Details

Time bar (total: 6.5s)

analyze343.0ms (5.3%)

Algorithm
1×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 (46.4%)

Results
1.5s2133×body2048valid
502.0ms1205×body1024valid
419.0ms1513×body512valid
281.0ms2567×body128valid
137.0ms730×body256valid
86.0ms108×body4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify30.0ms (0.5%)

Algorithm
1×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
35.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶35.0b
(/.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)
✓2.4b
(-.f64 1 (cos.f64 x))
✓15.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series9.0ms (0.1%)

Counts
3 → 20
Calls

3 calls:

6.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms
(-.f64 1 (cos.f64 x))
1.0ms
(cos.f64 x)

rewrite13.0ms (0.2%)

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

3 calls:

6.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms
(-.f64 1 (cos.f64 x))
1.0ms
(cos.f64 x)

simplify83.0ms (1.3%)

Algorithm
1×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

prune85.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1026108
Fresh000
Picked101
Done000
Total1036109
Error
0.0b
Counts
109 → 6
Alt Table
StatusErrorProgram
28.0b
(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
35.1b
(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
▶16.1b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
34.5b
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))
35.2b
(*.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))))
35.4b
(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (*.f64 x (fma.f64 x (fma.f64 (cos.f64 x) (cos.f64 x) (cos.f64 x)) x)))
Compiler

Compiled 1934 to 973 computations (49.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓0.4b
(+.f64 1 (cos.f64 x))
✓15.4b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series31.0ms (0.5%)

Counts
4 → 40
Calls

4 calls:

13.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
13.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
3.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
1.0ms
(+.f64 1 (cos.f64 x))

rewrite25.0ms (0.4%)

Algorithm
1×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))
5.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms
(+.f64 1 (cos.f64 x))

simplify102.0ms (1.6%)

Algorithm
1×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
02042912
15042230
217672192
346432192
449352192

prune137.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2024206
Fresh415
Picked101
Done000
Total2075212
Error
0b
Counts
212 → 5
Alt Table
StatusErrorProgram
35.1b
(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
▶0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
15.9b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
0.5b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
16.5b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
Compiler

Compiled 4320 to 1919 computations (55.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.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)

series25.0ms (0.4%)

Counts
3 → 28
Calls

3 calls:

11.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
10.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
3.0ms
(/.f64 (sin.f64 x) x)

rewrite21.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
45×add-sqr-sqrt_binary64
40×times-frac_binary64
33×*-un-lft-identity_binary64
33×add-cube-cbrt_binary64
19×add-cbrt-cube_binary64
Counts
3 → 111
Calls

3 calls:

9.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms
(/.f64 (sin.f64 x) x)

simplify117.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
594×associate-/l*_binary64
557×associate-*l/_binary64
473×associate-*l*_binary64
464×associate-*r/_binary64
426×times-frac_binary64
Counts
139 → 154
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01862636
14692390
213092366
345062354
449472354
550472354

prune102.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1540154
Fresh044
Picked011
Done000
Total1545159
Error
0b
Counts
159 → 5
Alt Table
StatusErrorProgram
35.1b
(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
15.9b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
▶0.5b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
16.5b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
Compiler

Compiled 2960 to 1560 computations (47.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b
(/.f64 (tan.f64 (/.f64 x 2)) x)
✓0.5b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

series30.0ms (0.5%)

Counts
2 → 24
Calls

2 calls:

17.0ms
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
13.0ms
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

rewrite171.0ms (2.7%)

Algorithm
1×rewrite-expression-head
Rules
1976×times-frac_binary64
849×*-un-lft-identity_binary64
849×add-sqr-sqrt_binary64
849×add-cube-cbrt_binary64
107×div-inv_binary64
Counts
2 → 730
Calls

2 calls:

20.0ms
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
4.0ms
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))

simplify1.2s (17.9%)

Algorithm
1×egg-herbie
Rules
814×associate-/r/_binary64
545×associate-/l/_binary64
475×associate-/r*_binary64
397×associate-*r/_binary64
357×*-commutative_binary64
Counts
754 → 969
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
074030088
1143228497
2415627762
3446727536
4496127536
5495227536

prune714.0ms (11.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New101101011
Fresh033
Picked011
Done011
Total101151016
Error
0b
Counts
1016 → 5
Alt Table
StatusErrorProgram
35.1b
(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
15.9b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
✓0.5b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
16.5b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
Compiler

Compiled 30769 to 18360 computations (40.3% saved)

regimes160.0ms (2.5%)

Accuracy

Total 0.1b remaining (82.1%)

Threshold costs 0.1b (82.1%)

Counts
90 → 1
Compiler

Compiled 2783 to 1815 computations (34.8% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
21017

end73.0ms (1.1%)

Compiler

Compiled 87 to 57 computations (34.5% saved)

Profiling

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