Details

Time bar (total: 6.3s)

analyze621.0ms (9.8%)

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)

sample3.9s (60.9%)

Results
1.9s2035×body2048valid
633.0ms1194×body1024valid
592.0ms1552×body512valid
348.0ms2598×body128valid
204.0ms785×body256valid
122.0ms92×body4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify23.0ms (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
29.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶29.0b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(cos.f64 x)
✓1.3b
(-.f64 1 (cos.f64 x))
✓14.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series8.0ms (0.1%)

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 (0.2%)

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)

simplify90.0ms (1.4%)

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

prune93.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9810108
Fresh000
Picked101
Done000
Total9910109
Error
0.0b
Counts
109 → 10
Alt Table
StatusErrorProgram
29.0b
(/.f64 (log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
34.6b
(-.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))))
29.0b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
29.0b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
28.2b
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x))
29.3b
(*.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))))
29.1b
(/.f64 (-.f64 (*.f64 1 1) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
▶15.3b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
29.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
28.8b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
Compiler

Compiled 2052 to 1057 computations (48.5% saved)

localize11.0ms (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))
✓0.3b
(+.f64 1 (cos.f64 x))
✓14.6b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series41.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

18.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
17.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms
(+.f64 1 (cos.f64 x))

rewrite32.0ms (0.5%)

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:

12.0ms
(/.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)))
3.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms
(+.f64 1 (cos.f64 x))

simplify99.0ms (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

prune157.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2024206
Fresh729
Picked101
Done000
Total2106216
Error
0b
Counts
216 → 6
Alt Table
StatusErrorProgram
28.8b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
15.1b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
0.3b
(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
29.0b
(/.f64 (log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
14.7b
(*.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))
▶0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Compiler

Compiled 4366 to 1947 computations (55.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series26.0ms (0.4%)

Counts
3 → 28
Calls

3 calls:

12.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
11.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms
(/.f64 (sin.f64 x) x)

rewrite22.0ms (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:

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

simplify114.0ms (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 → 176
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01862636
14692390
213092366
345062354
449472354
550472354

prune128.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1751176
Fresh235
Picked011
Done000
Total1775182
Error
0b
Counts
182 → 5
Alt Table
StatusErrorProgram
28.8b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
15.1b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
14.7b
(*.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))
▶0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x)))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Compiler

Compiled 3474 to 1800 computations (48.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x)))
✓0.2b
(*.f64 (cos.f64 (*.f64 1/2 x)) x)
0.2b
(/.f64 (sin.f64 x) x)
✓0.2b
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))

series26.0ms (0.4%)

Counts
3 → 20
Calls

3 calls:

12.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x)))
10.0ms
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
5.0ms
(*.f64 (cos.f64 (*.f64 1/2 x)) x)

rewrite28.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
31×add-cbrt-cube_binary64
31×add-exp-log_binary64
23×add-sqr-sqrt_binary64
16×associate-*l*_binary64
16×*-un-lft-identity_binary64
Counts
3 → 91
Calls

3 calls:

14.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x)))
4.0ms
(/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x))
3.0ms
(*.f64 (cos.f64 (*.f64 1/2 x)) x)

simplify216.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
810×associate-/l*_binary64
543×fma-def_binary64
395×associate-/l/_binary64
363×*-commutative_binary64
178×associate-/r/_binary64
Counts
111 → 164
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01832886
14732379
216172369
341942359
449812359
549542359

prune208.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2030203
Fresh033
Picked011
Done011
Total2035208
Error
0b
Counts
208 → 5
Alt Table
StatusErrorProgram
28.8b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
15.1b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (cos.f64 x) x)))
14.7b
(*.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))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (*.f64 1/2 x)) (*.f64 (cos.f64 (*.f64 1/2 x)) x)))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Compiler

Compiled 4849 to 2860 computations (41% saved)

regimes404.0ms (6.4%)

Accuracy

Total 0.1b remaining (79.3%)

Threshold costs 0.1b (79.3%)

Counts
169 → 1
Compiler

Compiled 5628 to 3789 computations (32.7% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
21017

end86.0ms (1.4%)

Compiler

Compiled 102 to 65 computations (36.3% saved)

Profiling

Loading profile data...