Details

Time bar (total: 12.1s)

analyze1.8s (14.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
0%99.9%0.1%11
0%99.9%0.1%12
0%99.9%0.1%13
0%99.9%0.1%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample5.9s (49%)

Results
3.0s4047×body1024valid
2.2s2033×body2048valid
509.0ms1374×body512valid
133.0ms525×body256valid
40.0ms275×body128valid
5.0msbody4096valid
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify15.0ms (0.1%)

Algorithm
egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11011
21511
32211
42911
54611
67211
79311
811011
912011
1012411
1112611
1211211

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
39.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
39.8b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.4b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.4b
(cos.f64 (+.f64 x eps))

series13.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

8.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms
(cos.f64 (+.f64 x eps))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
add-log-exp_binary64
Counts
2 → 42
Calls

2 calls:

6.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.0ms
(cos.f64 (+.f64 x eps))

simplify80.0ms (0.7%)

Algorithm
egg-herbie
Rules
757×fma-neg_binary64
498×cancel-sign-sub-inv_binary64
477×fma-def_binary64
311×sub-neg_binary64
244×distribute-rgt-in_binary64
Counts
90 → 92
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01341274
13091207
29651144
323731120
445221120
548381120

prune85.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New84892
Fresh000
Picked101
Done000
Total85893
Error
0.2b
Counts
93 → 8
Alt Table
StatusErrorProgram
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
25.9b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
39.9b
(log.f64 (/.f64 (exp.f64 (cos.f64 (+.f64 x eps))) (exp.f64 (cos.f64 x))))
14.1b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
40.2b
(fma.f64 (*.f64 (cbrt.f64 (cos.f64 (+.f64 x eps))) (cbrt.f64 (cos.f64 (+.f64 x eps)))) (cbrt.f64 (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x)))
29.4b
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 eps 3) (sin.f64 x))) (*.f64 1/24 (*.f64 (pow.f64 eps 4) (cos.f64 x)))) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 eps 2) (cos.f64 x))) (*.f64 eps (sin.f64 x))))
39.9b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
Compiler

Compiled 1869 to 650 computations (65.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
0.0b
(+.f64 x (+.f64 eps x))
0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
4.3b
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

series44.0ms (0.4%)

Counts
4 → 96
Calls

4 calls:

20.0ms
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
15.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
5.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
4.0ms
(+.f64 x (+.f64 eps x))

rewrite33.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
10×add-sqr-sqrt_binary64
Counts
4 → 71
Calls

4 calls:

11.0ms
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
8.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
6.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
4.0ms
(+.f64 x (+.f64 eps x))

simplify147.0ms (1.2%)

Algorithm
egg-herbie
Rules
549×fma-def_binary64
428×*-commutative_binary64
417×cancel-sign-sub-inv_binary64
354×sub-neg_binary64
330×distribute-rgt-neg-in_binary64
Counts
167 → 164
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01843349
15002908
215282564
336862549
447102549
549852549
649252549

prune194.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1568164
Fresh347
Picked101
Done000
Total16012172
Error
0.1b
Counts
172 → 12
Alt Table
StatusErrorProgram
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
25.9b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
22.4b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
14.1b
(log1p.f64 (expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
36.6b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
14.8b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))) (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
32.7b
(*.f64 (sin.f64 (*.f64 1/2 eps)) (+.f64 (*.f64 (sin.f64 (*.f64 1/2 eps)) (fma.f64 x x -2)) (*.f64 (*.f64 (cos.f64 (*.f64 1/2 eps)) x) -2)))
28.5b
(*.f64 -2 (exp.f64 (log.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
14.7b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))
29.4b
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 eps 3) (sin.f64 x))) (*.f64 1/24 (*.f64 (pow.f64 eps 4) (cos.f64 x)))) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 eps 2) (cos.f64 x))) (*.f64 eps (sin.f64 x))))
32.9b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))) 3)))
Compiler

Compiled 4173 to 2919 computations (30.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))))
0.2b
(log1p.f64 (expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
0.3b
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))
4.3b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

series79.0ms (0.7%)

Counts
4 → 96
Calls

4 calls:

36.0ms
(expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))))
18.0ms
(log1p.f64 (expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
13.0ms
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))
11.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

rewrite66.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 52
Calls

4 calls:

