Details

Time bar (total: 11.9s)

analyze2.6s (21.7%)

Algorithm
1×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)

sample216.0ms (1.8%)

Algorithm
1×intervals
Results
67.0ms79×body1024valid
27.0ms131×body128valid
16.0ms30×body512valid
6.0ms16×body256valid
3.0ms19×body128invalid
1.0ms6×body128nan
Compiler

Compiled 64 to 50 computations (21.9% saved)

simplify52.0ms (0.4%)

Algorithm
1×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

prune6.0ms (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)))
14.7b
(+.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)

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))
✓8.3b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
✓18.7b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series301.0ms (2.5%)

Counts
4 → 80
Calls

4 calls:

169.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
69.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
44.0ms
(/.f64 x (tan.f64 B))
18.0ms
(/.f64 F (sin.f64 B))

rewrite21.0ms (0.2%)

Algorithm
1×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:

7.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
3.0ms
(/.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)

simplify170.0ms (1.4%)

Algorithm
1×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

prune446.0ms (3.7%)

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
39.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (sqrt.f64 (tan.f64 B))) (/.f64 x (sqrt.f64 (tan.f64 B)))))
9.7b
(-.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)))
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)) (sin.f64 B)))
38.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.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)))
15.2b
(-.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))))
32.7b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
29.4b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
35.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
▶9.6b
(-.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)))
Compiler

Compiled 10273 to 5740 computations (44.1% saved)

localize17.0ms (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))
18.7b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series247.0ms (2.1%)

Counts
2 → 44
Calls

2 calls:

174.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
73.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite11.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
17×add-exp-log_binary64
12×add-sqr-sqrt_binary64
9×add-cbrt-cube_binary64
7×associate-*r*_binary64
7×*-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))

simplify127.0ms (1.1%)

Algorithm
1×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

prune392.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2691270
Fresh189
Picked011
Done000
Total27010280
Error
0.0b
Counts
280 → 10
Alt Table
StatusErrorProgram
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)) (sin.f64 B)))
38.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
37.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (sqrt.f64 (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)))
▶9.7b
(-.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)))
15.2b
(-.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))))
32.7b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
29.4b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
35.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
✓9.6b
(-.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)))
Compiler

Compiled 10542 to 6400 computations (39.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
✓0.3b
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
✓0.4b
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
✓18.7b
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

series317.0ms (2.7%)

Counts
3 → 80
Calls

3 calls:

137.0ms
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
136.0ms
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
43.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

rewrite24.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
45×times-frac_binary64
36×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
25×associate-*r*_binary64
Counts
3 → 116
Calls

3 calls:

9.0ms
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
4.0ms
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
2.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

simplify170.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
347×fma-def_binary64
295×fma-neg_binary64
245×associate-*r*_binary64
228×associate-/l*_binary64
215×associate-/r*_binary64
Counts
196 → 268
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05327772
114827320
249837320
351997320

prune408.0ms (3.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3090309
Fresh088
Picked011
Done011
Total30910319
Error
0.0b
Counts
319 → 10
Alt Table
StatusErrorProgram
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)) (sin.f64 B)))
38.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
37.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (sqrt.f64 (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)))
✓9.7b
(-.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)))
15.2b
(-.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))))
32.7b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
29.4b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
35.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
✓9.6b
(-.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)))
Compiler

Compiled 12624 to 7554 computations (40.2% saved)

localize17.0ms (0.1%)

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))
✓8.3b
(*.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)))
✓19.2b
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

series271.0ms (2.3%)

Counts
3 → 68
Calls

3 calls:

132.0ms
(*.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)))
89.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)
50.0ms
(*.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))

rewrite27.0ms (0.2%)

Algorithm
1×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:

9.0ms
(*.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)))
5.0ms
(*.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)

simplify156.0ms (1.3%)

Algorithm
1×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

prune506.0ms (4.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New3750375
Fresh077
Picked011
Done022
Total37510385
Error
0.0b
Counts
385 → 10
Alt Table
StatusErrorProgram
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)) (sin.f64 B)))
38.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
37.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (sqrt.f64 (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)))
✓9.7b
(-.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)))
15.2b
(-.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))))
32.7b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
29.4b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
35.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
✓9.6b
(-.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)))
Compiler

Compiled 18478 to 11516 computations (37.7% saved)

regimes1.2s (10.1%)

Accuracy

Total 0.2b remaining (77.9%)

Threshold costs 0.2b (77.9%)

Counts
182 → 3
Compiler

Compiled 18652 to 12844 computations (31.1% saved)

bsearch195.0ms (1.6%)

Steps
ItersRangePoint
9
0.00737178278892891
22677133.435409427
22161619.295327645
10
-6.943659643005233e+40
-2.4409010565986352e+22
-2.4974421569274437e+22
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02971
13671
24371
34771
45071
55171
65071

end1.0ms (0%)

Compiler

Compiled 50 to 29 computations (42% saved)

sample4.0s (33.5%)

Algorithm
1×intervals
Results
1.8s2231×body1024valid
726.0ms4130×body128valid
546.0ms1086×body512valid
186.0ms552×body256valid
117.0ms697×body128invalid
15.0ms112×body128nan
3.0ms1×body2048valid
1.0ms1×body1024invalid
Compiler

Compiled 310 to 205 computations (33.9% saved)

Profiling

Loading profile data...