Details

Time bar (total: 4.2s)

analyze369.0ms (8.9%)

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)

sample68.0ms (1.6%)

Algorithm
intervals
Results
30.0ms70×body2048valid
10.0ms42×body1024valid
9.0ms54×body512valid
4.0ms25×body256valid
3.0ms61×body128valid
2.0msbody4096valid
Compiler

Compiled 20 to 14 computations (30% saved)

simplify36.0ms (0.9%)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
35.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
35.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(cos.f64 x)
2.4b
(-.f64 1 (cos.f64 x))
17.2b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series8.0ms (0.2%)

Counts
3 → 20
Calls

3 calls:

4.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)

rewrite16.0ms (0.4%)

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:

8.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms
(-.f64 1 (cos.f64 x))
1.0ms
(cos.f64 x)

simplify112.0ms (2.7%)

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

prune87.0ms (2.1%)

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
35.8b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
35.8b
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
18.0b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
35.6b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
35.8b
(/.f64 (log.f64 (/.f64 (exp.f64 1) (exp.f64 (cos.f64 x)))) (*.f64 x x))
35.7b
(/.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)))
28.1b
(fma.f64 (*.f64 x x) -1/24 1/2)
34.6b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
Compiler

Compiled 1940 to 977 computations (49.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b
(*.f64 (sin.f64 x) (sin.f64 x))
0.3b
(+.f64 1 (cos.f64 x))
17.3b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series66.0ms (1.6%)

Counts
4 → 40
Calls

4 calls:

24.0ms
(+.f64 1 (cos.f64 x))
19.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
17.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
5.0ms
(*.f64 (sin.f64 x) (sin.f64 x))

rewrite33.0ms (0.8%)

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:

9.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
7.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms
(+.f64 1 (cos.f64 x))

simplify135.0ms (3.2%)

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

prune206.0ms (4.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1988206
Fresh527
Picked101
Done000
Total20410214
Error
0b
Counts
214 → 10
Alt Table
StatusErrorProgram
17.3b
(*.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))
35.8b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
17.9b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
36.0b
(/.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
18.4b
(/.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (cbrt.f64 (sin.f64 x))) (+.f64 1 (cos.f64 x))) (*.f64 x x))
0.2b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.7b
(*.f64 (/.f64 (/.f64 (sin.f64 x) (*.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (cbrt.f64 (+.f64 1 (cos.f64 x))))) x) (/.f64 (/.f64 (sin.f64 x) (cbrt.f64 (+.f64 1 (cos.f64 x)))) x))
17.1b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) (cbrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)))) x) (/.f64 (cbrt.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x))) x))
18.0b
(/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (-.f64 -1 (cos.f64 x))) (*.f64 x x))
35.6b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
Compiler

Compiled 4564 to 2081 computations (54.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (sin.f64 x) x)
0.1b
(sin.f64 x)
0.2b
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
0.3b
(tan.f64 (/.f64 x 2))

series26.0ms (0.6%)

Counts
4 → 32
Calls

4 calls:

13.0ms
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
8.0ms
(tan.f64 (/.f64 x 2))
3.0ms
(/.f64 (sin.f64 x) x)
2.0ms
(sin.f64 x)

rewrite17.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
13×associate-*l*_binary64
Counts
4 → 84
Calls

4 calls:

8.0ms
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
2.0ms
(/.f64 (sin.f64 x) x)
2.0ms
(tan.f64 (/.f64 x 2))
1.0ms
(sin.f64 x)

simplify144.0ms (3.5%)

Algorithm
egg-herbie
Rules
721×fma-neg_binary64
607×cancel-sign-sub-inv_binary64
305×associate-*l*_binary64
271×fma-def_binary64
265×associate-*r*_binary64
Counts
116 → 146
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01601756
13721616
29701606
330121606
444001606
549891606
649401606

prune171.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1451146
Fresh279
Picked011
Done000
Total1479156
Error
0b
Counts
156 → 9
Alt Table
StatusErrorProgram
17.3b
(*.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))
35.8b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
18.4b
(/.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (cbrt.f64 (sin.f64 x))) (+.f64 1 (cos.f64 x))) (*.f64 x x))
0.2b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.7b
(*.f64 (/.f64 (/.f64 (sin.f64 x) (*.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (cbrt.f64 (+.f64 1 (cos.f64 x))))) x) (/.f64 (/.f64 (sin.f64 x) (cbrt.f64 (+.f64 1 (cos.f64 x)))) x))
0.2b
(/.f64 (/.f64 (*.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (cos.f64 (/.f64 x 2))) x)
36.0b
(/.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
18.0b
(/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (-.f64 -1 (cos.f64 x))) (*.f64 x x))
35.6b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
Compiler

Compiled 2933 to 1549 computations (47.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series20.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

16.0ms
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (cos.f64 (/.f64 x 2)))
2.0ms
(cos.f64 (/.f64 x 2))
2.0ms
(sin.f64 (/.f64 x 2))

rewrite12.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
12×add-cbrt-cube_binary64
12×add-exp-log_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
3 → 44
Calls

3 calls:

6.0ms
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (cos.f64 (/.f64 x 2)))
2.0ms
(cos.f64 (/.f64 x 2))
2.0ms
(sin.f64 (/.f64 x 2))

simplify104.0ms (2.5%)

Algorithm
egg-herbie
Rules
601×times-frac_binary64
570×associate-/l*_binary64
432×associate-/l/_binary64
383×associate-*l/_binary64
306×fma-def_binary64
Counts
80 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01281458
13251244
210451236
342631236
447741236
549511236

prune103.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New93093
Fresh077
Picked011
Done011
Total939102
Error
0b
Counts
102 → 9
Alt Table
StatusErrorProgram
17.3b
(*.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))
35.8b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
18.4b
(/.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (cbrt.f64 (sin.f64 x))) (+.f64 1 (cos.f64 x))) (*.f64 x x))
0.2b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.7b
(*.f64 (/.f64 (/.f64 (sin.f64 x) (*.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (cbrt.f64 (+.f64 1 (cos.f64 x))))) x) (/.f64 (/.f64 (sin.f64 x) (cbrt.f64 (+.f64 1 (cos.f64 x)))) x))
0.2b
(/.f64 (/.f64 (*.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x 2))) (cos.f64 (/.f64 x 2))) x)
36.0b
(/.f64 (/.f64 (/.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2) (+.f64 1 (cos.f64 x))) (*.f64 x x))
18.0b
(/.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (-.f64 -1 (cos.f64 x))) (*.f64 x x))
35.6b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
Compiler

Compiled 2202 to 1412 computations (35.9% saved)

regimes283.0ms (6.8%)

Accuracy

Total 0.2b remaining (86.3%)

Threshold costs 0.2b (86.3%)

Counts
153 → 1
Compiler

Compiled 5376 to 3427 computations (36.3% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01121
11221
21221

end1.0ms (0%)

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample2.1s (50.4%)

Algorithm
intervals
Results
898.0ms1962×body2048valid
296.0ms1127×body1024valid
261.0ms1469×body512valid
138.0ms2591×body128valid
91.0ms746×body256valid
50.0ms105×body4096valid
Compiler

Compiled 184 to 123 computations (33.2% saved)

Profiling

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