Details

Time bar (total: 19.1s)

analyze2.8s (14.5%)

Algorithm
1×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%99.6%0.4%8
0%99.6%0.4%9
0%99.6%0.4%10
0%99.6%0.4%11
0%99.6%0.4%12
0%99.6%0.4%13
0%99.6%0.4%14
Compiler

Compiled 24 to 16 computations (33.3% saved)

sample88.0ms (0.5%)

Algorithm
1×intervals
Results
16.0ms256×body128valid
12.0ms184×body128invalid
Compiler

Compiled 55 to 39 computations (29.1% saved)

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
24×associate-+l+_binary64
22×associate-+r+_binary64
17×+-commutative_binary64
4×*-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01622
12722
24722
36722
46722
56722

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.0b
Counts
1 → 1
Alt Table
StatusErrorProgram
▶0.0b
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
Compiler

Compiled 46 to 30 computations (34.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 x y) (*.f64 z t))
0.0b
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
0.0b
(+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

rewrite48.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
19×add-log-exp_binary64
10×sum-log_binary64
3×+-commutative_binary64
3×flip-+_binary64
3×*-un-lft-identity_binary64
Counts
3 → 38
Calls

3 calls:

12.0ms
(+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))
6.0ms
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
3.0ms
(+.f64 (*.f64 x y) (*.f64 z t))
Compiler

Compiled 1014 to 161 computations (84.1% saved)

series180.0ms (0.9%)

Error
0.0b
Counts
3 → 108
Calls

3 calls:

80.0ms
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
50.0ms
(+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))
28.0ms
(+.f64 (*.f64 x y) (*.f64 z t))
Compiler

Compiled 3579 to 2275 computations (36.4% saved)

simplify93.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
799×distribute-rgt-in_binary64
756×distribute-lft-in_binary64
490×associate-*l*_binary64
374×associate-*r*_binary64
255×unswap-sqr_binary64
Counts
146 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0962264
13042219
211122201
345702201
452582201

prune23.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New81384
Fresh000
Picked011
Done000
Total81485
Error
0.0b
Counts
85 → 4
Alt Table
StatusErrorProgram
38.7b
(+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3)) (+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b))))) (*.f64 c i))
▶37.2b
(+.f64 (cbrt.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3)) (*.f64 c i))
✓0.0b
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
42.9b
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3)) (+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))))
Compiler

Compiled 1039 to 270 computations (74% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x))
0.0b
(+.f64 (*.f64 a b) (*.f64 t z))
0.3b
(pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3)
37.7b
(cbrt.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3))

rewrite66.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
12×cbrt-prod_binary64
11×add-log-exp_binary64
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
Counts
4 → 72
Calls

4 calls:

9.0ms
(+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x))
5.0ms
(pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3)
5.0ms
(cbrt.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3))
3.0ms
(+.f64 (*.f64 a b) (*.f64 t z))
Compiler

Compiled 1943 to 485 computations (75% saved)

series536.0ms (2.8%)

Error
0.0b
Counts
4 → 168
Calls

4 calls:

281.0ms
(pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3)
68.0ms
(+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x))
49.0ms
(cbrt.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3))
32.0ms
(+.f64 (*.f64 a b) (*.f64 t z))
Compiler

Compiled 15570 to 10209 computations (34.4% saved)

simplify233.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
800×+-commutative_binary64
674×distribute-rgt-out_binary64
413×unswap-sqr_binary64
388×associate-*r*_binary64
301×associate-*l*_binary64
Counts
240 → 180
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
046311115
1146210641
229649059
352389059

prune48.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1800180
Fresh022
Picked011
Done011
Total1804184
Error
0.0b
Counts
184 → 4
Alt Table
StatusErrorProgram
▶38.7b
(+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3)) (+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b))))) (*.f64 c i))
✓37.2b
(+.f64 (cbrt.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3)) (*.f64 c i))
✓0.0b
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
42.9b
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3)) (+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))))
Compiler

Compiled 3158 to 863 computations (72.7% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b)))
1.8b
(+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b))))
4.0b
(+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3))
39.0b
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3)) (+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b)))))

rewrite130.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
26×*-un-lft-identity_binary64
18×add-sqr-sqrt_binary64
16×add-cube-cbrt_binary64
15×times-frac_binary64
8×add-cbrt-cube_binary64
Counts
4 → 101
Calls

4 calls:

18.0ms
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3)) (+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b)))))
11.0ms
(+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b))))
11.0ms
(*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b)))
9.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3))
Compiler

