Details

Time bar (total: 11.9s)

analyze2.1s (17.7%)

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
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%93.6%6.4%8
9.4%84.3%6.4%9
14.8%75.7%9.5%10
16%71.4%12.6%11
20.9%65.7%13.4%12
24.2%60.5%15.3%13
24.8%58.6%16.6%14
Compiler

Compiled 31 to 24 computations (22.6% saved)

sample5.0s (41.7%)

Results
2.3s2206×body1024valid
1.2s4305×body128valid
761.0ms1171×body512valid
310.0ms801×body128invalid
255.0ms568×body256valid
10.0msbody2048valid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify53.0ms (0.4%)

Algorithm
egg-herbie
Rules
640×distribute-rgt-neg-in_binary64
474×fma-neg_binary64
418×distribute-lft-neg-in_binary64
379×div-sub_binary64
378×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02335
14928
210028
319528
439128
5107528
6254328
7420028
8495528

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
12.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
12.7b
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (*.f64 F F) 2) (*.f64 2 x)) (neg.f64 (/.f64 1 2)))))
Compiler

Compiled 153 to 108 computations (29.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 F (sin.f64 B))
0.2b
(/.f64 x (tan.f64 B))
5.0b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
18.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series240.0ms (2%)

Counts
4 → 80
Calls

4 calls:

133.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
45.0ms
(/.f64 x (tan.f64 B))
41.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
20.0ms
(/.f64 F (sin.f64 B))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
30×times-frac_binary64
22×add-exp-log_binary64
Counts
4 → 123
Calls

4 calls:

8.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
2.0ms
(/.f64 x (tan.f64 B))
2.0ms
(/.f64 F (sin.f64 B))
2.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

simplify193.0ms (1.6%)

Algorithm
egg-herbie
Rules
302×fma-def_binary64
223×*-commutative_binary64
221×associate-*r*_binary64
218×fma-neg_binary64
202×+-commutative_binary64
Counts
203 → 271
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05005883
113605603
245185575
349845575
449325575

prune330.0ms (2.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New26110271
Fresh101
Picked101
Done000
Total26310273
Error
0.0b
Counts
273 → 10
Alt Table
StatusErrorProgram
31.2b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
34.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
41.0b
(-.f64 (-.f64 (/.f64 1 (sin.f64 B)) (+.f64 (/.f64 x (*.f64 (sin.f64 B) (pow.f64 F 2))) (/.f64 1 (*.f64 (sin.f64 B) (pow.f64 F 2))))) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
10.7b
(-.f64 (*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10305 to 5770 computations (44% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
0.2b
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
0.2b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
18.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series215.0ms (1.8%)

Counts
2 → 44
Calls

2 calls:

137.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
78.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
17×add-exp-log_binary64
12×add-sqr-sqrt_binary64
add-cbrt-cube_binary64
associate-*r*_binary64
*-un-lft-identity_binary64
Counts
2 → 52
Calls

2 calls:

4.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
4.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

simplify130.0ms (1.1%)

Algorithm
egg-herbie
Rules
829×fma-def_binary64
324×cancel-sign-sub-inv_binary64
258×sub-neg_binary64
210×fma-neg_binary64
171×associate-*r*_binary64
Counts
96 → 153
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02983456
18193211
228793191
348063191
449733191
549423191

prune343.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2682270
Fresh279
Picked011
Done000
Total27010280
Error
0.0b
Counts
280 → 10
Alt Table
StatusErrorProgram
31.2b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
34.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
41.0b
(-.f64 (/.f64 (-.f64 1 (+.f64 (/.f64 x (pow.f64 F 2)) (/.f64 1 (pow.f64 F 2)))) (sin.f64 B)) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 1 (/.f64 (sin.f64 B) (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
Compiler

Compiled 10570 to 6434 computations (39.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
0.2b
(/.f64 (sin.f64 B) (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
0.2b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
18.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series78.0ms (0.7%)

Counts
1 → 28
Calls

1 calls:

77.0ms
(/.f64 (sin.f64 B) (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-exp-log_binary64
add-cbrt-cube_binary64
div-exp_binary64
associate-/l*_binary64
*-un-lft-identity_binary64
Counts
1 → 25
Calls

1 calls:

5.0ms
(/.f64 (sin.f64 B) (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))

simplify90.0ms (0.8%)

Algorithm
egg-herbie
Rules
569×associate-/r*_binary64
535×associate-/l*_binary64
462×fma-def_binary64
258×cancel-sign-sub-inv_binary64
243×fma-neg_binary64
Counts
53 → 79
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01882019
15221826
217451701
347571701
449701701
549621701

prune366.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2681269
Fresh178
Picked011
Done011
Total26910279
Error
0.0b
Counts
279 → 10
Alt Table
StatusErrorProgram
33.6b
(-.f64 (/.f64 1 (/.f64 (sin.f64 B) 1)) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
31.2b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
34.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
10.7b
(-.f64 (/.f64 1 (/.f64 (sin.f64 B) (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
Compiler

Compiled 10774 to 6698 computations (37.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
0.7b
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))
5.0b
(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2)))
18.1b
(sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))

series224.0ms (1.9%)

Counts
3 → 60
Calls

3 calls:

143.0ms
(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2)))
52.0ms
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))
29.0ms
(sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))

rewrite33.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
71×add-exp-log_binary64
55×add-sqr-sqrt_binary64
47×prod-exp_binary64
44×unpow-prod-down_binary64
25×sqrt-prod_binary64
Counts
3 → 139
Calls

3 calls:

9.0ms
(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2)))
8.0ms
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))
1.0ms
(sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))

simplify170.0ms (1.4%)

Algorithm
egg-herbie
Rules
524×times-frac_binary64
354×associate-*r*_binary64
324×fma-neg_binary64
229×fma-def_binary64
219×associate-*l*_binary64
Counts
199 → 268
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04106768
111096198
238936109
348926109
449046109

prune495.0ms (4.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New3610361
Fresh077
Picked011
Done022
Total36110371
Error
0.0b
Counts
371 → 10
Alt Table
StatusErrorProgram
33.6b
(-.f64 (/.f64 1 (/.f64 (sin.f64 B) 1)) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
31.2b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
34.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
10.7b
(-.f64 (/.f64 1 (/.f64 (sin.f64 B) (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))) (/.f64 x (tan.f64 B)))
12.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
Compiler

Compiled 15712 to 9406 computations (40.1% saved)

regimes1.4s (11.4%)

Accuracy

Total 0.2b remaining (76.8%)

Threshold costs 0.2b (76.8%)

Counts
201 → 3
Compiler

Compiled 21032 to 14588 computations (30.6% saved)

bsearch204.0ms (1.7%)

Steps
ItersRangePoint
9
2.7884346193169787
38626262.338627286
37847795.092115104
9
-2.386734405602019e+29
-3.324188022566048e+22
-3.3661477811092286e+22
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03599
14699
26099
37599
48399
58699
68499

end195.0ms (1.6%)

Compiler

Compiled 366 to 239 computations (34.7% saved)

Profiling

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