Details

Time bar (total: 53.2s)

analyze2.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample77.0ms (0.1%)

Algorithm
intervals
Results
36.0ms124×body1024valid
17.0ms36×body2048valid
7.0ms42×body512valid
3.0ms42×body128valid
2.0ms12×body256valid
Compiler

Compiled 18 to 20 computations (-11.1% saved)

simplify103.0ms (0.2%)

Algorithm
egg-herbie
Counts
4 → 4
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
07214
17214

prune2.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New044
Fresh044
Picked000
Done000
Total088
Error
34.2b
Counts
8 → 4
Compiler

Compiled 10 to 9 computations (10% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

3.6b
(sin.f64 (+.f64 x eps))
1.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.6b
(sin.f64 (+.f64 x eps))

rewrite12.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_1805 *-un-lft-identity_binary64_1783
add-log-exp_binary64_1822
add-cube-cbrt_binary64_1818 cancel-sign-sub-inv_binary64_1749
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 sin-sum_binary64_1916 pow1_binary64_1844
flip3--_binary64_1787 difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735 diff-log_binary64_1875 diff-sin_binary64_1933 associate--l+_binary64_1720 flip--_binary64_1758 sub-neg_binary64_1776
Counts
2 → 26
Calls

4 calls:

6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
0.0ms
(sin.f64 (+.f64 x eps))

series116.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

76.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
39.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 368 to 288 computations (21.7% saved)

simplify64.0ms (0.1%)

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
05023755

prune175.0ms (0.3%)

Pruning

39 alts after pruning (38 fresh and 1 done)

PrunedKeptTotal
New153550
Fresh033
Picked000
Done011
Total153954
Error
0.4b
Counts
54 → 39
Compiler

Compiled 1021 to 530 computations (48.1% saved)

localize11.0ms (0%)

Local error

Found 6 expressions with local error:

3.7b
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.0b
(+.f64 x (+.f64 x eps))
0.0b
(+.f64 x (+.f64 x eps))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.7b
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite23.0ms (0%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64_1783
add-log-exp_binary64_1822
add-sqr-sqrt_binary64_1805
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-cube-cbrt_binary64_1818 pow1_binary64_1844
distribute-lft-out_binary64_1734 associate-*l*_binary64_1724 sum-log_binary64_1874 associate-*r*_binary64_1723
associate-+r+_binary64_1715 +-commutative_binary64_1713 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 flip-+_binary64_1757 sin-cos-mult_binary64_1939 *-commutative_binary64_1714 flip3-+_binary64_1786 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
Counts
3 → 41
Calls

6 calls:

7.0ms
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms
(+.f64 x (+.f64 x eps))
0.0ms
(+.f64 x (+.f64 x eps))
0.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series246.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

121.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
65.0ms
(+.f64 x (+.f64 x eps))
59.0ms
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
Compiler

Compiled 876 to 792 computations (9.6% saved)

simplify73.0ms (0.1%)

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
050491281

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify6.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

3.6b
(sin.f64 (+.f64 x eps))
1.3b
(-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) 1) (sin.f64 x))
1.3b
(-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) 1) (sin.f64 x))
3.6b
(sin.f64 (+.f64 x eps))

rewrite16.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_1805
*-un-lft-identity_binary64_1783
add-log-exp_binary64_1822
difference-of-squares_binary64_1752 add-cube-cbrt_binary64_1818 cancel-sign-sub-inv_binary64_1749
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 pow1_binary64_1844
flip3--_binary64_1787 sqr-pow_binary64_1755 unpow-prod-down_binary64_1862 distribute-lft-out--_binary64_1735 diff-log_binary64_1875 flip--_binary64_1758 sub-neg_binary64_1776 sin-sum_binary64_1916
Counts
2 → 26
Calls

4 calls:

10.0ms
(-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) 1) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) 1) (sin.f64 x))
0.0ms
(sin.f64 (+.f64 x eps))

series117.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

79.0ms
(-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) 1) (sin.f64 x))
38.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 400 to 320 computations (20% saved)

simplify67.0ms (0.1%)

