Details

Time bar (total: 5.7s)

analyze939.0ms (16.4%)

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)

sample3.2s (56.4%)

Results
1.7s2036×body2048valid
497.0ms1124×body1024valid
453.0ms1554×body512valid
297.0ms2652×body128valid
152.0ms780×body256valid
78.0ms110×body4096valid
Compiler

Compiled 29 to 20 computations (31% 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
30.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶30.1b
(/.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
✓3.0b
(-.f64 1 (cos.f64 x))
✓15.8b
(/.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))

rewrite68.0ms (1.2%)

Algorithm
2×batch-egg-rewrite
Rules
818×log1p-expm1-u_binary64
818×expm1-log1p-u_binary64
259×prod-diff_binary64
102×egg-rr
76×add-sqr-sqrt_binary64
Counts
2 → 102
Calls

2 calls:

65.0ms
(-.f64 1 (cos.f64 x))
65.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0718
115218
2201318
3551518
000
100

simplify95.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
773×distribute-rgt-neg-in_binary64
612×associate-*l*_binary64
477×fma-def_binary64
440×associate-*r*_binary64
414×unswap-sqr_binary64
Counts
118 → 119
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035224
197220
2252214
3734212
42974212
54635212
64939212
74940212

prune118.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1118119
Fresh000
Picked101
Done000
Total1128120
Error
0.0b
Counts
120 → 8
Alt Table
StatusErrorProgram
30.1b
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
34.2b
(fma.f64 x (*.f64 x -1/24) 1/2)
30.1b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
28.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
16.9b
(/.f64 (/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 x x))
▶16.5b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
30.1b
(/.f64 (*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))) (*.f64 x x))
30.1b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 3141 to 1555 computations (50.5% 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 (+.f64 1 (cos.f64 x))))
✓0.3b
(*.f64 (sin.f64 x) (sin.f64 x))
✓0.4b
(+.f64 1 (cos.f64 x))
✓15.9b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))

series36.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

15.0ms
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
12.0ms
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
7.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms
(+.f64 1 (cos.f64 x))

rewrite77.0ms (1.4%)

Algorithm
2×batch-egg-rewrite
Rules
482×prod-diff_binary64
212×expm1-udef_binary64
212×log1p-udef_binary64
154×egg-rr
126×add-sqr-sqrt_binary64
Counts
4 → 154
Calls

4 calls:

75.0ms
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
75.0ms
(*.f64 (sin.f64 x) (sin.f64 x))
75.0ms
(+.f64 1 (cos.f64 x))
75.0ms
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01146
125430
2343330
3502230
000
100

simplify88.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
920×times-frac_binary64
500×sub-neg_binary64
452×fma-neg_binary64
259×*-commutative_binary64
195×unswap-sqr_binary64
Counts
194 → 187
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054564
1155556
2429496
31294496
43137496
54855496
64873496
74946496

prune127.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1843187
Fresh347
Picked101
Done000
Total1887195
Error
0b
Counts
195 → 7
Alt Table
StatusErrorProgram
30.1b
(-.f64 (pow.f64 x -2) (/.f64 (cos.f64 x) (*.f64 x x)))
34.2b
(fma.f64 x (*.f64 x -1/24) 1/2)
30.1b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
28.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
16.4b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
16.6b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
▶16.2b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
Compiler

Compiled 3434 to 1920 computations (44.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
✓0.3b
(pow.f64 (sin.f64 x) 2)
0.4b
(+.f64 1 (cos.f64 x))
✓15.8b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

series24.0ms (0.4%)

Counts
3 → 12
Calls

3 calls:

15.0ms
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
5.0ms
(pow.f64 (sin.f64 x) 2)
4.0ms
(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))

rewrite65.0ms (1.1%)

Algorithm
2×batch-egg-rewrite
Rules
519×log-prod_binary64
191×fma-def_binary64
184×expm1-udef_binary64
184×log1p-udef_binary64
166×log-pow_binary64
Counts
3 → 117
Calls

3 calls:

63.0ms
(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
63.0ms
(pow.f64 (sin.f64 x) 2)
63.0ms
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01138
123230
2266230
3503030
000
100

simplify100.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
792×fma-def_binary64
649×cancel-sign-sub-inv_binary64
542×distribute-rgt-neg-in_binary64
446×sub-neg_binary64
404×distribute-lft-neg-in_binary64
Counts
129 → 140
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
042192
1121184
2331176
31022174
43021174
54362174
64745174
74972174
84935174

prune123.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1831184
Fresh156
Picked011
Done000
Total1847191
Error
0b
Counts
191 → 7
Alt Table
StatusErrorProgram
30.1b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
16.5b
(*.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (*.f64 x x)))
28.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
▶16.4b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
34.2b
(fma.f64 x (*.f64 x -1/24) 1/2)
16.6b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
✓16.2b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
Compiler

Compiled 3370 to 1986 computations (41.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓15.9b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))

series24.0ms (0.4%)

Counts
2 → 24
Calls

2 calls:

13.0ms
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
11.0ms
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))

rewrite88.0ms (1.5%)

Algorithm
2×batch-egg-rewrite
Rules
630×prod-diff_binary64
546×log-prod_binary64
180×expm1-udef_binary64
180×log1p-udef_binary64
165×log-div_binary64
Counts
2 → 67
Calls

2 calls:

87.0ms
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
87.0ms
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0928
120128
2269028
3499428
4600428
000
100

simplify52.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
773×distribute-rgt-neg-in_binary64
636×associate-*l*_binary64
474×fma-def_binary64
454×associate-*r*_binary64
414×unswap-sqr_binary64
Counts
91 → 85
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
039480
1106476
2278470
3816468
43224468
55114468

prune60.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New84185
Fresh145
Picked011
Done101
Total86692
Error
0b
Counts
92 → 6
Alt Table
StatusErrorProgram
30.1b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
28.7b
(*.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) (/.f64 1 x))
16.0b
(*.f64 (tan.f64 (/.f64 x 2)) (*.f64 (sin.f64 x) (pow.f64 x -2)))
✓16.4b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (*.f64 x x))
34.2b
(fma.f64 x (*.f64 x -1/24) 1/2)
16.6b
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x)))
Compiler

Compiled 1430 to 874 computations (38.9% saved)

regimes202.0ms (3.5%)

Accuracy

Total 0.2b remaining (88%)

Threshold costs 0.2b (88%)

Counts
66 → 3
Compiler

Compiled 2703 to 1619 computations (40.1% saved)

bsearch32.0ms (0.6%)

Steps
ItersRangePoint
2
3.2433934134552804e-12
4.41257979979231e-12
4.021636854798944e-12
10
-8513831026.117983
-0.00020900364237139832
-0.00485777750271224
Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
7×*-commutative_binary64
4×+-commutative_binary64
3×sub-neg_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02977
14477
25277
35677
45777
55677

end110.0ms (1.9%)

Compiler

Compiled 169 to 118 computations (30.2% saved)

Profiling

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