Details

Time bar (total: 5.5s)

analyze349.0ms (6.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
78.1%21.9%0%13
78.1%21.8%0%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample3.0s (54.3%)

Results
1.5s2107×body2048valid
463.0ms1129×body1024valid
441.0ms1532×body512valid
286.0ms2593×body128valid
160.0ms794×body256valid
66.0ms101×body4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify23.0ms (0.4%)

Algorithm
egg-herbie
Rules
426×fma-def_binary64
293×fma-neg_binary64
85×div-sub_binary64
74×associate-/l*_binary64
63×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11612
22712
34012
47212
511012
615812
725312
838312
952612
1064012
1162512
1257012

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
29.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
29.5b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 x)
1.9b
(-.f64 1 (cos.f64 x))
13.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series12.0ms (0.2%)

Counts
3 → 20
Calls

3 calls:

8.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)

rewrite14.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
prod-diff_binary64
add-cbrt-cube_binary64
Counts
3 → 72
Calls

3 calls:

7.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms
(-.f64 1 (cos.f64 x))
1.0ms
(cos.f64 x)

simplify95.0ms (1.7%)

Algorithm
egg-herbie
Rules
666×fma-neg_binary64
414×associate-*l*_binary64
405×times-frac_binary64
398×fma-def_binary64
365×associate-*r*_binary64
Counts
92 → 108
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01331257
13071122
29311062
335911062
448901062
549081062

prune94.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1008108
Fresh000
Picked101
Done000
Total1018109
Error
0.0b
Counts
109 → 8
Alt Table
StatusErrorProgram
14.5b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
29.3b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
28.8b
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
33.5b
(-.f64 (fma.f64 1/720 (pow.f64 x 4) 1/2) (fma.f64 1/24 (*.f64 x x) (*.f64 1/40320 (pow.f64 x 6))))
29.3b
(/.f64 (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 x (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x)))
29.8b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)))) (cbrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
47.8b
(/.f64 (*.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (-.f64 1 (sqrt.f64 (cos.f64 x)))) (*.f64 x x))
29.6b
(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (*.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
Compiler

Compiled 2028 to 1039 computations (48.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
0.6b
(+.f64 1 (cos.f64 x))
13.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series34.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

15.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
12.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
6.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms
(+.f64 1 (cos.f64 x))

rewrite27.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube_binary64
32×add-exp-log_binary64
25×*-un-lft-identity_binary64
22×times-frac_binary64
17×add-sqr-sqrt_binary64
Counts
4 → 122
Calls

4 calls:

8.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
6.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

simplify102.0ms (1.9%)

Algorithm
egg-herbie
Rules
610×associate-*l/_binary64
540×associate-/r/_binary64
423×fma-def_binary64
335×fma-neg_binary64
214×cancel-sign-sub-inv_binary64
Counts
162 → 206
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02042904
15042230
217672192
346432192
449352192

prune176.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1988206
Fresh707
Picked101
Done000
Total2068214
Error
0b
Counts
214 → 8
Alt Table
StatusErrorProgram
0.5b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
0.2b
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
0.5b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
13.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))
14.7b
(/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 x x) (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))))
14.5b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 (cos.f64 x) 1)) (*.f64 x x))
13.7b
(*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (fma.f64 x (pow.f64 (cos.f64 x) 3) x)) (/.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1) 1) x))
0.2b
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
Compiler

Compiled 4472 to 2023 computations (54.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b
(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b
(/.f64 (sin.f64 x) x)

series35.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

13.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
10.0ms
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
9.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms
(/.f64 (sin.f64 x) x)

rewrite29.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
40×times-frac_binary64
34×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
20×add-cbrt-cube_binary64
Counts
4 → 122
Calls

4 calls:

10.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
9.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
2.0ms
(/.f64 (sin.f64 x) x)
0.0ms
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))

simplify154.0ms (2.8%)

Algorithm
egg-herbie
Rules
594×associate-/l*_binary64
557×associate-*l/_binary64
474×associate-*l*_binary64
464×associate-*r/_binary64
426×times-frac_binary64
Counts
162 → 164
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01973137
14712856
213112828
345082816
449492816
549962816
649622816

prune272.0ms (5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1604164
Fresh527
Picked101
Done000
Total1666172
Error
0b
Counts
172 → 6
Alt Table
StatusErrorProgram
0.2b
(expm1.f64 (log1p.f64 (*.f64 (*.f64 (sin.f64 x) (/.f64 1 x)) (/.f64 (tan.f64 (/.f64 x 2)) x))))
14.3b
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))))
0.5b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
0.1b
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2)))))))
14.2b
(expm1.f64 (log1p.f64 (/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))))
13.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))
Compiler

Compiled 3582 to 2076 computations (42% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2)))))
0.1b
(*.f64 x (cos.f64 (/.f64 x 2)))
0.1b
(/.f64 (sin.f64 x) x)
0.2b
(/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2))))

series21.0ms (0.4%)

Counts
3 → 36
Calls

3 calls:

10.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2)))))
8.0ms
(/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2))))
3.0ms
(*.f64 x (cos.f64 (/.f64 x 2)))

rewrite40.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
31×add-cbrt-cube_binary64
31×add-exp-log_binary64
23×add-sqr-sqrt_binary64
16×associate-*l*_binary64
16×*-un-lft-identity_binary64
Counts
3 → 91
Calls

3 calls:

19.0ms
(*.f64 x (cos.f64 (/.f64 x 2)))
9.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2)))))
4.0ms
(/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2))))

simplify161.0ms (2.9%)

Algorithm
egg-herbie
Rules
559×fma-def_binary64
438×associate-/l/_binary64
380×*-commutative_binary64
206×fma-neg_binary64
204×cancel-sign-sub-inv_binary64
Counts
127 → 175
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01873074
14832567
217212557
333362547
447532547
549692547
649982547
749112547

prune244.0ms (4.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2122214
Fresh235
Picked101
Done000
Total2155220
Error
0b
Counts
220 → 5
Alt Table
StatusErrorProgram
0.2b
(expm1.f64 (log1p.f64 (/.f64 (*.f64 (sin.f64 x) (/.f64 (sin.f64 (/.f64 x 2)) (*.f64 x (cos.f64 (/.f64 x 2))))) x)))
13.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x) (/.f64 (sqrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))
0.2b
(expm1.f64 (log1p.f64 (*.f64 (*.f64 (sin.f64 x) (/.f64 1 x)) (/.f64 (tan.f64 (/.f64 x 2)) x))))
0.2b
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (/.f64 (sin.f64 (/.f64 x 2)) x) (cos.f64 (/.f64 x 2))))))
0.5b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
Compiler

Compiled 5509 to 3444 computations (37.5% saved)

regimes483.0ms (8.8%)

Accuracy

Total 0.1b remaining (84.2%)

Threshold costs 0.1b (84.2%)

Counts
231 → 1
Compiler

Compiled 8139 to 5643 computations (30.7% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
unpow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01529
11929
21829

end94.0ms (1.7%)

Compiler

Compiled 128 to 93 computations (27.3% saved)

Profiling

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