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04953783
14953783

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

11.0b
(-.f64 (log.f64 (exp.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
3.6b
(sin.f64 (+.f64 x eps))
3.3b
(log.f64 (exp.f64 (sin.f64 (+.f64 x eps))))
0.1b
(exp.f64 (sin.f64 (+.f64 x eps)))
0.1b
(exp.f64 (sin.f64 (+.f64 x eps)))
3.3b
(log.f64 (exp.f64 (sin.f64 (+.f64 x eps))))
3.6b
(sin.f64 (+.f64 x eps))
11.0b
(-.f64 (log.f64 (exp.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))

rewrite26.0ms (0%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64_1783
11×add-sqr-sqrt_binary64_1805
add-cube-cbrt_binary64_1818
log-prod_binary64_1869
exp-prod_binary64_1835 add-log-exp_binary64_1822 pow1_binary64_1844
log-pow_binary64_1872
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 associate--l+_binary64_1720 sin-sum_binary64_1916
exp-sum_binary64_1829 cancel-sign-sub-inv_binary64_1749
distribute-lft-out--_binary64_1735
flip3--_binary64_1787 rem-exp-log_binary64_1823 difference-of-squares_binary64_1752 diff-log_binary64_1875 flip--_binary64_1758 sub-neg_binary64_1776 rem-log-exp_binary64_1824
Counts
4 → 57
Calls

8 calls:

9.0ms
(-.f64 (log.f64 (exp.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
4.0ms
(log.f64 (exp.f64 (sin.f64 (+.f64 x eps))))
4.0ms
(exp.f64 (sin.f64 (+.f64 x eps)))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(exp.f64 (sin.f64 (+.f64 x eps)))

series489.0ms (0.9%)

Counts
4 → 48
Calls

4 calls:

203.0ms
(-.f64 (log.f64 (exp.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
157.0ms
(log.f64 (exp.f64 (sin.f64 (+.f64 x eps))))
87.0ms
(exp.f64 (sin.f64 (+.f64 x eps)))
42.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 1018 to 761 computations (25.2% saved)

simplify83.0ms (0.2%)

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049691579
149691579

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

3.6b
(sin.f64 (+.f64 x eps))
0.2b
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps))))
0.1b
(sqrt.f64 (sin.f64 (+.f64 x eps)))
0.1b
(sqrt.f64 (sin.f64 (+.f64 x eps)))
0.2b
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps))))
3.6b
(sin.f64 (+.f64 x eps))
3.6b
(sin.f64 (+.f64 x eps))
7.8b
(-.f64 (*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))

rewrite37.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64_1805
19×pow1_binary64_1844
18×sqrt-prod_binary64_1799
13×add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
swap-sqr_binary64_1750 pow1/2_binary64_1863 sqrt-pow1_binary64_1801
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 associate-*l*_binary64_1724 add-log-exp_binary64_1822 associate-*r*_binary64_1723
pow-prod-up_binary64_1853
unswap-sqr_binary64_1751
cancel-sign-sub-inv_binary64_1749 pow-sqr_binary64_1756 pow-prod-down_binary64_1854
rem-sqrt-square_binary64_1796 sin-sum_binary64_1916
flip3--_binary64_1787 difference-of-squares_binary64_1752 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 sqrt-unprod_binary64_1803 pow-plus_binary64_1846 diff-log_binary64_1875 *-commutative_binary64_1714 rem-square-sqrt_binary64_1795 flip--_binary64_1758 sub-neg_binary64_1776 sqr-abs_binary64_1798 pow2_binary64_1864
Counts
4 → 81
Calls

8 calls:

12.0ms
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps))))
11.0ms
(-.f64 (*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(sqrt.f64 (sin.f64 (+.f64 x eps)))

series202.0ms (0.4%)

Counts
4 → 44
Calls

4 calls:

83.0ms
(-.f64 (*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
44.0ms
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (sin.f64 (+.f64 x eps))))
39.0ms
(sin.f64 (+.f64 x eps))
36.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 882 to 628 computations (28.8% saved)

simplify52.0ms (0.1%)

