Details

Time bar (total: 6.3s)

analyze352.0ms (5.6%)

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)

sample65.0ms (1%)

Algorithm
1×intervals
Results
27.0ms50×body2048valid
12.0ms45×body1024valid
8.0ms54×body512valid
4.0ms75×body128valid
3.0ms7×body4096valid
3.0ms25×body256valid
Compiler

Compiled 20 to 14 computations (30% saved)

simplify28.0ms (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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
32.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶32.6b
(/.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 2 expressions with local error:

NewErrorProgram
✓2.6b
(-.f64 1 (cos.f64 x))
✓12.4b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite12.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
9×prod-diff_binary64
7×add-cbrt-cube_binary64
Counts
2 → 63
Calls

2 calls:

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

series12.0ms (0.2%)

Counts
2 → 16
Calls

2 calls:

10.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms
(-.f64 1 (cos.f64 x))

simplify112.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
626×fma-neg_binary64
411×associate-*l*_binary64
405×times-frac_binary64
353×associate-*r*_binary64
344×fma-def_binary64
Counts
79 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01251152
12831017
2853961
33327961
44699961
54954961
64828961

prune86.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1227129
Fresh000
Picked101
Done000
Total1237130
Error
0.0b
Counts
130 → 7
Alt Table
StatusErrorProgram
32.7b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
30.8b
(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
31.8b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
▶13.2b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
32.8b
(*.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))))
32.7b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
32.6b
(/.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 1726 to 863 computations (50% saved)

localize10.0ms (0.2%)

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)))
✓0.3b
(+.f64 1 (cos.f64 x))
✓12.7b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

rewrite27.0ms (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))
6.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

series55.0ms (0.9%)

Counts
4 → 40
Calls

4 calls:

27.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
21.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
1.0ms
(+.f64 1 (cos.f64 x))

simplify113.0ms (1.8%)

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 → 287
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02042912
15042230
217672192
346432192
449352192

prune195.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2834287
Fresh516
Picked101
Done000
Total2895294
Error
0b
Counts
294 → 5
Alt Table
StatusErrorProgram
12.6b
(/.f64 (/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) x) x)
0.6b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
32.6b
(/.f64 (*.f64 1 (-.f64 1 (cos.f64 x))) (*.f64 x x))
▶0.2b
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
32.6b
(/.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 4339 to 1931 computations (55.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
✓0.1b
(/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))
✓0.1b
(/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x)
0.3b
(+.f64 1 (cos.f64 x))

rewrite76.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
297×times-frac_binary64
194×*-un-lft-identity_binary64
189×add-sqr-sqrt_binary64
141×add-cube-cbrt_binary64
58×associate-*r*_binary64
Counts
3 → 276
Calls

3 calls:

42.0ms
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
7.0ms
(/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x)
4.0ms
(/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))

series64.0ms (1%)

Counts
3 → 28
Calls

3 calls:

28.0ms
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
22.0ms
(/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x)
14.0ms
(/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))

simplify223.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
893×fma-def_binary64
346×associate-*r/_binary64
301×associate-*l/_binary64
256×associate-/l*_binary64
226×associate-/l/_binary64
Counts
304 → 563
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03717060
19796596
231286468
343546466
449906466

prune364.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New5920592
Fresh044
Picked011
Done000
Total5925597
Error
0b
Counts
597 → 5
Alt Table
StatusErrorProgram
12.6b
(/.f64 (/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) x) x)
▶0.6b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
32.6b
(/.f64 (*.f64 1 (-.f64 1 (cos.f64 x))) (*.f64 x x))
✓0.2b
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
32.6b
(/.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 12336 to 6263 computations (49.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sin.f64 x)
✓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)))

rewrite106.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
1985×times-frac_binary64
859×*-un-lft-identity_binary64
859×add-sqr-sqrt_binary64
859×add-cube-cbrt_binary64
108×div-inv_binary64
Counts
4 → 769
Calls

4 calls:

20.0ms
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
6.0ms
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
3.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
1.0ms
(sin.f64 x)

series91.0ms (1.5%)

Counts
4 → 40
Calls

4 calls:

37.0ms
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
32.0ms
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
20.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
1.0ms
(sin.f64 x)

simplify953.0ms (15.2%)

Algorithm
1×egg-herbie
Rules
820×associate-/r/_binary64
549×associate-/l/_binary64
476×associate-/r*_binary64
400×associate-*r/_binary64
361×*-commutative_binary64
Counts
809 → 1570
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
077330857
1150029250
2429728519
3458828295
4496728295
5495528295

prune854.0ms (13.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New156911570
Fresh123
Picked011
Done011
Total157051575
Error
0b
Counts
1575 → 5
Alt Table
StatusErrorProgram
13.3b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓0.2b
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
12.6b
(/.f64 (/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) x) x)
✓0.6b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
32.6b
(/.f64 (*.f64 1 (-.f64 1 (cos.f64 x))) (*.f64 x x))
Compiler

Compiled 31274 to 18691 computations (40.2% saved)

regimes361.0ms (5.8%)

Accuracy

Total 0.1b remaining (80.2%)

Threshold costs 0.1b (80.2%)

Compiler

Compiled 5498 to 3769 computations (31.4% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
21017

end1.0ms (0%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample2.1s (33.1%)

Algorithm
1×intervals
Results
1.0s1989×body2048valid
276.0ms1106×body1024valid
245.0ms1515×body512valid
127.0ms2553×body128valid
94.0ms737×body256valid
46.0ms100×body4096valid
Compiler

Compiled 92 to 62 computations (32.6% saved)

Profiling

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