Details

Time bar (total: 16.1s)

analyze763.0ms (4.7%)

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
12.5%87.4%0.1%5
18.7%81.2%0.1%6
21.9%78%0.1%7
23.4%76.5%0.1%8
24.2%75.7%0.1%9
24.6%75.3%0.1%10
24.8%75.1%0.1%11
24.9%75%0.1%12
24.9%75%0.1%13
25%75%0.1%14
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample78.0ms (0.5%)

Algorithm
intervals
Results
31.0ms110×body1024valid
28.0ms44×body2048valid
6.0ms44×body512valid
2.0ms20×body256valid
2.0ms38×body128valid
Compiler

Compiled 15 to 15 computations (0% saved)

simplify99.0ms (0.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
07211
17211

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
38.3b
Counts
2 → 1
Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

3.5b
(tan.f64 (+.f64 x eps))
1.6b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.6b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.5b
(tan.f64 (+.f64 x eps))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_1464 *-un-lft-identity_binary64_1442
add-log-exp_binary64_1481 tan-quot_binary64_1601
cancel-sign-sub-inv_binary64_1408 add-cube-cbrt_binary64_1477
add-cbrt-cube_binary64_1478 frac-sub_binary64_1451 add-exp-log_binary64_1480 pow1_binary64_1503 tan-sum_binary64_1577
sub-neg_binary64_1435 flip3--_binary64_1446 flip--_binary64_1417 diff-log_binary64_1534 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
Counts
2 → 27
Calls

4 calls:

7.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms
(tan.f64 (+.f64 x eps))
0.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
0.0ms
(tan.f64 (+.f64 x eps))

series447.0ms (2.8%)

Counts
2 → 24
Calls

2 calls:

275.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
172.0ms
(tan.f64 (+.f64 x eps))
Compiler

Compiled 904 to 607 computations (32.9% saved)

simplify39.0ms (0.2%)

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
055011566

prune121.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New48351
Fresh000
Picked101
Done000
Total49352
Error
0.3b
Counts
52 → 3
Compiler

Compiled 1273 to 511 computations (59.9% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (tan.f64 x) (tan.f64 eps))
0.1b
(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b
(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b
(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b
(*.f64 (tan.f64 x) (tan.f64 eps))
3.6b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite41.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity_binary64_1442
23×add-sqr-sqrt_binary64_1464
16×add-cube-cbrt_binary64_1477
13×times-frac_binary64_1448
tan-quot_binary64_1601
add-cbrt-cube_binary64_1478 add-log-exp_binary64_1481 add-exp-log_binary64_1480
pow1_binary64_1503
distribute-lft-out_binary64_1393
associate-/l*_binary64_1387
associate-*r*_binary64_1382 associate-/r*_binary64_1386 cancel-sign-sub-inv_binary64_1408 associate-/l/_binary64_1389 associate-*l*_binary64_1383
associate-/r/_binary64_1388 flip3--_binary64_1446 flip--_binary64_1417 flip3-+_binary64_1445 flip-+_binary64_1416 frac-add_binary64_1450 difference-of-squares_binary64_1411
associate-*r/_binary64_1384 cbrt-undiv_binary64_1476 cbrt-unprod_binary64_1475 sum-log_binary64_1533 div-inv_binary64_1439 sub-neg_binary64_1435 clear-num_binary64_1441 +-commutative_binary64_1372 frac-sub_binary64_1451 pow-prod-down_binary64_1513 *-commutative_binary64_1373 frac-2neg_binary64_1453 diff-log_binary64_1534 frac-times_binary64_1452 prod-exp_binary64_1491 distribute-lft-out--_binary64_1394 associate-*l/_binary64_1385 div-exp_binary64_1493 unswap-sqr_binary64_1410
Counts
4 → 88
Calls

8 calls:

13.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
8.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
7.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))
5.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
0.0ms
(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (12.2%)

Counts
4 → 48
Calls

4 calls:

982.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
536.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
252.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
194.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))
Compiler

Compiled 2088 to 1335 computations (36.1% saved)

simplify66.0ms (0.4%)

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
051964229

prune220.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New12511136
Fresh022
Picked101
Done000
Total12613139
Error
0.1b
Counts
139 → 13
Compiler

