Details

Time bar (total: 5.9s)

analyze1.2s (19.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
0%100%0%4
12.5%87.5%0%5
18.7%81.2%0%6
21.9%78.1%0%7
23.4%76.5%0%8
23.4%76.5%0%9
23.4%76.5%0%10
23.6%76.3%0%11
23.7%76.2%0%12
23.7%76.2%0%13
23.7%76.2%0%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample3.2s (55%)

Results
1.7s2095×body2048valid
510.0ms1118×body1024valid
451.0ms1510×body512valid
290.0ms2645×body128valid
165.0ms785×body256valid
73.0ms103×body4096valid
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify25.0ms (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
26.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶26.3b
(/.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 3 expressions with local error:

NewErrorProgram
✓0.0b
(cos.f64 x)
✓2.7b
(-.f64 1 (cos.f64 x))
✓13.7b
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series11.0ms (0.2%)

Counts
3 → 20
Calls

3 calls:

7.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)

rewrite15.0ms (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))
4.0ms
(-.f64 1 (cos.f64 x))
1.0ms
(cos.f64 x)

simplify88.0ms (1.5%)

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

prune128.0ms (2.2%)

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
37.2b
(-.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))))
▶14.2b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
45.1b
(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 (cos.f64 x)))))
25.8b
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
26.3b
(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (*.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
26.4b
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 (cos.f64 x) (*.f64 x x)))
26.3b
(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
26.4b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
26.3b
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
26.4b
(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
Compiler

Compiled 2020 to 1043 computations (48.4% 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))
✓0.5b
(+.f64 1 (cos.f64 x))
✓13.5b
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

series38.0ms (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))
14.0ms
(/.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))

rewrite30.0ms (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:

9.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
7.0ms
(/.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))

simplify100.0ms (1.7%)

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

prune196.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2015206
Fresh639
Picked101
Done000
Total2088216
Error
0b
Counts
216 → 8
Alt Table
StatusErrorProgram
26.3b
(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (cos.f64 x)))) (*.f64 x x))
0.2b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
22.4b
(/.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 6)) (+.f64 1 (cos.f64 x))) (*.f64 x x))
25.8b
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
13.9b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
14.2b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
26.4b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
▶0.2b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
Compiler

Compiled 4400 to 1983 computations (54.9% saved)

localize8.0ms (0.1%)

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)))

series29.0ms (0.5%)

Counts
3 → 28
Calls

3 calls:

13.0ms
(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
12.0ms
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
3.0ms
(/.f64 (sin.f64 x) x)

rewrite21.0ms (0.4%)

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)))
2.0ms
(/.f64 (sin.f64 x) x)

simplify108.0ms (1.8%)

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 → 147
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01762266
14332003
213331993
340881989
447491989
551731989

prune119.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1452147
Fresh257
Picked011
Done000
Total1478155
Error
0b
Counts
155 → 8
Alt Table
StatusErrorProgram
▶0.2b
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
14.2b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
0.2b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (/.f64 1 x)) (tan.f64 (/.f64 x 2))) x)
25.8b
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
13.9b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
0.2b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
26.4b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
✓0.2b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
Compiler

Compiled 2806 to 1420 computations (49.4% saved)

localize9.0ms (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))

series36.0ms (0.6%)

Counts
3 → 36
Calls

3 calls:

13.0ms
(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
12.0ms
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
11.0ms
(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite20.0ms (0.3%)

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

simplify113.0ms (1.9%)

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 → 132
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01692493
14092220
213932212
341352208
446532208
549522208

prune111.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1320132
Fresh066
Picked011
Done011
Total1328140
Error
0b
Counts
140 → 8
Alt Table
StatusErrorProgram
✓0.2b
(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
14.2b
(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
0.2b
(/.f64 (*.f64 (*.f64 (sin.f64 x) (/.f64 1 x)) (tan.f64 (/.f64 x 2))) x)
25.8b
(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
13.9b
(/.f64 (*.f64 (tan.f64 (/.f64 x 2)) (sin.f64 x)) (*.f64 x x))
0.2b
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
26.4b
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (cos.f64 x)))))
✓0.2b
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
Compiler

Compiled 2448 to 1472 computations (39.9% saved)

regimes149.0ms (2.5%)

Accuracy

Total 0.1b remaining (89.8%)

Threshold costs 0.1b (89.8%)

Counts
80 → 1
Compiler

Compiled 2658 to 1689 computations (36.5% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11017
21017

end106.0ms (1.8%)

Compiler

Compiled 127 to 88 computations (30.7% saved)

Profiling

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