Details

Time bar (total: 5.7s)

analyze25.0ms (0.4%)

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

Compiled 10 to 7 computations (30% saved)

sample83.0ms (1.4%)

Algorithm
1×intervals
Results
36.0ms105×body1024valid
23.0ms43×body2048valid
8.0ms41×body512valid
3.0ms49×body128valid
3.0ms18×body256valid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify11.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
15×sub-neg_binary64
14×cancel-sign-sub-inv_binary64
10×distribute-rgt-in_binary64
9×neg-mul-1_binary64
8×associate--r+_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11011
21511
32111
42711
54211
66511
77811
89011
99211
108611
117211

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
35.3b
Counts
1 → 1
Alt Table
StatusErrorProgram
▶35.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 18 to 12 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.5b
(sin.f64 (+.f64 x eps))

rewrite41.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Error
23.1b
Rules
5×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
4×add-log-exp_binary64
3×add-cube-cbrt_binary64 cancel-sign-sub-inv_binary64
2×sin-sum_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
1×diff-sin_binary64 diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 associate--l+_binary64
Counts
2 → 26
Calls

2 calls:

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

Compiled 375 to 99 computations (73.6% saved)

series61.0ms (1.1%)

Error
9.9b
Counts
2 → 24
Calls

2 calls:

20.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 697 to 408 computations (41.5% saved)

simplify80.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
293×associate-+l-_binary64
288×distribute-rgt-neg-in_binary64
287×neg-mul-1_binary64
281×distribute-lft-neg-in_binary64
274×sub-neg_binary64
Counts
50 → 40
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0103838
1253815
2632771
32084755
44820755
55027755

prune44.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New34640
Fresh000
Picked101
Done000
Total35641
Error
0.2b
Counts
41 → 6
Alt Table
StatusErrorProgram
23.5b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
29.3b
(*.f64 eps (-.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 1/2 (sin.f64 x)) (*.f64 eps (*.f64 1/6 (cos.f64 x)))))))
▶23.5b
(-.f64 (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
39.0b
(-.f64 (cbrt.f64 (pow.f64 (sin.f64 (+.f64 eps x)) 3)) (sin.f64 x))
29.4b
(+.f64 (*.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6))) (*.f64 (sin.f64 x) (-.f64 (*.f64 1/24 (pow.f64 eps 4)) (*.f64 1/2 (*.f64 eps eps)))))
28.6b
(+.f64 (*.f64 (pow.f64 x 3) (+.f64 1/6 (*.f64 (cos.f64 eps) -1/6))) (+.f64 (sin.f64 eps) (-.f64 (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 (sin.f64 eps) -1/2)))) x)))
Compiler

Compiled 707 to 336 computations (52.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
0.1b
(*.f64 (sin.f64 eps) (cos.f64 x))
0.1b
(*.f64 (cos.f64 eps) (sin.f64 x))
1.9b
(-.f64 (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite100.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
15×add-sqr-sqrt_binary64
11×add-log-exp_binary64 *-un-lft-identity_binary64
9×add-cube-cbrt_binary64
8×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
6×associate-*l*_binary64 associate-*r*_binary64
Counts
4 → 66
Calls

4 calls:

8.0ms
(-.f64 (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
4.0ms
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
4.0ms
(*.f64 (cos.f64 eps) (sin.f64 x))
4.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))
Compiler

Compiled 1417 to 267 computations (81.2% saved)

series151.0ms (2.6%)

Error
0.2b
Counts
4 → 48
Calls

4 calls:

37.0ms
(-.f64 (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
33.0ms
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x)))
28.0ms
(*.f64 (cos.f64 eps) (sin.f64 x))
26.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))
Compiler

Compiled 1948 to 1098 computations (43.6% saved)

simplify131.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
570×cancel-sign-sub-inv_binary64
489×sub-neg_binary64
398×*-commutative_binary64
250×neg-mul-1_binary64
239×distribute-rgt-in_binary64
Counts
114 → 83
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02082287
15562215
216512071
338392066
446632066
550042066

prune88.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New75883
Fresh325
Picked101
Done000
Total791089
Error
0.1b
Counts
89 → 10
Alt Table
StatusErrorProgram
27.3b
(-.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 3) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) 3)) (+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))))) (sin.f64 x))
27.3b
(-.f64 (cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) 3)) (sin.f64 x))
1.8b
(*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
27.2b
(/.f64 (-.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (+.f64 (cos.f64 eps) 1) (sin.f64 x))))))
22.3b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
31.4b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
23.5b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
29.3b
(*.f64 eps (-.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 1/2 (sin.f64 x)) (*.f64 eps (*.f64 1/6 (cos.f64 x)))))))
▶0.5b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
29.3b
(+.f64 (*.f64 (cos.f64 x) (-.f64 eps (*.f64 1/6 (pow.f64 eps 3)))) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2)))
Compiler

Compiled 2029 to 813 computations (59.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
2.2b
(+.f64 (cos.f64 eps) -1)

rewrite129.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
14×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
8×add-log-exp_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 associate-*r*_binary64
6×associate-*l*_binary64
3×flip3-+_binary64 flip-+_binary64
Counts
4 → 68
Calls

