Details

Time bar (total: 8.1s)

analyze971.0ms (12%)

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
0%74.9%25.1%8
6.2%68.6%25.1%9
7.8%67.1%25.1%10
10.1%64.7%25.1%11
14.8%47.6%37.6%12
15.8%36.8%47.4%13
16.6%35.1%48.3%14
Compiler

Compiled 22 to 17 computations (22.7% saved)

sample113.0ms (1.4%)

Algorithm
intervals
Results
18.0ms256×body128valid
14.0ms197×body128invalid
10.0ms146×body128nan
Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify125.0ms (1.5%)

Algorithm
egg-herbie
Rules
898×fma-neg_binary64
522×fma-def_binary64
417×neg-sub0_binary64
408×neg-mul-1_binary64
378×prod-exp_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01625
12925
25125
310225
421925
546425
6122525
7241625
8370325
9471425
10487425
11422425
12460825
13455525
14494225

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.3b
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
Compiler

Compiled 77 to 57 computations (26% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (sqrt.f64 (exp.f64 t)) t)
0.0b
(sqrt.f64 (exp.f64 t))
0.0b
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b
(*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

series255.0ms (3.1%)

Counts
4 → 68
Calls

4 calls:

221.0ms
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
29.0ms
(*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
2.0ms
(pow.f64 (sqrt.f64 (exp.f64 t)) t)
2.0ms
(sqrt.f64 (exp.f64 t))

rewrite26.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
20×add-exp-log_binary64
18×add-sqr-sqrt_binary64
15×*-un-lft-identity_binary64
15×add-cube-cbrt_binary64
14×associate-*r*_binary64
Counts
4 → 100
Calls

4 calls:

11.0ms
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
6.0ms
(*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))
3.0ms
(pow.f64 (sqrt.f64 (exp.f64 t)) t)
1.0ms
(sqrt.f64 (exp.f64 t))

simplify146.0ms (1.8%)

Algorithm
egg-herbie
Rules
731×fma-def_binary64
434×fma-neg_binary64
304×associate-*l*_binary64
286×associate-*r*_binary64
259×distribute-rgt-in_binary64
Counts
168 → 170
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02114050
15523586
219653419
347193419
449903419

prune156.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1637170
Fresh000
Picked101
Done000
Total1647171
Error
0.0b
Counts
171 → 7
Alt Table
StatusErrorProgram
0.6b
(*.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
1.4b
(*.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 z 2))) (cbrt.f64 (sqrt.f64 (*.f64 z 2))))) (cbrt.f64 (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
31.7b
(*.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x 1/2) y)) (*.f64 (sqrt.f64 (-.f64 (*.f64 x 1/2) y)) (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
31.4b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
0.3b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
Compiler

Compiled 4502 to 2612 computations (42% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (sqrt.f64 (exp.f64 t)) t)
0.0b
(sqrt.f64 (exp.f64 t))
0.0b
(*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series217.0ms (2.7%)

Counts
2 → 48
Calls

2 calls:

194.0ms
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
23.0ms
(*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
17×add-exp-log_binary64
14×add-sqr-sqrt_binary64
11×associate-*r*_binary64
10×prod-exp_binary64
add-cbrt-cube_binary64
Counts
2 → 55
Calls

2 calls:

10.0ms
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
6.0ms
(*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))

simplify101.0ms (1.2%)

Algorithm
egg-herbie
Rules
719×fma-def_binary64
360×sub-neg_binary64
283×associate-*r*_binary64
280×cancel-sign-sub-inv_binary64
246×associate-*l*_binary64
Counts
103 → 106
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01773217
14702963
216792776
346102776
451572776

prune167.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1701171
Fresh066
Picked011
Done000
Total1708178
Error
0.0b
Counts
178 → 8
Alt Table
StatusErrorProgram
1.4b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 2) (sqrt.f64 z)))
1.4b
(*.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 z 2))) (cbrt.f64 (sqrt.f64 (*.f64 z 2))))) (cbrt.f64 (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.6b
(*.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (sqrt.f64 (*.f64 z 2)))) (sqrt.f64 (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
31.7b
(*.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x 1/2) y)) (*.f64 (sqrt.f64 (-.f64 (*.f64 x 1/2) y)) (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
31.4b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (-.f64 (*.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
0.3b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
Compiler

