Details

Time bar (total: 3.7s)

analyze325.0ms (8.9%)

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)

sample95.0ms (2.6%)

Algorithm
1×intervals
Results
32.0ms64×body2048valid
9.0ms51×body512valid
6.0ms22×body1024valid
4.0ms86×body128valid
3.0ms27×body256valid
3.0ms6×body4096valid
Compiler

Compiled 20 to 14 computations (30% saved)

simplify24.0ms (0.7%)

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

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
31.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶31.0b
(/.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
✓2.9b
(-.f64 1 (cos.f64 x))
✓15.3b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series6.0ms (0.2%)

Counts
2 → 16
Calls

2 calls:

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

rewrite13.0ms (0.4%)

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))
4.0ms
(-.f64 1 (cos.f64 x))

simplify98.0ms (2.7%)

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

prune75.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New84791
Fresh000
Picked101
Done000
Total85792
Error
0.0b
Counts
92 → 7
Alt Table
StatusErrorProgram
31.7b
(fma.f64 (*.f64 x x) -1/24 1/2)
30.1b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
▶15.8b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
30.4b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
45.5b
(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 (cos.f64 x)))))
31.0b
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))) (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
31.0b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (-.f64 1 (cos.f64 x)) (-.f64 1 (cos.f64 x))) (-.f64 1 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 1690 to 841 computations (50.2% saved)

localize9.0ms (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))
✓0.5b
(+.f64 1 (cos.f64 x))
✓15.2b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series37.0ms (1%)

Counts
4 → 40
Calls

4 calls:

16.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
16.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
3.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms
(+.f64 1 (cos.f64 x))

rewrite29.0ms (0.8%)

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))

simplify93.0ms (2.5%)

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

prune127.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2042206
Fresh246
Picked101
Done000
Total2076213
Error
0b
Counts
213 → 6
Alt Table
StatusErrorProgram
31.7b
(fma.f64 (*.f64 x x) -1/24 1/2)
30.1b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
30.4b
(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
45.5b
(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 (cos.f64 x)))))
15.7b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
▶0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Compiler

Compiled 4332 to 1925 computations (55.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series25.0ms (0.7%)

Counts
3 → 28
Calls

3 calls:

10.0ms
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
9.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
5.0ms
(/.f64 (sin.f64 x) x)

rewrite21.0ms (0.6%)

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))
4.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms
(/.f64 (sin.f64 x) x)

simplify113.0ms (3.1%)

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 → 154
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01862636
14692390
213092366
345062354
449472354
550472354

prune97.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1531154
Fresh235
Picked011
Done000
Total1555160
Error
0b
Counts
160 → 5
Alt Table
StatusErrorProgram
31.7b
(fma.f64 (*.f64 x x) -1/24 1/2)
30.1b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
45.5b
(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 (cos.f64 x)))))
▶16.0b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Compiler

Compiled 2954 to 1554 computations (47.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓14.9b
(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))

series22.0ms (0.6%)

Counts
2 → 24
Calls

2 calls:

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

rewrite14.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
11×add-sqr-sqrt_binary64
7×associate-*r*_binary64
7×*-un-lft-identity_binary64
Counts
2 → 54
Calls

2 calls:

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

simplify68.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
644×fma-def_binary64
485×times-frac_binary64
402×associate-*l*_binary64
399×cancel-sign-sub-inv_binary64
369×associate-*r*_binary64
Counts
78 → 81
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01191631
12781414
28691406
335311404
451161404

prune48.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New81081
Fresh033
Picked011
Done011
Total81586
Error
0b
Counts
86 → 5
Alt Table
StatusErrorProgram
31.7b
(fma.f64 (*.f64 x x) -1/24 1/2)
30.1b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
45.5b
(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 (cos.f64 x)))))
✓16.0b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓0.1b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
Compiler

Compiled 1491 to 847 computations (43.2% saved)

regimes128.0ms (3.5%)

Accuracy

Total 0.1b remaining (71.4%)

Threshold costs 0.1b (71.4%)

Counts
68 → 1
Compiler

Compiled 2138 to 1419 computations (33.6% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
21017

end0.0ms (0%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample2.2s (59.3%)

Algorithm
1×intervals
Results
1.0s1995×body2048valid
303.0ms1109×body1024valid
245.0ms1487×body512valid
144.0ms2536×body128valid
97.0ms771×body256valid
47.0ms102×body4096valid
Compiler

Compiled 83 to 54 computations (34.9% saved)

Profiling

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