Details

Time bar (total: 11.6s)

analyze2.1s (18.1%)

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)

sample5.1s (43.7%)

Results
2.5s2277×body1024valid
1.2s4196×body128valid
789.0ms1198×body512valid
368.0ms579×body256valid
181.0ms778×body128invalid
10.0msbody2048valid
1.0msbody1024invalid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify53.0ms (0.5%)

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
14.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
14.6b
(-.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)))
14.6b
(+.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)

localize17.0ms (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))
8.1b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
17.4b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series251.0ms (2.2%)

Counts
4 → 80
Calls

4 calls:

147.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
44.0ms
(/.f64 x (tan.f64 B))
42.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
17.0ms
(/.f64 F (sin.f64 B))

rewrite20.0ms (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))
1.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

simplify163.0ms (1.4%)

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

prune338.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New26011271
Fresh101
Picked101
Done000
Total26211273
Error
0.0b
Counts
273 → 11
Alt Table
StatusErrorProgram
10.0b
(-.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)))
36.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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)))
14.6b
(-.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)))
14.6b
(-.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)))
38.9b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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))))
15.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
33.6b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
14.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
36.6b
(-.f64 (-.f64 (+.f64 (/.f64 x (*.f64 (sin.f64 B) (pow.f64 F 2))) (/.f64 1 (*.f64 (sin.f64 B) (pow.f64 F 2)))) (/.f64 1 (sin.f64 B))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10327 to 5782 computations (44% saved)

localize19.0ms (0.2%)

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))
0.3b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
17.4b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series216.0ms (1.9%)

Counts
2 → 44
Calls

2 calls:

149.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
68.0ms
(*.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))

simplify124.0ms (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

prune351.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2691270
Fresh1910
Picked011
Done000
Total27011281
Error
0.0b
Counts
281 → 11
Alt Table
StatusErrorProgram
10.0b
(-.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)))
36.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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)))
14.6b
(-.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)))
14.6b
(-.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)))
38.9b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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))))
15.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
33.6b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
36.6b
(-.f64 (/.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 F 2)) (/.f64 1 (pow.f64 F 2))) 1) (sin.f64 B)) (/.f64 x (tan.f64 B)))
14.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10588 to 6442 computations (39.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x (cos.f64 B))
0.2b
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
8.1b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
17.4b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series34.0ms (0.3%)

Counts
2 → 20
Calls

2 calls:

27.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
7.0ms
(*.f64 x (cos.f64 B))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 43
Calls

2 calls:

4.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms
(*.f64 x (cos.f64 B))

simplify72.0ms (0.6%)

Algorithm
egg-herbie
Rules
746×fma-neg_binary64
515×associate-/l*_binary64
459×times-frac_binary64
349×associate-*l*_binary64
309×distribute-rgt-neg-in_binary64
Counts
63 → 64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0110798
1265700
2952683
33688683
44677683
54938683

prune295.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2503253
Fresh369
Picked101
Done011
Total25410264
Error
0.0b
Counts
264 → 10
Alt Table
StatusErrorProgram
10.0b
(-.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)))
36.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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)))
30.1b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
14.7b
(-.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)) (/.f64 1 (sin.f64 B))))
33.6b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
38.9b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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))))
14.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
39.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sqrt.f64 (sin.f64 B))) (/.f64 (cos.f64 B) (sqrt.f64 (sin.f64 B)))))
Compiler

Compiled 10462 to 5577 computations (46.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
0.7b
(*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))
8.1b
(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)))
18.0b
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

series247.0ms (2.1%)

Counts
3 → 68
Calls

3 calls:

148.0ms
(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)))
50.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)
49.0ms
(*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
72×add-exp-log_binary64
47×prod-exp_binary64
35×add-sqr-sqrt_binary64
21×unpow-prod-down_binary64
20×associate-*l*_binary64
Counts
3 → 125
Calls

3 calls:

8.0ms
(*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)))
6.0ms
(*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))
1.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

simplify174.0ms (1.5%)

Algorithm
egg-herbie
Rules
421×associate-*r*_binary64
376×fma-def_binary64
287×fma-neg_binary64
243×associate-*l*_binary64
190×associate--l+_binary64
Counts
193 → 267
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05607303
115746751
248966751
350916751

prune500.0ms (4.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3750375
Fresh088
Picked011
Done011
Total37510385
Error
0.0b
Counts
385 → 10
Alt Table
StatusErrorProgram
10.0b
(-.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)))
36.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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)))
30.1b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
14.7b
(-.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)) (/.f64 1 (sin.f64 B))))
33.6b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
38.9b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
14.6b
(-.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))))
14.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
39.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sqrt.f64 (sin.f64 B))) (/.f64 (cos.f64 B) (sqrt.f64 (sin.f64 B)))))
Compiler

Compiled 18470 to 11515 computations (37.7% saved)

regimes1.1s (9.2%)

Accuracy

Total 0.2b remaining (75.7%)

Threshold costs 0.2b (75.7%)

Counts
168 → 3
Compiler

Compiled 17776 to 12172 computations (31.5% saved)

bsearch207.0ms (1.8%)

Steps
ItersRangePoint
10
0.0021829558383811938
30561733294828332.0
147382261.82062265
9
-3.368032410325591e+24
-3042867485031892.5
-3108929840052692.0
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03286
14286
25086
35486
45786
55886
65686

end191.0ms (1.6%)

Compiler

Compiled 338 to 220 computations (34.9% saved)

Profiling

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