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
050151473

prune2.8s (5.3%)

Pruning

160 alts after pruning (155 fresh and 5 done)

PrunedKeptTotal
New228129357
Fresh72633
Picked000
Done156
Total236160396
Error
0.2b
Counts
396 → 160
Compiler

Compiled 6687 to 3673 computations (45.1% saved)

localize13.0ms (0%)

Local error

Found 6 expressions with local error:

3.7b
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.0b
(+.f64 x (+.f64 x eps))
0.0b
(+.f64 x (+.f64 x eps))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.7b
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite24.0ms (0%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64_1783
add-log-exp_binary64_1822
add-sqr-sqrt_binary64_1805
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-cube-cbrt_binary64_1818 pow1_binary64_1844
distribute-lft-out_binary64_1734 associate-*l*_binary64_1724 sum-log_binary64_1874 associate-*r*_binary64_1723
associate-+r+_binary64_1715 +-commutative_binary64_1713 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 flip-+_binary64_1757 sin-cos-mult_binary64_1939 *-commutative_binary64_1714 flip3-+_binary64_1786 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
Counts
3 → 41
Calls

6 calls:

7.0ms
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms
(+.f64 x (+.f64 x eps))
6.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.0ms
(+.f64 x (+.f64 x eps))
0.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series254.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

129.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
63.0ms
(+.f64 x (+.f64 x eps))
61.0ms
(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
Compiler

Compiled 976 to 892 computations (8.6% saved)

simplify78.0ms (0.1%)

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
050491281

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b
(*.f64 eps (cos.f64 x))
0.1b
(*.f64 eps (cos.f64 x))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_1805
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-cube-cbrt_binary64_1818 associate-*l*_binary64_1724 *-un-lft-identity_binary64_1783 associate-*r*_binary64_1723 pow1_binary64_1844
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 *-commutative_binary64_1714 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751 add-log-exp_binary64_1822
Counts
1 → 18
Calls

2 calls:

4.0ms
(*.f64 eps (cos.f64 x))
0.0ms
(*.f64 eps (cos.f64 x))

series67.0ms (0.1%)

Counts
1 → 9
Calls

1 calls:

67.0ms
(*.f64 eps (cos.f64 x))
Compiler

Compiled 92 to 84 computations (8.7% saved)

simplify127.0ms (0.2%)

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 0 (119.0ms)

IterNodesCost
04760253
14760253

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

11.3b
(-.f64 (log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
3.6b
(sin.f64 (+.f64 x eps))
3.3b
(log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps))))
0.2b
(pow.f64 E.f64 (sin.f64 (+.f64 x eps)))
0.2b
(pow.f64 E.f64 (sin.f64 (+.f64 x eps)))
3.3b
(log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps))))
3.6b
(sin.f64 (+.f64 x eps))
11.3b
(-.f64 (log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))

rewrite30.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×log-prod_binary64_1869
13×add-sqr-sqrt_binary64_1805 *-un-lft-identity_binary64_1783
11×add-cube-cbrt_binary64_1818
unpow-prod-down_binary64_1862
associate--l+_binary64_1720
add-exp-log_binary64_1821
add-log-exp_binary64_1822 pow1_binary64_1844
add-cbrt-cube_binary64_1819 sin-sum_binary64_1916 pow-exp_binary64_1851 rem-log-exp_binary64_1824
unpow-prod-up_binary64_1861 sqr-pow_binary64_1755 pow-unpow_binary64_1860 cancel-sign-sub-inv_binary64_1749
e-exp-1_binary64_1828 pow-to-exp_binary64_1852
flip3--_binary64_1787 difference-of-squares_binary64_1752 log-pow_binary64_1872 distribute-lft-out--_binary64_1735 diff-log_binary64_1875 pow-pow_binary64_1855 flip--_binary64_1758 sub-neg_binary64_1776
Counts
4 → 71
Calls

8 calls:

11.0ms
(-.f64 (log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
5.0ms
(log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps))))
5.0ms
(pow.f64 E.f64 (sin.f64 (+.f64 x eps)))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(pow.f64 E.f64 (sin.f64 (+.f64 x eps)))

series680.0ms (1.3%)

Counts
4 → 48
Calls

4 calls:

265.0ms
(-.f64 (log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
228.0ms
(log.f64 (pow.f64 E.f64 (sin.f64 (+.f64 x eps))))
144.0ms
(pow.f64 E.f64 (sin.f64 (+.f64 x eps)))
42.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 1034 to 777 computations (24.9% saved)

simplify65.0ms (0.1%)

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
051011772

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

3.6b
(sin.f64 (+.f64 x eps))
0.2b
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps)))))
0.1b
(sqrt.f64 (sin.f64 (+.f64 x eps)))
0.1b
(sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps))))
0.2b
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps)))))
3.6b
(sin.f64 (+.f64 x eps))
3.6b
(sin.f64 (+.f64 x eps))
7.8b
(-.f64 (*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps))))) (sin.f64 x))

rewrite40.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_1805
11×pow1_binary64_1844
*-un-lft-identity_binary64_1783
add-cube-cbrt_binary64_1818
sqrt-prod_binary64_1799
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 associate-*l*_binary64_1724 add-log-exp_binary64_1822
pow-prod-down_binary64_1854
sqrt-pow1_binary64_1801 associate-*r*_binary64_1723
cancel-sign-sub-inv_binary64_1749
pow1/2_binary64_1863 unswap-sqr_binary64_1751 sin-sum_binary64_1916
flip3--_binary64_1787 swap-sqr_binary64_1750 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 sqrt-unprod_binary64_1803 diff-log_binary64_1875 *-commutative_binary64_1714 flip--_binary64_1758 sub-neg_binary64_1776
Counts
4 → 58
Calls

8 calls:

15.0ms
(-.f64 (*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps))))) (sin.f64 x))
12.0ms
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps)))))
4.0ms
(sin.f64 (+.f64 x eps))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps))))

series197.0ms (0.4%)

Counts
4 → 44
Calls

4 calls:

76.0ms
(-.f64 (*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps))))) (sin.f64 x))
44.0ms
(*.f64 (sqrt.f64 (sin.f64 (+.f64 x eps))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps)))))
40.0ms
(sin.f64 (+.f64 x eps))
37.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 942 to 704 computations (25.3% saved)

simplify73.0ms (0.1%)

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049691294
149691294

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 x (*.f64 (sin.f64 eps) -1/2))
0.1b
(sqrt.f64 (sin.f64 (+.f64 x eps)))
0.0b
(+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))
0.0b
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))
0.2b
(*.f64 (sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))) (sqrt.f64 (sin.f64 (+.f64 x eps))))
2.2b
(-.f64 (*.f64 (sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))) (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
3.6b
(sin.f64 (+.f64 x eps))
6.4b
(sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2))))))

rewrite38.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64_1805
13×sqrt-prod_binary64_1799
10×add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
pow1_binary64_1844
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 associate-*l*_binary64_1724 add-log-exp_binary64_1822 associate-*r*_binary64_1723
sqrt-div_binary64_1800 unswap-sqr_binary64_1751
cancel-sign-sub-inv_binary64_1749 pow1/2_binary64_1863 sqrt-pow1_binary64_1801 pow-prod-down_binary64_1854
flip-+_binary64_1757 associate-*l/_binary64_1726 flip3-+_binary64_1786
flip3--_binary64_1787 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 sqrt-unprod_binary64_1803 diff-log_binary64_1875 *-commutative_binary64_1714 rem-sqrt-square_binary64_1796 flip--_binary64_1758 sub-neg_binary64_1776 sin-sum_binary64_1916
Counts
4 → 69
Calls

8 calls:

11.0ms
(*.f64 (sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))) (sqrt.f64 (sin.f64 (+.f64 x eps))))
11.0ms
(-.f64 (*.f64 (sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))) (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))
3.0ms
(sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2))))))
0.0ms
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))

series893.0ms (1.7%)