4 calls:

7.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
5.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
4.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 1441 to 642 computations (55.4% saved)

series159.0ms (2.8%)

Error
0.0b
Counts
4 → 40
Calls

4 calls:

38.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
34.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
28.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
12.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 1959 to 1319 computations (32.7% saved)

simplify101.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
555×cancel-sign-sub-inv_binary64
492×distribute-rgt-in_binary64
430×distribute-lft-in_binary64
275×associate--l+_binary64
239×unsub-neg_binary64
Counts
108 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02141993
15921913
218931830
346771830
450751830

prune127.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New78684
Fresh549
Picked101
Done000
Total841094
Error
0.0b
Counts
94 → 10
Alt Table
StatusErrorProgram
22.3b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
31.4b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
▶0.2b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (/.f64 (*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x))) (-.f64 (cos.f64 eps) -1))))
23.5b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
29.3b
(*.f64 eps (-.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 1/2 (sin.f64 x)) (*.f64 eps (*.f64 1/6 (cos.f64 x)))))))
17.1b
(*.f64 1 (+.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x)))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.6b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 eps) 1)) (cbrt.f64 (-.f64 (cos.f64 eps) 1))) (cbrt.f64 (-.f64 (cos.f64 eps) 1))))))
0.5b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x)))))
0.6b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (cbrt.f64 (pow.f64 (*.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x)) 3))))
1.7b
(*.f64 1 (+.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
Compiler

Compiled 2041 to 1075 computations (47.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x)))
0.2b
(/.f64 (*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x))) (-.f64 (cos.f64 eps) -1))
0.2b
(*.f64 (sin.f64 eps) (sin.f64 eps))
0.3b
(-.f64 (cos.f64 eps) -1)

rewrite211.0ms (3.7%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
23×add-sqr-sqrt_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64 *-un-lft-identity_binary64
16×pow1_binary64
14×add-cube-cbrt_binary64
13×associate-*r*_binary64
Counts
4 → 102
Calls

4 calls:

12.0ms
(/.f64 (*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x))) (-.f64 (cos.f64 eps) -1))
10.0ms
(*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x)))
5.0ms
(*.f64 (sin.f64 eps) (sin.f64 eps))
4.0ms
(-.f64 (cos.f64 eps) -1)
Compiler

Compiled 2727 to 927 computations (66% saved)

series171.0ms (3%)

Error
0.0b
Counts
4 → 32
Calls

4 calls:

61.0ms
(/.f64 (*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x))) (-.f64 (cos.f64 eps) -1))
43.0ms
(*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x)))
12.0ms
(*.f64 (sin.f64 eps) (sin.f64 eps))
10.0ms
(-.f64 (cos.f64 eps) -1)
Compiler

Compiled 2137 to 1434 computations (32.9% saved)

simplify114.0ms (2%)

Algorithm
1×egg-herbie
Rules
236×associate-*l*_binary64
209×distribute-rgt-neg-out_binary64
202×cancel-sign-sub-inv_binary64
197×associate-*r*_binary64
181×log-prod_binary64
Counts
134 → 114
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02242547
15812202
223132134
343272123
449412123

prune159.0ms (2.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1140114
Fresh099
Picked011
Done000
Total11410124
Error
0.0b
Counts
124 → 10
Alt Table
StatusErrorProgram
22.3b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
31.4b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
0.2b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (/.f64 (*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (neg.f64 (sin.f64 x))) (-.f64 (cos.f64 eps) -1))))
23.5b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
29.3b
(*.f64 eps (-.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 1/2 (sin.f64 x)) (*.f64 eps (*.f64 1/6 (cos.f64 x)))))))
17.1b
(*.f64 1 (+.f64 (*.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x)))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.6b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 eps) 1)) (cbrt.f64 (-.f64 (cos.f64 eps) 1))) (cbrt.f64 (-.f64 (cos.f64 eps) 1))))))
0.5b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x)))))
0.6b
(*.f64 1 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (cbrt.f64 (pow.f64 (*.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x)) 3))))
1.7b
(*.f64 1 (+.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
Compiler

Compiled 2371 to 1170 computations (50.7% saved)

regimes1.0s (18.2%)

Accuracy

Total 0.3b remaining (74.1%)

Threshold costs 0.3b (74.1%)

Compiler

Compiled 15035 to 9802 computations (34.8% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
8×*-commutative_binary64
6×+-commutative_binary64
5×neg-mul-1_binary64 neg-sub0_binary64
4×sub-neg_binary64
2×unsub-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01731
12931
23729
34529
45029
55329
65429
75329

end1.0ms (0%)

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.6s (46%)

Algorithm
1×intervals
Results
1.0s3490×body1024valid
644.0ms1217×body2048valid
268.0ms1344×body512valid
89.0ms1352×body128valid
74.0ms596×body256valid
1.0ms1×body4096valid
Compiler

Compiled 264 to 176 computations (33.3% saved)

Profiling

Loading profile data...