Details

Time bar (total: 5.0s)

analyze991.0ms (19.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
9.4%90.4%0.2%8
9.4%90.4%0.2%9
10.9%88.9%0.2%10
25.9%73.9%0.2%11
47.1%52.7%0.2%12
55.3%44.5%0.2%13
59.2%40.6%0.2%14
Compiler

Compiled 22 to 15 computations (31.8% saved)

sample90.0ms (1.8%)

Algorithm
intervals
Results
15.0ms256×body128valid
Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify56.0ms (1.1%)

Algorithm
egg-herbie
Rules
508×fma-neg_binary64
504×associate-*l/_binary64
466×div-sub_binary64
450×cancel-sign-sub-inv_binary64
403×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01425
13025
27025
317722
448619
5108719
6253419
7443419
8515619

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
2.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.4b
(-.f64 x (/.f64 (*.f64 (*.f64 y 2) z) (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t))))
2.7b
(-.f64 x (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))
Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 x (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))
5.2b
(/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))
5.5b
(/.f64 (*.f64 y t) (*.f64 2 z))

series90.0ms (1.8%)

Counts
3 → 120
Calls

3 calls:

43.0ms
(-.f64 x (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))
31.0ms
(/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))
16.0ms
(/.f64 (*.f64 y t) (*.f64 2 z))

rewrite44.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt_binary64
105×*-un-lft-identity_binary64
77×times-frac_binary64
71×add-cube-cbrt_binary64
63×prod-diff_binary64
Counts
3 → 165
Calls

3 calls:

11.0ms
(-.f64 x (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))
6.0ms
(/.f64 (*.f64 y t) (*.f64 2 z))
5.0ms
(/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))

simplify200.0ms (4%)

Algorithm
egg-herbie
Rules
325×cancel-sign-sub-inv_binary64
304×distribute-neg-frac_binary64
221×times-frac_binary64
203×associate-/l*_binary64
182×associate-*r/_binary64
Counts
285 → 252
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038410579
110577887
233516717
347866717

prune231.0ms (4.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2475252
Fresh101
Picked101
Done000
Total2495254
Error
0b
Counts
254 → 5
Alt Table
StatusErrorProgram
1.0b
(+.f64 x (/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))))
2.7b
(-.f64 x (*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))))
34.2b
(-.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))) (/.f64 (cbrt.f64 y) (sqrt.f64 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))))
23.0b
(-.f64 x (*.f64 (sqrt.f64 (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))) (sqrt.f64 (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))))
25.4b
(fma.f64 2 (/.f64 z t) x)
Compiler

Compiled 10023 to 5115 computations (49% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 2 (/.f64 z t))
0.0b
(+.f64 x (/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))))
4.4b
(/.f64 y (*.f64 2 (/.f64 z t)))
5.2b
(/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))

series111.0ms (2.2%)

Counts
4 → 120
Calls

4 calls:

43.0ms
(/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))
43.0ms
(+.f64 x (/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))))
15.0ms
(/.f64 y (*.f64 2 (/.f64 z t)))
10.0ms
(*.f64 2 (/.f64 z t))

rewrite46.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt_binary64
68×*-un-lft-identity_binary64
63×times-frac_binary64
44×add-cube-cbrt_binary64
20×add-cbrt-cube_binary64
Counts
4 → 162
Calls

4 calls:

17.0ms
(+.f64 x (/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))))
7.0ms
(/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))
5.0ms
(*.f64 2 (/.f64 z t))
4.0ms
(/.f64 y (*.f64 2 (/.f64 z t)))

simplify225.0ms (4.5%)

Algorithm
egg-herbie
Rules
510×fma-def_binary64
205×div-sub_binary64
190×associate-/l*_binary64
184×distribute-frac-neg_binary64
175×cancel-sign-sub-inv_binary64
Counts
282 → 272
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03236334
18016214
226645954
346185954
449975954
549355954

prune224.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2711272
Fresh134
Picked011
Done000
Total2725277
Error
0b
Counts
277 → 5
Alt Table
StatusErrorProgram
32.9b
(+.f64 x (/.f64 (sqrt.f64 (neg.f64 y)) (/.f64 (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))) (sqrt.f64 (neg.f64 y)))))
1.0b
(+.f64 x (/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))))
2.7b
(-.f64 x (*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))))
23.0b
(-.f64 x (*.f64 (sqrt.f64 (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))) (sqrt.f64 (/.f64 y (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))))
25.4b
(fma.f64 2 (/.f64 z t) x)
Compiler

