Details

Time bar (total: 15.4s)

analyze2.1s (13.9%)

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 (32.3%)

Results
2.5s2257×body1024valid
1.1s4310×body128valid
837.0ms1128×body512valid
240.0ms550×body256valid
199.0ms828×body128invalid
19.0ms11×body2048valid
1.0msbody1024invalid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify51.0ms (0.3%)

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
13.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.3b
(+.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)))))
13.2b
(-.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)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (tan.f64 B))
0.1b
(/.f64 F (sin.f64 B))
8.5b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
15.9b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series249.0ms (1.6%)

Counts
4 → 80
Calls

4 calls:

153.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
40.0ms
(/.f64 x (tan.f64 B))
40.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
16.0ms
(/.f64 F (sin.f64 B))

rewrite19.0ms (0.1%)

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))
3.0ms
(/.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)

simplify159.0ms (1%)

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

prune369.0ms (2.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New25813271
Fresh101
Picked101
Done000
Total26013273
Error
0.0b
Counts
273 → 13
Alt Table
StatusErrorProgram
13.3b
(-.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))))
13.4b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (cbrt.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))) (cbrt.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)))
35.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
32.5b
(-.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))))
23.1b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)) 3)) (/.f64 x (tan.f64 B)))
34.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 B)) 3)))
13.2b
(-.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)))
8.6b
(-.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)))
13.3b
(-.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)))
13.3b
(-.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)))
29.9b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.6b
(-.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)))
30.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10461 to 5878 computations (43.8% 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 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
0.3b
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
15.9b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series195.0ms (1.3%)

Counts
2 → 44
Calls

2 calls:

126.0ms
(/.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:

5.0ms
(/.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))

simplify129.0ms (0.8%)

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

prune411.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2655270
Fresh4812
Picked101
Done000
Total27013283
Error
0.0b
Counts
283 → 13
Alt Table
StatusErrorProgram
13.4b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (cbrt.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))) (cbrt.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)))
35.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
32.5b
(-.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))))
23.1b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)) 3)) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
34.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 B)) 3)))
8.6b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
13.3b
(-.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)))
29.9b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.7b
(-.f64 (/.f64 (*.f64 F (*.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))) (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (/.f64 (*.f64 (*.f64 F (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)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
30.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10776 to 6571 computations (39% 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 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
0.3b
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
15.9b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series187.0ms (1.2%)

Counts
2 → 56
Calls

2 calls:

126.0ms
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
61.0ms
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite30.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
180×times-frac_binary64
100×*-un-lft-identity_binary64
100×add-sqr-sqrt_binary64
100×add-cube-cbrt_binary64
48×unpow-prod-down_binary64
Counts
2 → 169
Calls

2 calls:

7.0ms
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
4.0ms
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

simplify217.0ms (1.4%)

Algorithm
egg-herbie
Rules
273×associate-/r/_binary64
273×fma-neg_binary64
268×*-commutative_binary64
253×associate-*r*_binary64
246×sub-neg_binary64
Counts
225 → 366
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04948996
112428644
244528532
348708532
449268532

prune678.0ms (4.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New4803483
Fresh4812
Picked101
Done000
Total48511496
Error
0.0b
Counts
496 → 11
Alt Table
StatusErrorProgram
35.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
8.7b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 1 (/.f64 (tan.f64 B) x)))
32.5b
(-.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))))
8.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
8.6b
(-.f64 (/.f64 F (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2)) (/.f64 (sin.f64 B) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2)))) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
29.9b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (*.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (/.f64 (*.f64 (*.f64 F (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)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 B)) 3)))
30.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 19044 to 10642 computations (44.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))))
0.3b
(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
0.3b
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
15.9b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series251.0ms (1.6%)

Counts
2 → 56
Calls

2 calls:

125.0ms
(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
125.0ms
(*.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))))

rewrite60.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
311×times-frac_binary64
179×add-sqr-sqrt_binary64
157×*-un-lft-identity_binary64
153×add-cube-cbrt_binary64
80×associate-*r*_binary64
Counts
2 → 253
Calls

2 calls:

19.0ms
(*.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))))
6.0ms
(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))

simplify298.0ms (1.9%)

Algorithm
egg-herbie
Rules
302×cancel-sign-sub-inv_binary64
252×sub-neg_binary64
240×fma-neg_binary64
236×associate-*r*_binary64
215×fma-def_binary64
Counts
309 → 454
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043810696
111209832
237719642
348019642
449939642
549309642

prune955.0ms (6.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New6491650
Fresh1910
Picked101
Done000
Total65110661
Error
0.0b
Counts
661 → 10
Alt Table
StatusErrorProgram
32.5b
(-.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))))
8.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
8.6b
(-.f64 (/.f64 F (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2)) (/.f64 (sin.f64 B) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2)))) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
8.7b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 1 (/.f64 (tan.f64 B) x)))
29.9b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
30.9b
(-.f64 (*.f64 F (/.f64 -1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
8.6b
(-.f64 (/.f64 (*.f64 (*.f64 F (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)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (cbrt.f64 (pow.f64 (/.f64 x (tan.f64 B)) 3)))
30.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 26542 to 15872 computations (40.2% saved)

regimes3.7s (24.1%)

Accuracy

Total 0.2b remaining (78.6%)

Threshold costs 0.2b (78.6%)

Counts
449 → 3
Compiler

Compiled 48996 to 34264 computations (30.1% saved)

bsearch42.0ms (0.3%)

Steps
ItersRangePoint
1
1995845.7212479336
815518231474.0066
1281406620.2027764
1
-3.546638116797885e+30
-4.883497167538938e+26
-3.9384766394149384e+28
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03074
14174
24874
35274
45574
55674
65574

end196.0ms (1.3%)

Compiler

Compiled 336 to 226 computations (32.7% saved)

Profiling

Loading profile data...