Details

Time bar (total: 4.3s)

analyze359.0ms (8.3%)

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)

sample65.0ms (1.5%)

Algorithm
1×intervals
Results
28.0ms52×body2048valid
10.0ms39×body1024valid
10.0ms52×body512valid
5.0ms91×body128valid
2.0ms20×body256valid
1.0ms2×body4096valid
Compiler

Compiled 20 to 14 computations (30% saved)

simplify28.0ms (0.6%)

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
30.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶30.4b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓2.4b
(-.f64 1 (cos.f64 x))
✓11.1b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite15.0ms (0.3%)

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:

8.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms
(-.f64 1 (cos.f64 x))

series12.0ms (0.3%)

Counts
2 → 16
Calls

2 calls:

9.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms
(-.f64 1 (cos.f64 x))

simplify113.0ms (2.6%)

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

prune79.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1209129
Fresh000
Picked101
Done000
Total1219130
Error
0.0b
Counts
130 → 9
Alt Table
StatusErrorProgram
30.5b
(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
30.3b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
44.0b
(/.f64 (fma.f64 1/720 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/24 1/2))) (*.f64 x x))
32.6b
(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
30.1b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x)))) x) (/.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) x))
30.4b
(/.f64 (+.f64 1 (*.f64 (neg.f64 1) (cos.f64 x))) (*.f64 x x))
46.9b
(/.f64 (*.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (-.f64 1 (sqrt.f64 (cos.f64 x)))) (*.f64 x x))
30.5b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
▶11.8b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
Compiler

Compiled 1788 to 907 computations (49.3% saved)

localize10.0ms (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))
✓0.4b
(+.f64 1 (cos.f64 x))
✓11.3b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

rewrite29.0ms (0.7%)

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:

10.0ms
(/.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)))
4.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

series59.0ms (1.4%)

Counts
4 → 40
Calls

4 calls:

30.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
22.0ms
(/.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 (2.6%)

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 → 287
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02042904
15042230
217672192
346432192
449352192

prune182.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2843287
Fresh538
Picked011
Done000
Total2897296
Error
0b
Counts
296 → 7
Alt Table
StatusErrorProgram
30.5b
(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
30.3b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.2b
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
30.5b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
✓11.8b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
▶0.1b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
Compiler

Compiled 4376 to 1956 computations (55.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite20.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64
22×times-frac_binary64
21×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
19×add-cbrt-cube_binary64
Counts
3 → 93
Calls

3 calls:

6.0ms
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
6.0ms
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
3.0ms
(/.f64 (sin.f64 x) x)

series67.0ms (1.5%)

Counts
3 → 28
Calls

3 calls:

31.0ms
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
28.0ms
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
7.0ms
(/.f64 (sin.f64 x) x)

simplify124.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
744×fma-def_binary64
593×associate-/l/_binary64
549×associate-*l/_binary64
440×associate-*l*_binary64
391×associate-/r*_binary64
Counts
121 → 191
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01762266
14332003
213331993
340881989
447491989
551731989

prune134.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1892191
Fresh235
Picked101
Done011
Total1926198
Error
0b
Counts
198 → 6
Alt Table
StatusErrorProgram
30.3b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
▶0.1b
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
0.1b
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
0.2b
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
30.5b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
✓11.8b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
Compiler

Compiled 2745 to 1373 computations (50% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite20.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64
22×times-frac_binary64
21×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
19×add-cbrt-cube_binary64
Counts
3 → 90
Calls

3 calls:

6.0ms
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
3.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)

series78.0ms (1.8%)

Counts
3 → 36
Calls

3 calls:

29.0ms
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
28.0ms
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
21.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify128.0ms (3%)

Algorithm
1×egg-herbie
Rules
582×fma-def_binary64
564×associate-/l/_binary64
528×associate-*l/_binary64
426×associate-*l*_binary64
419×associate-*r/_binary64
Counts
126 → 192
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01692493
14092220
213932212
341352208
446532208
549522208

prune108.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1920192
Fresh044
Picked011
Done011
Total1926198
Error
0b
Counts
198 → 6
Alt Table
StatusErrorProgram
30.3b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
✓0.1b
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
0.1b
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
0.2b
(*.f64 (/.f64 1 x) (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
30.5b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
✓11.8b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
Compiler

Compiled 2409 to 1443 computations (40.1% saved)

regimes339.0ms (7.8%)

Accuracy

Total 0.1b remaining (86.1%)

Threshold costs 0.1b (86.1%)

Compiler

Compiled 4990 to 3339 computations (33.1% saved)

simplify3.0ms (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)

sample2.2s (51.2%)

Algorithm
1×intervals
Results
1.1s2010×body2048valid
302.0ms1112×body1024valid
250.0ms1478×body512valid
139.0ms2568×body128valid
87.0ms728×body256valid
50.0ms104×body4096valid
Compiler

Compiled 108 to 70 computations (35.2% saved)

Profiling

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