Counts
4 → 46
Calls

4 calls:

393.0ms
(-.f64 (*.f64 (sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))) (sqrt.f64 (sin.f64 (+.f64 x eps)))) (sin.f64 x))
278.0ms
(*.f64 (sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))))) (sqrt.f64 (sin.f64 (+.f64 x eps))))
174.0ms
(sqrt.f64 (+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2))))))
47.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 2763 to 1861 computations (32.6% saved)

simplify78.0ms (0.1%)

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
051133902

prune7.9s (14.8%)

Pruning

327 alts after pruning (317 fresh and 10 done)

PrunedKeptTotal
New268172440
Fresh5145150
Picked000
Done01010
Total273327600
Error
0.2b
Counts
600 → 327
Compiler

Compiled 14139 to 8149 computations (42.4% saved)

localize15.0ms (0%)

Local error

Found 6 expressions with local error:

3.7b
(cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2)))
0.0b
(+.f64 x (+.f64 x eps))
0.0b
(+.f64 x (+.f64 x eps))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2)))
3.7b
(cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2))

rewrite19.0ms (0%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64_1783
add-log-exp_binary64_1822
add-sqr-sqrt_binary64_1805
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-cube-cbrt_binary64_1818 pow1_binary64_1844
distribute-lft-out_binary64_1734 associate-*l*_binary64_1724 sum-log_binary64_1874 associate-*r*_binary64_1723
associate-+r+_binary64_1715 +-commutative_binary64_1713 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 flip-+_binary64_1757 sin-cos-mult_binary64_1939 *-commutative_binary64_1714 flip3-+_binary64_1786 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
Counts
3 → 41
Calls

6 calls:

8.0ms
(+.f64 x (+.f64 x eps))
5.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2)))
3.0ms
(cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2))
0.0ms
(+.f64 x (+.f64 x eps))
0.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2)))

series253.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

130.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2)))
62.0ms
(+.f64 x (+.f64 x eps))
61.0ms
(cos.f64 (/.f64 (*.f64 1 (+.f64 x (+.f64 x eps))) 2))
Compiler

Compiled 1012 to 928 computations (8.3% saved)

simplify99.0ms (0.2%)

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
048831194
148831194

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

7.8b
(*.f64 eps (*.f64 x x))
0.0b
(*.f64 1/2 (*.f64 eps (*.f64 x x)))
0.0b
(*.f64 1/2 (*.f64 eps (*.f64 x x)))
7.8b
(*.f64 eps (*.f64 x x))

rewrite15.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 pow1_binary64_1844
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 pow-prod-down_binary64_1854
associate-*l*_binary64_1724
add-sqr-sqrt_binary64_1805
add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
*-commutative_binary64_1714 add-log-exp_binary64_1822 associate-*r*_binary64_1723
unswap-sqr_binary64_1751
Counts
2 → 40
Calls

4 calls:

7.0ms
(*.f64 1/2 (*.f64 eps (*.f64 x x)))
5.0ms
(*.f64 eps (*.f64 x x))
0.0ms
(*.f64 1/2 (*.f64 eps (*.f64 x x)))
0.0ms
(*.f64 eps (*.f64 x x))

series125.0ms (0.2%)

Counts
2 → 12
Calls

2 calls:

70.0ms
(*.f64 1/2 (*.f64 eps (*.f64 x x)))
55.0ms
(*.f64 eps (*.f64 x x))
Compiler

Compiled 216 to 192 computations (11.1% saved)

simplify77.0ms (0.1%)

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
05366511

localize14.0ms (0%)

Local error

Found 6 expressions with local error:

0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x)))))
0.1b
(*.f64 eps (sin.f64 x))
0.0b
(-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x))))
0.0b
(-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x))))
0.1b
(*.f64 eps (sin.f64 x))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x)))))

rewrite28.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64_1805
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783 pow1_binary64_1844
associate-*l*_binary64_1724 associate-*r*_binary64_1723
add-log-exp_binary64_1822
cancel-sign-sub-inv_binary64_1749 sub-neg_binary64_1776
flip3--_binary64_1787 associate-*r/_binary64_1725 distribute-lft-in_binary64_1732 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 *-commutative_binary64_1714 distribute-rgt-in_binary64_1733 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751 flip--_binary64_1758
diff-log_binary64_1875
Counts
3 → 54
Calls