61.0ms
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))
2.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
0.0ms
(expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))))
0.0ms
(log1p.f64 (expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))

simplify142.0ms (1.2%)

Algorithm
egg-herbie
Rules
784×fma-neg_binary64
631×cancel-sign-sub-inv_binary64
284×associate-*r*_binary64
252×distribute-rgt-neg-in_binary64
236×distribute-lft-neg-in_binary64
Counts
148 → 128
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02263905
16593616
223373510
344053496
449683496
549683496

prune174.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1271128
Fresh11011
Picked011
Done000
Total12812140
Error
0.1b
Counts
140 → 12
Alt Table
StatusErrorProgram
28.5b
(*.f64 -2 (exp.f64 (log.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
29.4b
(fma.f64 1/6 (*.f64 (sin.f64 x) (pow.f64 eps 3)) (fma.f64 (cos.f64 x) (fma.f64 (pow.f64 eps 4) 1/24 (*.f64 (*.f64 eps eps) -1/2)) (neg.f64 (*.f64 eps (sin.f64 x)))))
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
25.9b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
22.4b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
14.1b
(log1p.f64 (expm1.f64 (*.f64 -2 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
36.6b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
14.8b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))) (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
32.7b
(*.f64 (sin.f64 (*.f64 1/2 eps)) (+.f64 (*.f64 (sin.f64 (*.f64 1/2 eps)) (fma.f64 x x -2)) (*.f64 (*.f64 (cos.f64 (*.f64 1/2 eps)) x) -2)))
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
14.7b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))
32.9b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))) 3)))
Compiler

Compiled 4119 to 3161 computations (23.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
0.5b
(*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
0.6b
(cbrt.f64 (sin.f64 (/.f64 eps 2)))
4.3b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

series844.0ms (7%)

Counts
3 → 48
Calls

3 calls:

387.0ms
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
258.0ms
(*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
199.0ms
(cbrt.f64 (sin.f64 (/.f64 eps 2)))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
15×*-un-lft-identity_binary64
15×add-cube-cbrt_binary64
12×associate-*r*_binary64
Counts
3 → 79
Calls

3 calls:

7.0ms
(*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
6.0ms
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
2.0ms
(cbrt.f64 (sin.f64 (/.f64 eps 2)))

simplify117.0ms (1%)

Algorithm
egg-herbie
Rules
960×fma-neg_binary64
406×distribute-rgt-neg-in_binary64
392×distribute-lft-neg-in_binary64
390×fma-def_binary64
345×*-commutative_binary64
Counts
127 → 150
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01712997
14052733
212002411
326892311
448062311
549872311

prune322.0ms (2.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2241225
Fresh01010
Picked011
Done101
Total22512237
Error
0.1b
Counts
237 → 12
Alt Table
StatusErrorProgram
28.5b
(*.f64 -2 (exp.f64 (log.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
29.4b
(fma.f64 1/6 (*.f64 (sin.f64 x) (pow.f64 eps 3)) (fma.f64 (cos.f64 x) (fma.f64 (pow.f64 eps 4) 1/24 (*.f64 (*.f64 eps eps) -1/2)) (neg.f64 (*.f64 eps (sin.f64 x)))))
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
25.9b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
22.4b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
24.1b
(*.f64 -2 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 (*.f64 eps 1/2)) 2)) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))
14.8b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))) (cbrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
32.7b
(*.f64 (sin.f64 (*.f64 1/2 eps)) (+.f64 (*.f64 (sin.f64 (*.f64 1/2 eps)) (fma.f64 x x -2)) (*.f64 (*.f64 (cos.f64 (*.f64 1/2 eps)) x) -2)))
25.9b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
36.6b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
14.7b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))
32.9b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))) 3)))
Compiler

Compiled 8330 to 6759 computations (18.9% saved)

regimes1.6s (13.1%)

Accuracy

Total 0.3b remaining (57.3%)

Threshold costs 0.3b (57.3%)

Counts
226 → 3
Compiler

Compiled 14174 to 10433 computations (26.4% saved)

bsearch108.0ms (0.9%)

Steps
ItersRangePoint
8
0.00014690515572541568
0.8960898488574148
0.002845823794585604
9
-4307.745195556134
-0.0006637061522229891
-0.0027738346999691818
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03274
14974
26074
36774
47074
57074

end257.0ms (2.1%)

Compiler

Compiled 377 to 275 computations (27.1% saved)

Profiling

Loading profile data...