Details

Time bar (total: 6.7s)

analyze3.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
75%25%0%3
87.5%12.5%0%4
93.7%6.2%0%5
96.8%3.1%0%6
98.4%1.6%0%7
99.2%0.8%0%8
99.6%0.4%0%9
99.8%0.2%0%10
99.9%0.1%0%11
99.9%0%0%12
99.9%0%0%13
99.9%0%0%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample2.5s (37%)

Results
1.3s2087×body2048valid
380.0ms1121×body1024valid
352.0ms1510×body512valid
231.0ms2643×body128valid
121.0ms778×body256valid
64.0ms117×body4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify24.0ms (0.4%)

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
30.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶30.3b
(/.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
✓2.5b
(-.f64 1 (cos.f64 x))
✓13.6b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series6.0ms (0.1%)

Counts
2 → 16
Calls

2 calls:

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

rewrite21.0ms (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:

7.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms
(-.f64 1 (cos.f64 x))

simplify101.0ms (1.5%)

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 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01251152
12831017
2853961
33327961
44699961
54954961
64828961

prune80.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New86591
Fresh000
Picked101
Done000
Total87592
Error
0.0b
Counts
92 → 5
Alt Table
StatusErrorProgram
▶14.1b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
30.3b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
33.2b
(-.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))))
29.7b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
30.4b
(/.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 1644 to 813 computations (50.5% saved)

localize9.0ms (0.1%)

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))
✓0.5b
(+.f64 1 (cos.f64 x))
✓13.5b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series43.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

20.0ms
(/.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))
4.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms
(+.f64 1 (cos.f64 x))

rewrite28.0ms (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)))
4.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

simplify110.0ms (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
02042904
15042230
217672192
346432192
449352192

prune161.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2033206
Fresh314
Picked011
Done000
Total2065211
Error
0b
Counts
211 → 5
Alt Table
StatusErrorProgram
✓14.1b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
30.3b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
▶0.3b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
0.3b
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
0.6b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
Compiler

Compiled 4349 to 1934 computations (55.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
✓0.2b
(/.f64 (tan.f64 (/.f64 x 2)) x)
✓0.3b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

series47.0ms (0.7%)

Counts
3 → 36
Calls

3 calls:

24.0ms
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
12.0ms
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
10.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite185.0ms (2.8%)

Algorithm
1×rewrite-expression-head
Rules
1985×times-frac_binary64
858×*-un-lft-identity_binary64
858×add-sqr-sqrt_binary64
858×add-cube-cbrt_binary64
108×div-inv_binary64
Counts
3 → 760
Calls

3 calls:

19.0ms
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
7.0ms
(/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify1.2s (18.6%)

Algorithm
1×egg-herbie
Rules
820×associate-/r/_binary64
549×associate-/l/_binary64
476×associate-/r*_binary64
400×associate-*r/_binary64
359×*-commutative_binary64
Counts
796 → 1018
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
076130766
1147129145
2423828408
3450828184
4496628184
5495128184

prune866.0ms (12.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New101711018
Fresh123
Picked011
Done011
Total101851023
Error
0b
Counts
1023 → 5
Alt Table
StatusErrorProgram
▶0.3b
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
13.9b
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
✓0.3b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
✓14.1b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
0.6b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
Compiler

Compiled 31055 to 18545 computations (40.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (/.f64 (sin.f64 x) 1) x)
✓0.2b
(/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))
✓0.2b
(/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x)
0.5b
(+.f64 1 (cos.f64 x))

series26.0ms (0.4%)

Counts
3 → 28
Calls

3 calls:

13.0ms
(/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x)
9.0ms
(/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x)))
3.0ms
(/.f64 (/.f64 (sin.f64 x) 1) x)

rewrite36.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
189×times-frac_binary64
137×*-un-lft-identity_binary64
105×add-sqr-sqrt_binary64
105×add-cube-cbrt_binary64
34×associate-/l*_binary64
Counts
3 → 201
Calls

3 calls:

9.0ms
(/.f64 (/.f64 (sin.f64 x) 1) 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)))

simplify152.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
721×fma-def_binary64
696×times-frac_binary64
503×associate-/l*_binary64
458×associate-/r*_binary64
353×associate-*l*_binary64
Counts
229 → 303
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02884205
16064069
216624007
342784007
453264007

prune278.0ms (4.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New3300330
Fresh022
Picked011
Done022
Total3305335
Error
0b
Counts
335 → 5
Alt Table
StatusErrorProgram
✓0.3b
(*.f64 (/.f64 (/.f64 (sin.f64 x) 1) x) (/.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) x))
13.9b
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) (pow.f64 x 2)))
✓0.3b
(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
✓14.1b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
0.6b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
Compiler

Compiled 8193 to 4259 computations (48% saved)

regimes690.0ms (10.3%)

Accuracy

Total 0.1b remaining (76.3%)

Threshold costs 0.1b (76.3%)

Counts
336 → 1
Compiler

Compiled 12660 to 8601 computations (32.1% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
21017

end79.0ms (1.2%)

Compiler

Compiled 113 to 75 computations (33.6% saved)

Profiling

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