6 calls:

8.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x)))))
5.0ms
(*.f64 eps (sin.f64 x))
5.0ms
(-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x))))
0.0ms
(-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x))))
0.0ms
(*.f64 eps (sin.f64 x))

series395.0ms (0.7%)

Counts
3 → 32
Calls

3 calls:

195.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x)))))
128.0ms
(-.f64 (cos.f64 x) (*.f64 1/2 (*.f64 eps (sin.f64 x))))
71.0ms
(*.f64 eps (sin.f64 x))
Compiler

Compiled 942 to 833 computations (11.6% saved)

simplify75.0ms (0.1%)

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049471505
149471505

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

1.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
0.1b
(*.f64 (sqrt.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (sqrt.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
0.0b
(sqrt.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
0.0b
(sqrt.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
1.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.6b
(sin.f64 (+.f64 x eps))
3.6b
(sin.f64 (+.f64 x eps))

rewrite28.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64_1805 *-un-lft-identity_binary64_1783
add-log-exp_binary64_1822
add-cube-cbrt_binary64_1818 cancel-sign-sub-inv_binary64_1749
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 sin-sum_binary64_1916 pow1_binary64_1844
flip3--_binary64_1787 difference-of-squares_binary64_1752 distribute-lft-out--_binary64_1735 diff-log_binary64_1875 diff-sin_binary64_1933 associate--l+_binary64_1720 flip--_binary64_1758 sub-neg_binary64_1776
Counts
4 → 52
Calls

8 calls:

7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
(sin.f64 (+.f64 x eps))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(sqrt.f64 (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))

series250.0ms (0.5%)

Counts
4 → 44
Calls

4 calls:

80.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
80.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
46.0ms
(sin.f64 (+.f64 x eps))
44.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 1376 to 842 computations (38.8% saved)

simplify77.0ms (0.1%)

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
048961350
148961350

localize31.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6))) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x))) (sin.f64 eps)))) (sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps)))))
0.1b
(*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6)))
0.1b
(sqrt.f64 (*.f64 1 (sin.f64 (+.f64 x eps))))
0.0b
(*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x)))
3.0b
(*.f64 (sin.f64 eps) (*.f64 x x))
3.6b
(sin.f64 (+.f64 x eps))
5.4b
(sqrt.f64 (-.f64 (*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6))) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x))) (sin.f64 eps))))
6.0b
(-.f64 (*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6))) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x))) (sin.f64 eps)))

rewrite51.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64_1805 pow1_binary64_1844
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-log-exp_binary64_1822
associate-*r/_binary64_1725 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783 frac-sub_binary64_1792
flip3--_binary64_1787 cancel-sign-sub-inv_binary64_1749 sqrt-div_binary64_1800 flip--_binary64_1758
flip-+_binary64_1757 flip3-+_binary64_1786 associate--r+_binary64_1719
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 associate-*l*_binary64_1724 sqrt-prod_binary64_1799 diff-log_binary64_1875 pow-prod-down_binary64_1854
associate--l+_binary64_1720 sub-neg_binary64_1776
distribute-lft-in_binary64_1732 pow1/2_binary64_1863 associate--r-_binary64_1722 *-commutative_binary64_1714 distribute-rgt-in_binary64_1733 sqrt-pow1_binary64_1801 unswap-sqr_binary64_1751 rem-sqrt-square_binary64_1796 sin-sum_binary64_1916 associate-*r*_binary64_1723
Counts
4 → 72
Calls

8 calls:

17.0ms
(-.f64 (*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6))) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x))) (sin.f64 eps)))
14.0ms
(sqrt.f64 (-.f64 (*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6))) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x))) (sin.f64 eps))))
6.0ms
(*.f64 (sin.f64 eps) (*.f64 x x))
4.0ms
(sin.f64 (+.f64 x eps))
0.0ms
(*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x)))

series517.0ms (1%)

