Details

Time bar (total: 11.1s)

analyze1.7s (15.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.6%0.4%0
0%99.6%0.4%1
0%99.6%0.4%2
0%99.6%0.4%3
0%99.6%0.4%4
0%99.6%0.4%5
0%99.6%0.4%6
0%99.6%0.4%7
0%74.7%25.3%8
0%74.7%25.3%9
0%65.4%34.6%10
0%51.4%48.6%11
0%51.4%48.6%12
0%51.4%48.6%13
0%51.4%48.6%14
Compiler

Compiled 30 to 21 computations (30% saved)

sample137.0ms (1.2%)

Algorithm
intervals
Results
26.0ms305×body128nan
25.0ms256×body128valid
3.0ms28×body128invalid
Compiler

Compiled 67 to 49 computations (26.9% saved)

simplify59.0ms (0.5%)

Algorithm
egg-herbie
Rules
2664×associate-+l+_binary64
1041×associate-+r+_binary64
923×+-commutative_binary64
*-commutative_binary64
distribute-lft-in_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02132
14032
29932
334232
498632
5120832
6120832
7120832
8120832
9226032
10226032
11222632
12222632
13197432
14195832

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
Compiler

Compiled 58 to 40 computations (31% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c)))
0.0b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
0.1b
(*.f64 (-.f64 b 1/2) (log.f64 c))
0.3b
(*.f64 x (log.f64 y))

rewrite156.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
38×add-log-exp_binary64
25×sum-log_binary64
20×add-sqr-sqrt_binary64
18×log-prod_binary64
16×*-un-lft-identity_binary64
Counts
4 → 95
Calls

4 calls:

14.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
13.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c)))
6.0ms
(*.f64 (-.f64 b 1/2) (log.f64 c))
4.0ms
(*.f64 x (log.f64 y))
Compiler

Compiled 3009 to 1007 computations (66.5% saved)

series559.0ms (5%)

Error
0.1b
Counts
4 → 95
Calls

4 calls:

261.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c)))
217.0ms
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
23.0ms
(*.f64 (-.f64 b 1/2) (log.f64 c))
18.0ms
(*.f64 x (log.f64 y))
Compiler

Compiled 5333 to 3336 computations (37.4% saved)

simplify120.0ms (1.1%)

Algorithm
egg-herbie
Rules
874×associate--l+_binary64
269×associate-+r+_binary64
257×associate-+l+_binary64
247×cancel-sign-sub-inv_binary64
236×+-commutative_binary64
Counts
190 → 145
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03504745
18664318
232274141
350844141

prune125.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1387145
Fresh000
Picked101
Done000
Total1397146
Error
0.0b
Counts
146 → 7
Alt Table
StatusErrorProgram
33.2b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))) (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))))
0.4b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 (+.f64 -1/2 b) (log.f64 (sqrt.f64 c)))) (*.f64 (log.f64 (sqrt.f64 c)) (-.f64 b 1/2))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 (+.f64 -1/2 b) (*.f64 2 (log.f64 (cbrt.f64 c))))) (*.f64 (log.f64 (cbrt.f64 c)) (-.f64 b 1/2))) (*.f64 y i))
57.5b
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) 3) (pow.f64 (*.f64 y i) 3)) (+.f64 (*.f64 (*.f64 y i) (*.f64 y i)) (*.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (-.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 y i))))))
0.3b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (log.f64 y) (cbrt.f64 x))) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
0.1b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y)))) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
Compiler

Compiled 3017 to 1179 computations (60.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y))))
0.3b
(+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y))))
0.6b
(cbrt.f64 y)
0.6b
(cbrt.f64 y)

rewrite254.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
60×log-prod_binary64
54×distribute-lft-in_binary64
54×distribute-rgt-in_binary64
36×cbrt-prod_binary64
27×*-un-lft-identity_binary64
Counts
4 → 112
Calls

4 calls:

8.0ms
(+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y))))
6.0ms
(*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y))))
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 4231 to 1786 computations (57.8% saved)

series132.0ms (1.2%)

