Details

Time bar (total: 11.4s)

analyze2.1s (18.5%)

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)

sample4.8s (42.6%)

Results
2.3s2281×body1024valid
1.2s4277×body128valid
716.0ms1103×body512valid
254.0ms585×body256valid
207.0ms810×body128invalid
16.0ms10×body2048valid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify51.0ms (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
12.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.1b
(+.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)))))
12.0b
(-.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)))
Compiler

Compiled 153 to 108 computations (29.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 F (sin.f64 B))
0.1b
(/.f64 x (tan.f64 B))
6.1b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
14.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series227.0ms (2%)

Counts
4 → 80
Calls

4 calls:

128.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
41.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
40.0ms
(/.f64 x (tan.f64 B))
18.0ms
(/.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:

9.0ms
(*.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)

simplify157.0ms (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

prune327.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New25912271
Fresh101
Picked101
Done000
Total26112273
Error
0.0b
Counts
273 → 12
Alt Table
StatusErrorProgram
8.4b
(-.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)))
35.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
12.1b
(-.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))))
32.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
12.1b
(-.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)))
28.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
9.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) 1) (*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
12.0b
(-.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)))
12.1b
(-.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)))
12.1b
(-.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)))
Compiler

Compiled 10365 to 5800 computations (44% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (tan.f64 B))
0.2b
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
0.3b
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
14.2b
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

series289.0ms (2.5%)

Counts
3 → 80
Calls

3 calls:

131.0ms
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
120.0ms
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
38.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

rewrite23.0ms (0.2%)

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

simplify157.0ms (1.4%)

Algorithm
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

prune424.0ms (3.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New3072309
Fresh11011
Picked011
Done000
Total30813321
Error
0.0b
Counts
321 → 13
Alt Table
StatusErrorProgram
8.4b
(-.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)))
35.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
12.1b
(-.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)))
28.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
30.3b
(-.f64 (*.f64 F (/.f64 (/.f64 -1 F) (sin.f64 B))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
9.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) 1) (*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
33.0b
(-.f64 (*.f64 F (/.f64 1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
12.0b
(-.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)))
12.1b
(-.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)))
12.1b
(-.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)))
12.1b
(-.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))))
Compiler

Compiled 12774 to 7655 computations (40.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 F) (cbrt.f64 F))
0.5b
(cbrt.f64 F)
2.7b
(*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
14.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series403.0ms (3.5%)

Counts
3 → 52
Calls

3 calls:

333.0ms
(*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
38.0ms
(*.f64 (cbrt.f64 F) (cbrt.f64 F))
31.0ms
(cbrt.f64 F)

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt_binary64
31×cbrt-prod_binary64
28×associate-*l*_binary64
27×*-un-lft-identity_binary64
27×add-cube-cbrt_binary64
Counts
3 → 112
Calls

3 calls:

9.0ms
(*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
4.0ms
(*.f64 (cbrt.f64 F) (cbrt.f64 F))
1.0ms
(cbrt.f64 F)

simplify125.0ms (1.1%)

Algorithm
egg-herbie
Rules
691×times-frac_binary64
413×associate-*r*_binary64
354×associate-*l*_binary64
310×unswap-sqr_binary64
299×fma-neg_binary64
Counts
164 → 215
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03524320
19703944
235693844
344763787
453933787

prune424.0ms (3.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New3270327
Fresh01111
Picked011
Done011
Total32713340
Error
0.0b
Counts
340 → 13
Alt Table
StatusErrorProgram
8.4b
(-.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)))
35.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
12.1b
(-.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)))
28.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
30.3b
(-.f64 (*.f64 F (/.f64 (/.f64 -1 F) (sin.f64 B))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
9.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) 1) (*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
33.0b
(-.f64 (*.f64 F (/.f64 1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
12.0b
(-.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)))
12.1b
(-.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)))
12.1b
(-.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)))
12.1b
(-.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))))
Compiler

Compiled 15033 to 7893 computations (47.5% saved)

localize15.0ms (0.1%)

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))
6.1b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
14.2b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series27.0ms (0.2%)

Counts
2 → 20
Calls

2 calls:

20.0ms
(/.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))

simplify70.0ms (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

prune306.0ms (2.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New2512253
Fresh2810
Picked011
Done022
Total25313266
Error
0.0b
Counts
266 → 13
Alt Table
StatusErrorProgram
30.3b
(-.f64 (*.f64 F (/.f64 (/.f64 -1 F) (sin.f64 B))) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (/.f64 (*.f64 x (cos.f64 B)) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))))
8.4b
(-.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)))
35.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
12.1b
(-.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)))
28.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
9.7b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) 1) (*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
38.6b
(-.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)))))
33.0b
(-.f64 (*.f64 F (/.f64 1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
12.0b
(-.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)))
12.1b
(-.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)))
12.1b
(-.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))))
Compiler

Compiled 10342 to 5491 computations (46.9% saved)

regimes957.0ms (8.4%)

Accuracy

Total 0.2b remaining (79.8%)

Threshold costs 0.2b (79.8%)

Counts
147 → 3
Compiler

Compiled 14980 to 10132 computations (32.4% saved)

bsearch116.0ms (1%)

Steps
ItersRangePoint
7
70.32492494732747
2780455177.700001
360268048.4305206
4
-15075350121773.389
-9789801094472.744
-9954974501575.89
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
02868
13568
24268
34668
44968
55068
64968

end227.0ms (2%)

Compiler

Compiled 390 to 249 computations (36.2% saved)

Profiling

Loading profile data...