Counts
4 → 36
Calls

4 calls:

228.0ms
(sqrt.f64 (-.f64 (*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6))) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x))) (sin.f64 eps))))
157.0ms
(-.f64 (*.f64 (cos.f64 eps) (+.f64 x (*.f64 (pow.f64 x 3) -1/6))) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 eps) (*.f64 x x))) (sin.f64 eps)))
84.0ms
(*.f64 (sin.f64 eps) (*.f64 x x))
49.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 2134 to 1616 computations (24.3% saved)

simplify66.0ms (0.1%)

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
052453444

prune13.6s (25.5%)

Pruning

486 alts after pruning (471 fresh and 15 done)

PrunedKeptTotal
New247172419
Fresh13299312
Picked000
Done01515
Total260486746
Error
0.2b
Counts
746 → 486
Compiler

Compiled 8186 to 4213 computations (48.5% saved)

simplify380.0ms (0.7%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0501426805

regimes5.7s (10.6%)

Compiler

Compiled 34192 to 23719 computations (30.6% saved)

bsearch78.0ms (0.1%)

Steps
ItersRangePoint
8
2.1697776046776103e-07
0.0007572542386218229
0.0007460669567238816
5
-0.002487885533578501
-0.0007296864550878135
-0.0009986885707327965
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes1.2s (2.3%)

Compiler

Compiled 6389 to 5253 computations (17.8% saved)

bsearch59.0ms (0.1%)

Steps
ItersRangePoint
8
2.1697776046776103e-07
0.0007572542386218229
0.000701317829132117
5
-0.002487885533578501
-0.0007296864550878135
-0.0008790196068280468
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes749.0ms (1.4%)

Compiler

Compiled 6347 to 5223 computations (17.7% saved)

bsearch0.0ms (0%)

regimes181.0ms (0.3%)

Compiler

Compiled 1119 to 1016 computations (9.2% saved)

bsearch0.0ms (0%)

regimes232.0ms (0.4%)

Compiler

Compiled 840 to 776 computations (7.6% saved)

bsearch1.0ms (0%)

Compiler

Compiled 7 to 6 computations (14.3% saved)

regimes146.0ms (0.3%)

Compiler

Compiled 405 to 398 computations (1.7% saved)

bsearch76.0ms (0.1%)

Steps
ItersRangePoint
8
2.1697776046776103e-07
0.0007572542386218229
0.00011414825082033838
10
-402421519390.3741
-0.002487885533578501
-0.0025328896187052515
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes88.0ms (0.2%)

Compiler

Compiled 222 to 220 computations (0.9% saved)

bsearch67.0ms (0.1%)

Steps
ItersRangePoint
8
2.1697776046776103e-07
0.0007572542386218229
0.00016216259863038255
10
-402421519390.3741
-0.002487885533578501
-0.0025328896187052515
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes29.0ms (0.1%)

Compiler

Compiled 70 to 78 computations (-11.4% saved)

bsearch0.0ms (0%)

regimes38.0ms (0.1%)

Accuracy

Total 0.1b remaining (51.3%)

Threshold costs 0.1b (51.3%)

Compiler

Compiled 66 to 72 computations (-9.1% saved)

bsearch75.0ms (0.1%)

Steps
ItersRangePoint
8
0.0007572542386218229
22.913702724595534
9.458511693510916
10
-402421519390.3741
-0.002487885533578501
-1.006750103867893
Compiler

Compiled 254 to 155 computations (39% saved)

simplify8.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0174357
1174357

end0.0ms (0%)

sample13.0s (24.3%)

Algorithm
intervals
Results
1.0s3523×body1024valid
655.0ms1222×body2048valid
267.0ms1343×body512valid
83.0ms1344×body128valid
69.0ms561×body256valid
7.0msbody4096valid
Compiler

Compiled 11795 to 8190 computations (30.6% saved)

Pareto

0.4081559395696656

Profiling

Loading profile data...