Error
0.0b
Counts
4 → 18
Calls

4 calls:

45.0ms
(+.f64 (*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 x (log.f64 (cbrt.f64 y))))
45.0ms
(*.f64 x (*.f64 2 (log.f64 (cbrt.f64 y))))
14.0ms
(cbrt.f64 y)
14.0ms
(cbrt.f64 y)
Compiler

Compiled 1704 to 1194 computations (29.9% saved)

simplify116.0ms (1%)

Algorithm
egg-herbie
Rules
457×distribute-rgt-out_binary64
424×cancel-sign-sub-inv_binary64
395×*-commutative_binary64
298×distribute-rgt-neg-in_binary64
288×distribute-rgt-in_binary64
Counts
130 → 108
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01732040
13481767
29891551
328681527
443361527
547751527

prune122.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1062108
Fresh246
Picked101
Done000
Total1096115
Error
0.0b
Counts
115 → 6
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (*.f64 2 (log.f64 (*.f64 (pow.f64 y 1/6) (pow.f64 y 1/6))))) (*.f64 x (log.f64 (cbrt.f64 y)))) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 (+.f64 -1/2 b) (*.f64 2 (log.f64 (cbrt.f64 c))))) (*.f64 (log.f64 (cbrt.f64 c)) (-.f64 b 1/2))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (*.f64 (log.f64 y) 5/6)) (*.f64 (log.f64 (sqrt.f64 (cbrt.f64 y))) x)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
33.2b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))) (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))))
0.4b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))))) (*.f64 y i))
57.5b
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) 3) (pow.f64 (*.f64 y i) 3)) (+.f64 (*.f64 (*.f64 y i) (*.f64 y i)) (*.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (-.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 y i))))))
Compiler

Compiled 2862 to 1360 computations (52.5% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (pow.f64 y 1/6) (pow.f64 y 1/6))
0.6b
(cbrt.f64 y)
4.0b
(pow.f64 y 1/6)
4.0b
(pow.f64 y 1/6)

rewrite168.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
29×add-sqr-sqrt_binary64
24×unpow-prod-down_binary64
18×add-exp-log_binary64
17×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
Counts
4 → 97
Calls

4 calls:

6.0ms
(*.f64 (pow.f64 y 1/6) (pow.f64 y 1/6))
2.0ms
(pow.f64 y 1/6)
2.0ms
(pow.f64 y 1/6)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 3557 to 1983 computations (44.3% saved)

series58.0ms (0.5%)

Error
0.0b
Counts
4 → 12
Calls

4 calls:

14.0ms
(cbrt.f64 y)
13.0ms
(pow.f64 y 1/6)
13.0ms
(pow.f64 y 1/6)
11.0ms
(*.f64 (pow.f64 y 1/6) (pow.f64 y 1/6))
Compiler

Compiled 1339 to 951 computations (29% saved)

simplify86.0ms (0.8%)

Algorithm
egg-herbie
Rules
454×unswap-sqr_binary64
341×distribute-rgt-in_binary64
326×log-div_binary64
306×distribute-lft-in_binary64
290×associate-+l+_binary64
Counts
109 → 80
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
097868
1155796
2549727
31101719
44865719
55173719

prune73.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New80080
Fresh055
Picked011
Done000
Total80686
Error
0.0b
Counts
86 → 6
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (*.f64 2 (log.f64 (*.f64 (pow.f64 y 1/6) (pow.f64 y 1/6))))) (*.f64 x (log.f64 (cbrt.f64 y)))) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 (+.f64 -1/2 b) (*.f64 2 (log.f64 (cbrt.f64 c))))) (*.f64 (log.f64 (cbrt.f64 c)) (-.f64 b 1/2))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (*.f64 (log.f64 y) 5/6)) (*.f64 (log.f64 (sqrt.f64 (cbrt.f64 y))) x)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
33.2b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))) (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))))
0.4b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))))) (*.f64 y i))
57.5b
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) 3) (pow.f64 (*.f64 y i) 3)) (+.f64 (*.f64 (*.f64 y i) (*.f64 y i)) (*.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (-.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 y i))))))
Compiler