Compiled 4313 to 1573 computations (63.5% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))))
0.1b
(*.f64 (cos.f64 x) (cos.f64 eps))
0.1b
(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))
0.1b
(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b
(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
3.6b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

rewrite45.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
14×add-sqr-sqrt_binary64_1464
11×*-un-lft-identity_binary64_1442
add-log-exp_binary64_1481
add-cube-cbrt_binary64_1477
pow1_binary64_1503
cbrt-unprod_binary64_1475 prod-exp_binary64_1491
cbrt-undiv_binary64_1476 div-exp_binary64_1493
associate-*r*_binary64_1382 cancel-sign-sub-inv_binary64_1408 associate-*l*_binary64_1383 tan-quot_binary64_1601
times-frac_binary64_1448 difference-of-squares_binary64_1411 sin-mult_binary64_1597
associate-/r*_binary64_1386 sum-log_binary64_1533 associate-/l/_binary64_1389 div-inv_binary64_1439 associate-/r/_binary64_1388 sub-neg_binary64_1435 clear-num_binary64_1441 associate-/l*_binary64_1387 flip3--_binary64_1446 +-commutative_binary64_1372 frac-sub_binary64_1451 pow-prod-down_binary64_1513 *-commutative_binary64_1373 distribute-lft-out_binary64_1393 flip--_binary64_1417 frac-2neg_binary64_1453 diff-log_binary64_1534 flip3-+_binary64_1445 flip-+_binary64_1416 frac-add_binary64_1450 cos-mult_binary64_1596 distribute-lft-out--_binary64_1394 unswap-sqr_binary64_1410
Counts
4 → 73
Calls

8 calls:

20.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
8.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
5.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))
4.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))
0.0ms
(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))

series1.5s (9.6%)

Counts
4 → 47
Calls

4 calls:

981.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
261.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
197.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))
109.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))
Compiler

Compiled 2096 to 1341 computations (36% saved)

simplify93.0ms (0.6%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049593296
149593296

prune198.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1146120
Fresh6612
Picked101
Done000
Total12112133
Error
0.1b
Counts
133 → 12
Compiler

Compiled 4282 to 1407 computations (67.1% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))))
0.1b
(+.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) -1)))
0.1b
(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))
0.1b
(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))
0.2b
(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
0.3b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
3.5b
(+.f64 (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) -1)

rewrite48.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
12×add-sqr-sqrt_binary64_1464
10×*-un-lft-identity_binary64_1442
cbrt-unprod_binary64_1475 prod-exp_binary64_1491
cbrt-undiv_binary64_1476 div-exp_binary64_1493
add-log-exp_binary64_1481 pow1_binary64_1503 add-cube-cbrt_binary64_1477
times-frac_binary64_1448
associate-*r*_binary64_1382 div-inv_binary64_1439 associate-*l*_binary64_1383 difference-of-sqr--1_binary64_1413 sin-mult_binary64_1597
associate-/r*_binary64_1386 associate-/l/_binary64_1389 associate-/r/_binary64_1388 clear-num_binary64_1441 associate-/l*_binary64_1387 distribute-lft-out_binary64_1393 frac-2neg_binary64_1453 cos-mult_binary64_1596
sum-log_binary64_1533 +-commutative_binary64_1372 pow-prod-down_binary64_1513 *-commutative_binary64_1373 flip3-+_binary64_1445 flip-+_binary64_1416 unswap-sqr_binary64_1410
Counts
4 → 81
Calls

8 calls:

15.0ms
(+.f64 (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) -1)
8.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
8.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
6.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))
0.0ms
(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))

series1.0s (6.4%)

Counts
4 → 46
Calls

4 calls:

385.0ms
(+.f64 (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) -1)
265.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
262.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
114.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))
Compiler

Compiled 3244 to 1850 computations (43% saved)

simplify62.0ms (0.4%)

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
051213221

prune238.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1234127
Fresh11011
Picked101
Done000
Total12514139
Error
0.1b
Counts
139 → 14
Compiler

Compiled 6342 to 2049 computations (67.7% saved)

simplify241.0ms (1.5%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (199.0ms)