Compiled 6702 to 3126 computations (53.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 x (*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))))
0.1b
(/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))
5.2b
(*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))
5.5b
(/.f64 (*.f64 y t) (*.f64 2 z))

series111.0ms (2.2%)

Counts
3 → 120
Calls

3 calls:

50.0ms
(-.f64 x (*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))))
31.0ms
(*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))
30.0ms
(/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))

rewrite34.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
40×*-un-lft-identity_binary64
32×times-frac_binary64
25×add-cube-cbrt_binary64
21×associate-*r*_binary64
Counts
3 → 109
Calls

3 calls:

14.0ms
(/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))
9.0ms
(*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z)))))
3.0ms
(-.f64 x (*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))))

simplify152.0ms (3%)

Algorithm
egg-herbie
Rules
635×fma-def_binary64
234×fma-neg_binary64
231×associate-/r/_binary64
206×associate-/l/_binary64
205×distribute-rgt-neg-in_binary64
Counts
229 → 213
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02356000
16245773
221305441
348795441
449275441

prune196.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2481249
Fresh123
Picked011
Done011
Total2495254
Error
0b
Counts
254 → 5
Alt Table
StatusErrorProgram
32.9b
(+.f64 x (/.f64 (sqrt.f64 (neg.f64 y)) (/.f64 (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))) (sqrt.f64 (neg.f64 y)))))
1.0b
(+.f64 x (/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))))
2.7b
(-.f64 x (*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))))
22.5b
(-.f64 x (*.f64 (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))) (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z)))))
25.4b
(fma.f64 2 (/.f64 z t) x)
Compiler

Compiled 6485 to 3570 computations (44.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))) (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))))
5.0b
(*.f64 (/.f64 y z) t)
5.2b
(/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))
15.4b
(sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z)))

series156.0ms (3.1%)

Counts
4 → 120
Calls

4 calls:

74.0ms
(sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z)))
37.0ms
(*.f64 (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))) (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))))
30.0ms
(/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))
14.0ms
(*.f64 (/.f64 y z) t)

rewrite42.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt_binary64
79×sqrt-prod_binary64
77×times-frac_binary64
59×*-un-lft-identity_binary64
59×add-cube-cbrt_binary64
Counts
4 → 185
Calls

4 calls:

14.0ms
(*.f64 (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))) (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))))
4.0ms
(*.f64 (/.f64 y z) t)
2.0ms
(/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))
2.0ms
(sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z)))

simplify226.0ms (4.5%)

Algorithm
egg-herbie
Rules
848×fma-def_binary64
318×unswap-sqr_binary64
248×associate-*r*_binary64
245×associate-*l*_binary64
171×fma-neg_binary64
Counts
305 → 298
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03448065
17637626
229007468
348007442
451957442

prune506.0ms (10.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New4790479
Fresh022
Picked011
Done022
Total4795484
Error
0b
Counts
484 → 5
Alt Table
StatusErrorProgram
32.9b
(+.f64 x (/.f64 (sqrt.f64 (neg.f64 y)) (/.f64 (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))) (sqrt.f64 (neg.f64 y)))))
1.0b
(+.f64 x (/.f64 (neg.f64 y) (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))))
2.7b
(-.f64 x (*.f64 y (/.f64 1 (-.f64 z (/.f64 (*.f64 y t) (*.f64 2 z))))))
22.5b
(-.f64 x (*.f64 (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z))) (sqrt.f64 (/.f64 y (fma.f64 (*.f64 (/.f64 y z) t) -1/2 z)))))
25.4b
(fma.f64 2 (/.f64 z t) x)
Compiler

Compiled 17595 to 7845 computations (55.4% saved)

regimes279.0ms (5.6%)

Accuracy

Total 1.0b remaining (99.3%)

Threshold costs 1.0b (99.3%)

Counts
44 → 1
Compiler

Compiled 5200 to 3394 computations (34.7% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01321
12319
23219
33719
43919
53919

end1.0ms (0%)

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample938.0ms (18.8%)

Algorithm
intervals
Results
547.0ms8000×body128valid
Compiler

Compiled 142 to 92 computations (35.2% saved)

Profiling

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