Details

Time bar (total: 12.8s)

analyze2.1s (16.5%)

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 (39.3%)

Results
2.6s2353×body1024valid
999.0ms4180×body128valid
812.0ms1162×body512valid
254.0ms557×body256valid
246.0ms816×body128invalid
7.0msbody2048valid
1.0msbody1024invalid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify52.0ms (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
13.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.7b
(-.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)))
13.7b
(+.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))
6.4b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
17.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series254.0ms (2%)

Counts
4 → 80
Calls

4 calls:

131.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
61.0ms
(/.f64 x (tan.f64 B))
47.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
15.0ms
(/.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:

6.0ms
(*.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)

simplify162.0ms (1.3%)

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

prune387.0ms (3%)

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
10.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
35.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
16.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) 3))) (/.f64 x (tan.f64 B)))
13.8b
(-.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)))
13.7b
(-.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)))
10.1b
(-.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)))
13.7b
(-.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)))
13.7b
(-.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)))
32.1b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.5b
(-.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))))
30.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10331 to 5780 computations (44.1% saved)

localize16.0ms (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))
0.3b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
17.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series190.0ms (1.5%)

Counts
2 → 44
Calls

2 calls:

127.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
62.0ms
(*.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))

simplify123.0ms (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

prune357.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2700270
Fresh01010
Picked011
Done000
Total27011281
Error
0.0b
Counts
281 → 11
Alt Table
StatusErrorProgram
10.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
35.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
16.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) 3))) (/.f64 x (tan.f64 B)))
13.8b
(-.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)))
13.7b
(-.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)))
10.1b
(-.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)))
13.7b
(-.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)))
13.7b
(-.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)))
32.1b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.5b
(-.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))))
30.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10604 to 6444 computations (39.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))
0.6b
(cbrt.f64 (sin.f64 B))
1.0b
(*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
17.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series531.0ms (4.2%)

Counts
3 → 52
Calls

3 calls:

225.0ms
(*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))
170.0ms
(cbrt.f64 (sin.f64 B))
137.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))

rewrite47.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
166×add-exp-log_binary64
94×prod-exp_binary64
43×div-exp_binary64
38×cbrt-unprod_binary64
38×add-cbrt-cube_binary64
Counts
3 → 125
Calls

3 calls:

17.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
5.0ms
(*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))
1.0ms
(cbrt.f64 (sin.f64 B))

simplify182.0ms (1.4%)

Algorithm
egg-herbie
Rules
720×fma-def_binary64
287×unswap-sqr_binary64
258×associate-*r*_binary64
232×associate-*l*_binary64
212×fma-neg_binary64
Counts
177 → 205
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03527135
19113844
232613780
347323780
449803780
549453780

prune406.0ms (3.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3281329
Fresh099
Picked011
Done011
Total32812340
Error
0.0b
Counts
340 → 12
Alt Table
StatusErrorProgram
10.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
35.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
16.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) 3))) (/.f64 x (tan.f64 B)))
32.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (/.f64 -1 F))) (/.f64 x (tan.f64 B)))
13.8b
(-.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)))
13.7b
(-.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)))
10.1b
(-.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)))
13.7b
(-.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)))
13.7b
(-.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)))
32.1b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.5b
(-.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))))
30.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 16460 to 7032 computations (57.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 F (sin.f64 B))
0.2b
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
6.4b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
17.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series23.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

23.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite7.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×associate-*l*_binary64
10×times-frac_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
1 → 34
Calls

1 calls:

5.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

simplify94.0ms (0.7%)

Algorithm
egg-herbie
Rules
538×fma-def_binary64
518×times-frac_binary64
405×distribute-rgt-neg-in_binary64
331×cancel-sign-sub-inv_binary64
276×distribute-lft-neg-in_binary64
Counts
58 → 62
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
091840
1219766
2574759
31741757
43804757
54613757
64996757
74924757

prune368.0ms (2.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New2902292
Fresh189
Picked011
Done022
Total29113304
Error
0.0b
Counts
304 → 13
Alt Table
StatusErrorProgram
10.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
35.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
10.1b
(-.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)))
32.1b
(-.f64 (/.f64 -1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
16.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) 3))) (/.f64 x (tan.f64 B)))
32.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 (cbrt.f64 F) (cbrt.f64 (sin.f64 B))) (/.f64 -1 F))) (/.f64 x (tan.f64 B)))
13.8b
(-.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)))
13.7b
(-.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)))
14.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) (sin.f64 B)) (cos.f64 B))))
13.7b
(-.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)))
13.7b
(-.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)))
34.5b
(-.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))))
30.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 11610 to 5881 computations (49.3% saved)

regimes1.9s (14.9%)

Accuracy

Total 0.5b remaining (91.9%)

Threshold costs 0.5b (91.9%)

Counts
183 → 3
Compiler

Compiled 20648 to 13912 computations (32.6% saved)

bsearch204.0ms (1.6%)

Steps
ItersRangePoint
8
3.6952027034245e-13
4.059051578284806e-9
3.9610849852233585e-9
10
-48005301062892.2
-0.0009528000911870968
-176800826.1843296
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
03273
14473
25973
36973
47673
57873
67773

end245.0ms (1.9%)

Compiler

Compiled 428 to 270 computations (36.9% saved)

Profiling

Loading profile data...