IterNodesCost
047523606
147523606

regimes679.0ms (4.2%)

Compiler

Compiled 6774 to 4010 computations (40.8% saved)

bsearch92.0ms (0.6%)

Steps
ItersRangePoint
9
7.063657168295903e-09
0.030965969165772503
0.0003005423639412057
9
-748.9436314065143
-0.0004632039719346494
-0.0004779135616980856
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes624.0ms (3.9%)

Compiler

Compiled 5841 to 3440 computations (41.1% saved)

bsearch76.0ms (0.5%)

Steps
ItersRangePoint
9
7.063657168295903e-09
0.030965969165772503
5.145237123972309e-05
7
-0.0004632039719346494
-2.5005587671238633e-05
-5.4521779724529695e-05
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes521.0ms (3.2%)

Compiler

Compiled 4758 to 2834 computations (40.4% saved)

bsearch72.0ms (0.4%)

Steps
ItersRangePoint
9
7.063657168295903e-09
0.030965969165772503
1.4628684822663685e-05
7
-0.0004632039719346494
-2.5005587671238633e-05
-5.249116044875854e-05
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes506.0ms (3.1%)

Compiler

Compiled 4557 to 2711 computations (40.5% saved)

bsearch75.0ms (0.5%)

Steps
ItersRangePoint
9
7.063657168295903e-09
0.030965969165772503
2.0334861175695522e-07
9
-2.5005587671238633e-05
-1.1565112691136808e-10
-2.3891148664584584e-07
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes378.0ms (2.3%)

Compiler

Compiled 2457 to 1649 computations (32.9% saved)

bsearch71.0ms (0.4%)

Steps
ItersRangePoint
9
7.063657168295903e-09
0.030965969165772503
4.253898686838245e-07
9
-2.5005587671238633e-05
-1.1565112691136808e-10
-4.279669816718851e-07
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes353.0ms (2.2%)

Compiler

Compiled 2190 to 1502 computations (31.4% saved)

bsearch71.0ms (0.4%)

Steps
ItersRangePoint
9
2.1731103683894138e-16
7.063657168295903e-09
2.4458551765479364e-09
9
-2.5005587671238633e-05
-1.1565112691136808e-10
-3.4101296937992502e-09
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes249.0ms (1.5%)

Compiler

Compiled 1264 to 923 computations (27% saved)

bsearch65.0ms (0.4%)

Steps
ItersRangePoint
9
2.1731103683894138e-16
7.063657168295903e-09
2.4458551765479364e-09
9
-2.5005587671238633e-05
-1.1565112691136808e-10
-3.4743469135771167e-09
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes145.0ms (0.9%)

Compiler

Compiled 463 to 407 computations (12.1% saved)

bsearch63.0ms (0.4%)

Steps
ItersRangePoint
9
2.1731103683894138e-16
7.063657168295903e-09
3.443849149629188e-09
9
-2.5005587671238633e-05
-1.1565112691136808e-10
-4.893051242916851e-09
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes129.0ms (0.8%)

Compiler

Compiled 415 to 377 computations (9.2% saved)

bsearch52.0ms (0.3%)

Steps
ItersRangePoint
7
0.030965969165772503
0.7591345474719611
0.03124285192140815
9
-748.9436314065143
-0.0004632039719346494
-0.0004681071685224615
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes68.0ms (0.4%)

Compiler

Compiled 295 to 284 computations (3.7% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.1%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch0.0ms (0%)

regimes14.0ms (0.1%)

Accuracy

Total 0.2b remaining (70.8%)

Threshold costs 0.2b (70.8%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch29.0ms (0.2%)

Compiler

Compiled 712 to 407 computations (42.8% saved)

simplify13.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
02671097
12671097

end0.0ms (0%)

sample4.3s (26.9%)

Algorithm
intervals
Results
839.0ms3548×body1024valid
540.0ms1212×body2048valid
209.0ms1369×body512valid
61.0ms1305×body128valid
53.0ms563×body256valid
3.0msbody4096valid
Compiler

Compiled 2943 to 1737 computations (41% saved)

Pareto

0.8546772575633563

Profiling

Loading profile data...