Compiled 1896 to 1052 computations (44.5% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 x (*.f64 (log.f64 y) 5/6))
0.2b
(*.f64 (log.f64 (sqrt.f64 (cbrt.f64 y))) x)
0.3b
(*.f64 (log.f64 y) 5/6)
0.6b
(cbrt.f64 y)

rewrite113.0ms (1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
16×pow1_binary64
14×associate-*l*_binary64
14×add-sqr-sqrt_binary64
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
Counts
4 → 70
Calls

4 calls:

5.0ms
(*.f64 (log.f64 (sqrt.f64 (cbrt.f64 y))) x)
5.0ms
(*.f64 x (*.f64 (log.f64 y) 5/6))
3.0ms
(*.f64 (log.f64 y) 5/6)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 2187 to 977 computations (55.3% saved)

series103.0ms (0.9%)

Error
0.0b
Counts
4 → 18
Calls

4 calls:

46.0ms
(*.f64 (log.f64 (sqrt.f64 (cbrt.f64 y))) x)
21.0ms
(*.f64 x (*.f64 (log.f64 y) 5/6))
13.0ms
(cbrt.f64 y)
9.0ms
(*.f64 (log.f64 y) 5/6)
Compiler

Compiled 1795 to 1232 computations (31.4% saved)

simplify87.0ms (0.8%)

Algorithm
egg-herbie
Rules
547×log-prod_binary64
384×*-commutative_binary64
251×log-div_binary64
249×exp-sum_binary64
221×exp-prod_binary64
Counts
88 → 64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0127935
1255817
2735800
31498800
43491796
54762796
65047796

prune71.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New64064
Fresh044
Picked011
Done011
Total64670
Error
0.0b
Counts
70 → 6
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (*.f64 2 (log.f64 (*.f64 (pow.f64 y 1/6) (pow.f64 y 1/6))))) (*.f64 x (log.f64 (cbrt.f64 y)))) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 (+.f64 -1/2 b) (*.f64 2 (log.f64 (cbrt.f64 c))))) (*.f64 (log.f64 (cbrt.f64 c)) (-.f64 b 1/2))) (*.f64 y i))
0.2b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (*.f64 (log.f64 y) 5/6)) (*.f64 (log.f64 (sqrt.f64 (cbrt.f64 y))) x)) z) t) a) (*.f64 (-.f64 b 1/2) (log.f64 c))) (*.f64 y i))
33.2b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))) (sqrt.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 y i) (+.f64 (*.f64 (log.f64 y) x) z)))))))
0.4b
(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)))) (cbrt.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b))))) (*.f64 y i))
57.5b
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) 3) (pow.f64 (*.f64 y i) 3)) (+.f64 (*.f64 (*.f64 y i) (*.f64 y i)) (*.f64 (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z)))) (+.f64 (*.f64 (log.f64 c) (+.f64 -1/2 b)) (-.f64 (+.f64 a (+.f64 t (+.f64 (*.f64 (log.f64 y) x) z))) (*.f64 y i))))))
Compiler

Compiled 1761 to 876 computations (50.3% saved)

regimes3.6s (32.5%)

Accuracy

Total 0.1b remaining (75.1%)

Threshold costs 0.1b (75.1%)

Compiler

Compiled 84188 to 56530 computations (32.9% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02847
14147
24247
34147

end16.0ms (0.1%)

Remove

(sort z t a)

Compiler

Compiled 114 to 81 computations (28.9% saved)

sample3.1s (27.7%)

Algorithm
intervals
Results
899.0ms7996×body128valid
886.0ms9782×body128nan
117.0ms1149×body128invalid
1.0msbody512valid
0.0msbody1024valid
0.0msbody256valid
Compiler

Compiled 377 to 236 computations (37.4% saved)

Profiling

Loading profile data...