Compiled 6936 to 1158 computations (83.3% saved)

series1.4s (7.5%)

Error
0.0b
Counts
4 → 174
Calls

4 calls:

736.0ms
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3)) (+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b)))))
274.0ms
(+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b))))
203.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3))
146.0ms
(*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b)))
Compiler

Compiled 25417 to 15203 computations (40.2% saved)

simplify243.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
655×associate-*r*_binary64
545×associate-*l*_binary64
207×distribute-rgt-in_binary64
203×associate-/l*_binary64
187×distribute-lft-in_binary64
Counts
275 → 249
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
044714998
1132014107
2511614107

prune96.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2490249
Fresh011
Picked011
Done022
Total2494253
Error
0.0b
Counts
253 → 4
Alt Table
StatusErrorProgram
✓38.7b
(+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3)) (+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b))))) (*.f64 c i))
✓37.2b
(+.f64 (cbrt.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3)) (*.f64 c i))
✓0.0b
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
▶42.9b
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3)) (+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))))
Compiler

Compiled 8562 to 1788 computations (79.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))
1.6b
(+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i))))
3.2b
(+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3))
41.6b
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3)) (+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))))

rewrite151.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
26×*-un-lft-identity_binary64
18×add-sqr-sqrt_binary64
16×add-cube-cbrt_binary64
15×times-frac_binary64
8×add-cbrt-cube_binary64
Counts
4 → 101
Calls

4 calls:

18.0ms
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3)) (+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))))
16.0ms
(+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3))
14.0ms
(*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))
11.0ms
(+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i))))
Compiler

Compiled 8428 to 1066 computations (87.4% saved)

series8.8s (45.8%)

Error
0.0b
Counts
4 → 260
Calls

4 calls:

6.2s
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3)) (+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))))
1.1s
(+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3))
713.0ms
(+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i))))
346.0ms
(*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))
Compiler

Compiled 95160 to 50185 computations (47.3% saved)

simplify613.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
565×+-commutative_binary64
506×associate-+r+_binary64
390×*-commutative_binary64
364×times-frac_binary64
264×sub-neg_binary64
Counts
361 → 320
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0129342036
1383941526
2502341526

prune188.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3191320
Fresh000
Picked011
Done123
Total3204324
Error
0b
Counts
324 → 4
Alt Table
StatusErrorProgram
38.7b
(+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 t z) (*.f64 y x)) 3) (pow.f64 (*.f64 a b) 3)) (+.f64 (*.f64 (*.f64 a b) (*.f64 a b)) (*.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (-.f64 (+.f64 (*.f64 t z) (*.f64 y x)) (*.f64 a b))))) (*.f64 c i))
47.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 (pow.f64 (*.f64 c i) 3) (pow.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) 3)) (+.f64 (*.f64 (*.f64 c c) (*.f64 i i)) (*.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) (-.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) (*.f64 c i)))))) (cbrt.f64 (/.f64 (+.f64 (pow.f64 (*.f64 c i) 3) (pow.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) 3)) (+.f64 (*.f64 (*.f64 c c) (*.f64 i i)) (*.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) (-.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) (*.f64 c i))))))) (cbrt.f64 (/.f64 (+.f64 (pow.f64 (*.f64 c i) 3) (pow.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) 3)) (+.f64 (*.f64 (*.f64 c c) (*.f64 i i)) (*.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) (-.f64 (+.f64 (*.f64 a b) (+.f64 (*.f64 t z) (*.f64 y x))) (*.f64 c i)))))))
0.0b
(+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))
42.9b
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) 3) (pow.f64 (*.f64 c i) 3)) (+.f64 (*.f64 (*.f64 c i) (*.f64 c i)) (*.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (-.f64 (+.f64 (+.f64 (*.f64 a b) (*.f64 t z)) (*.f64 y x)) (*.f64 c i)))))
Compiler

Compiled 27956 to 5303 computations (81% saved)

regimes1.4s (7.4%)

Accuracy

Total 0.0b remaining (14.6%)

Threshold costs 0.0b (14.6%)

Compiler

Compiled 46366 to 21068 computations (54.6% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
3×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01622
12322
22322

end78.0ms (0.4%)

Remove

(sort c i)

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 207 to 135 computations (34.8% saved)

sample1.8s (9.7%)

Algorithm
1×intervals
Results
562.0ms8000×body128valid
411.0ms5830×body128invalid
Compiler

Compiled 374 to 145 computations (61.2% saved)

Profiling

Loading profile data...