_binary64
1877×fma-def_binary64
968×associate-/l/_binary64
705×associate-/r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11413
22013
32813
44113
55513
67213
78513
810213
912713
1015513
1121513
1235613
1366613
14120413
15174613
16189713
17200613
18224613
19245213
20199313
21235413
22240013
23260913
24273713
25281213
26298213
27298413
28300413
29300413
30385013
31513513

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
8.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series30.0ms (0.4%)

Counts
1 → 36
Calls

1 calls:

29.0ms
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt_binary64
53×*-un-lft-identity_binary64
42×times-frac_binary64
20×difference-of-squares_binary64
15×add-cube-cbrt_binary64
Counts
1 → 62
Calls

1 calls:

8.0ms
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

simplify111.0ms (1.7%)

Algorithm
egg-herbie
Rules
450×fma-def_binary64
293×times-frac_binary64
278×associate-/l*_binary64
255×distribute-rgt-in_binary64
189×distribute-lft-in_binary64
Counts
98 → 115
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01782629
14522552
214332416
347832407
448852405
549742405

prune89.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1096115
Fresh000
Picked011
Done000
Total1097116
Error
0b
Counts
116 → 7
Alt Table
StatusErrorProgram
34.5b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))) (+.f64 1 (sqrt.f64 (/.f64 y z)))) (/.f64 (cbrt.f64 (+.f64 y x)) (-.f64 1 (sqrt.f64 (/.f64 y z)))))
37.4b
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 z 2) x) (pow.f64 y 2)) (+.f64 (/.f64 (pow.f64 z 2) y) (+.f64 (/.f64 (*.f64 z x) y) (+.f64 z (/.f64 (pow.f64 z 3) (pow.f64 y 2)))))))
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
10.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))
39.0b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))
18.7b
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (*.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
23.0b
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))))
Compiler

Compiled 2780 to 1229 computations (55.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))
0.5b
(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))
0.6b
(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series433.0ms (6.6%)

Counts
3 → 108
Calls

3 calls:

276.0ms
(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))
128.0ms
(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))
28.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))

rewrite159.0ms (2.4%)

Algorithm
rewrite-expression-head
Rules
406×*-un-lft-identity_binary64
346×add-sqr-sqrt_binary64
311×times-frac_binary64
298×cbrt-prod_binary64
112×difference-of-squares_binary64
Counts
3 → 313
Calls

3 calls:

46.0ms
(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))
34.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))
7.0ms
(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))

simplify421.0ms (6.4%)

Algorithm
egg-herbie
Rules
406×*-commutative_binary64
260×+-commutative_binary64
200×associate-+r+_binary64
187×fma-def_binary64
129×cancel-sign-sub-inv_binary64
Counts
421 → 532
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0114024964
1356723645
2489823360
3498823360

prune1.0s (15.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New112321125
Fresh325
Picked101
Done011
Total112751132
Error
0b
Counts
1132 → 5
Alt Table
StatusErrorProgram
35.8b
(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 z (/.f64 (*.f64 z z) y))))
39.0b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
10.0b
(pow.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 3)
23.0b
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))))
Compiler

Compiled 66846 to 34029 computations (49.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))))
0.8b
(pow.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 3)
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series653.0ms (9.9%)

Counts
1 → 36
Calls

1 calls:

653.0ms
(pow.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 3)

rewrite28.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
94×*-un-lft-identity_binary64
94×add-sqr-sqrt_binary64
80×times-frac_binary64
76×cbrt-prod_binary64
41×cube-prod_binary64
Counts
1 → 103
Calls

1 calls:

11.0ms
(pow.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 3)

simplify144.0ms (2.2%)

Algorithm
egg-herbie
Rules
894×fma-def_binary64
461×times-frac_binary64
381×associate-/l*_binary64
348×associate-/r*_binary64
262×associate-*r*_binary64
Counts
139 → 126
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04436781
114066208
249666123
355556123

prune293.0ms (4.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3650365
Fresh033
Picked011
Done011
Total3655370
Error
0b
Counts
370 → 5
Alt Table
StatusErrorProgram
35.8b
(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 z (/.f64 (*.f64 z z) y))))
39.0b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
10.0b
(pow.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 3)
23.0b
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))))
Compiler

Compiled 15101 to 8322 computations (44.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (/.f64 y z) (/.f64 y z))
4.2b
(+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))
4.3b
(/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3)))
19.5b
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))))

series254.0ms (3.9%)

Counts
4 → 120
Calls

4 calls:

121.0ms
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))))
78.0ms
(/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3)))
32.0ms
(*.f64 (/.f64 y z) (/.f64 y z))
22.0ms
(+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))

rewrite98.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
273×add-sqr-sqrt_binary64
215×*-un-lft-identity_binary64
205×times-frac_binary64
108×difference-of-squares_binary64
83×associate-*l*_binary64
Counts
4 → 287
Calls

4 calls:

28.0ms
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))))
12.0ms
(/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3)))
10.0ms
(*.f64 (/.f64 y z) (/.f64 y z))
5.0ms
(+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))

simplify289.0ms (4.4%)

Algorithm
egg-herbie
Rules
368×distribute-rgt-in_binary64
332×distribute-lft-in_binary64
296×associate-/l*_binary64
289×associate-*l/_binary64
241×associate-*r/_binary64
Counts
407 → 430
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049912421
1154011628
2459511448
3486411448
4497911448

prune321.0ms (4.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New4300430
Fresh022
Picked011
Done022
Total4305435
Error
0b
Counts
435 → 5
Alt Table
StatusErrorProgram
35.8b
(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 z (/.f64 (*.f64 z z) y))))
39.0b
(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))
8.8b
(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
10.0b
(pow.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))) 3)
23.0b
(*.f64 (/.f64 (+.f64 y x) (-.f64 1 (pow.f64 (/.f64 y z) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (/.f64 y z) (/.f64 y z)) (*.f64 1 (/.f64 y z)))))
Compiler

Compiled 17465 to 8319 computations (52.4% saved)

regimes924.0ms (14%)

Accuracy

Total 0.4b remaining (94.3%)

Threshold costs 0.4b (94.3%)

Counts
119 → 3
Compiler

Compiled 10845 to 6831 computations (37% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
22×+-commutative_binary64
18×*-commutative_binary64
17×sub-neg_binary64
16×neg-sub0_binary64
16×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03299
15199
27099
39999
412699
515299
616499
716999
817099
916999

end1.0ms (0%)

Compiler

Compiled 69 to 42 computations (39.1% saved)

sample599.0ms (9.1%)

Algorithm
intervals
Results
288.0ms7998×body128valid
0.0msbody2048valid
0.0msbody256valid
Compiler

Compiled 176 to 113 computations (35.8% saved)

Profiling

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