Compiled 4584 to 2655 computations (42.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (exp.f64 t))
0.0b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b
(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))
0.4b
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

series279.0ms (3.4%)

Counts
3 → 84
Calls

3 calls:

224.0ms
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
32.0ms
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
22.0ms
(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))

rewrite42.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
35×distribute-lft-in_binary64
35×distribute-rgt-in_binary64
34×add-exp-log_binary64
27×add-sqr-sqrt_binary64
23×*-un-lft-identity_binary64
Counts
3 → 128
Calls

3 calls:

11.0ms
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
11.0ms
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
6.0ms
(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))

simplify126.0ms (1.6%)

Algorithm
egg-herbie
Rules
618×associate-*l*_binary64
565×associate-*r*_binary64
488×distribute-rgt-in_binary64
329×cancel-sign-sub-inv_binary64
293×fma-neg_binary64
Counts
212 → 186
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02935929
16235031
227104816
349864816

prune211.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2093212
Fresh336
Picked011
Done011
Total2128220
Error
0.0b
Counts
220 → 8
Alt Table
StatusErrorProgram
1.4b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 2) (sqrt.f64 z)))
1.4b
(*.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 z 2))) (cbrt.f64 (sqrt.f64 (*.f64 z 2))))) (cbrt.f64 (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
31.4b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))) (sqrt.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.9b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (sqrt.f64 (cbrt.f64 z)) (-.f64 (*.f64 1/2 x) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.9b
(*.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 1/2 x) (sqrt.f64 z)) (*.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (sqrt.f64 z)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
Compiler

Compiled 6046 to 3111 computations (48.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b
(*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))))
0.4b
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

series465.0ms (5.7%)

Counts
3 → 84
Calls

3 calls:

231.0ms
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
200.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
33.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))))

rewrite71.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
112×distribute-lft-in_binary64
112×distribute-rgt-in_binary64
55×add-exp-log_binary64
39×prod-exp_binary64
36×cancel-sign-sub-inv_binary64
Counts
3 → 182
Calls

3 calls:

19.0ms
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
14.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))))
12.0ms
(*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))

simplify270.0ms (3.3%)

Algorithm
egg-herbie
Rules
776×associate-*l*_binary64
668×associate-*r*_binary64
388×fma-neg_binary64
365×cancel-sign-sub-inv_binary64
348×*-commutative_binary64
Counts
266 → 235
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03938337
16997247
230317135
347197135
452127135

prune298.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2834287
Fresh325
Picked101
Done112
Total2887295
Error
0b
Counts
295 → 7
Alt Table
StatusErrorProgram
1.4b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 2) (sqrt.f64 z)))
1.4b
(*.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 z 2))) (cbrt.f64 (sqrt.f64 (*.f64 z 2))))) (cbrt.f64 (sqrt.f64 (*.f64 z 2)))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (*.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 2))) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.7b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 z)) (*.f64 (-.f64 (*.f64 1/2 x) y) (sqrt.f64 (sqrt.f64 z)))))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.5b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)) (pow.f64 (fabs.f64 (cbrt.f64 (exp.f64 t))) t))) (pow.f64 (sqrt.f64 (cbrt.f64 (exp.f64 t))) t))
0.6b
(*.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
Compiler

Compiled 9951 to 5675 computations (43% saved)

regimes1.8s (22.4%)

Accuracy

Total 0.3b remaining (93.9%)

Threshold costs 0.3b (93.9%)

Counts
112 → 1
Compiler

Compiled 40270 to 30846 computations (23.4% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01625
12225
22725
32925
43025
53025

end1.0ms (0%)

Compiler

Compiled 20 to 15 computations (25% saved)

sample2.2s (26.8%)

Algorithm
intervals
Results
573.0ms8000×body128valid
444.0ms6036×body128invalid
331.0ms4598×body128nan
Compiler

Compiled 235 to 183 computations (22.1% saved)

Profiling

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