Details

Time bar (total: 8.3s)

analyze2.0ms (0%)

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

Compiled 8 to 7 computations (12.5% saved)

sample76.0ms (0.9%)

Algorithm
1×intervals
Results
39.0ms119×body1024valid
15.0ms31×body2048valid
8.0ms43×body512valid
3.0ms23×body256valid
3.0ms40×body128valid
Compiler

Compiled 15 to 15 computations (0% saved)

simplify105.0ms (1.3%)

Algorithm
1×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
38.1b
Counts
2 → 1
Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.2b
(sin.f64 (+.f64 x eps))
1.8b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.8b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.2b
(sin.f64 (+.f64 x eps))

rewrite14.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
5×add-sqr-sqrt_binary64_1464 *-un-lft-identity_binary64_1442
4×add-log-exp_binary64_1481
3×cancel-sign-sub-inv_binary64_1408 add-cube-cbrt_binary64_1477
2×sin-sum_binary64_1575 add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480 pow1_binary64_1503
1×associate--l+_binary64_1379 sub-neg_binary64_1435 flip3--_binary64_1446 diff-sin_binary64_1592 flip--_binary64_1417 diff-log_binary64_1534 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
Counts
2 → 26
Calls

4 calls:

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

series119.0ms (1.4%)

Counts
2 → 22
Calls

2 calls:

74.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
45.0ms
(sin.f64 (+.f64 x eps))
Compiler

Compiled 368 to 288 computations (21.7% saved)

simplify71.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
04896675
14896675

prune54.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New44448
Fresh000
Picked101
Done000
Total45449
Error
0.2b
Counts
49 → 4
Compiler

Compiled 624 to 201 computations (67.8% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

3.8b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
0.1b
(*.f64 (sin.f64 x) (cos.f64 eps))
0.1b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
0.1b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
0.1b
(*.f64 (sin.f64 x) (cos.f64 eps))
0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
3.8b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

rewrite30.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64_1464
11×add-log-exp_binary64_1481 *-un-lft-identity_binary64_1442
9×add-cube-cbrt_binary64_1477
8×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480 pow1_binary64_1503
6×associate-*r*_binary64_1382 associate-*l*_binary64_1383
3×cancel-sign-sub-inv_binary64_1408
2×cbrt-unprod_binary64_1475 sum-log_binary64_1533 pow-prod-down_binary64_1513 *-commutative_binary64_1373 diff-log_binary64_1534 prod-exp_binary64_1491 unswap-sqr_binary64_1410
1×associate--l+_binary64_1379 sub-neg_binary64_1435 flip3--_binary64_1446 +-commutative_binary64_1372 flip--_binary64_1417 sin-cos-mult_binary64_1598 flip3-+_binary64_1445 flip-+_binary64_1416 difference-of-squares_binary64_1411 distribute-lft-out--_binary64_1394
Counts
4 → 66
Calls

8 calls:

9.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
6.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
5.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
5.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
0.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))

series533.0ms (6.4%)

Counts
4 → 41
Calls

4 calls:

190.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
145.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
109.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
88.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
Compiler

Compiled 1034 to 742 computations (28.2% saved)

simplify79.0ms (1%)

Algorithm
1×egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
055411808

prune129.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New9512107
Fresh213
Picked101
Done000
Total9813111
Error
0.1b
Counts
111 → 13
Compiler

Compiled 2318 to 687 computations (70.4% saved)

localize20.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
0.1b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.5b
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
2.7b
(+.f64 (cos.f64 eps) -1)
2.7b
(+.f64 (cos.f64 eps) -1)
2.7b
(+.f64 (cos.f64 eps) -1)

rewrite23.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
11×*-un-lft-identity_binary64_1442
10×add-log-exp_binary64_1481
8×add-sqr-sqrt_binary64_1464
5×add-cube-cbrt_binary64_1477
4×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480 flip3-+_binary64_1445 flip-+_binary64_1416 pow1_binary64_1503
3×sum-log_binary64_1533 cbrt-prod_binary64_1473 +-commutative_binary64_1372 difference-of-sqr--1_binary64_1413 distribute-lft-out_binary64_1393
2×cbrt-div_binary64_1474
1×pow1/3_binary64_1524
Counts
4 → 52
Calls

8 calls:

4.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
4.0ms
(+.f64 (cos.f64 eps) -1)
0.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

series701.0ms (8.5%)

Counts
4 → 23
Calls

4 calls:

628.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
26.0ms
(+.f64 (cos.f64 eps) -1)
25.0ms
(+.f64 (cos.f64 eps) -1)
22.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 2160 to 1291 computations (40.2% saved)

simplify68.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
059101610

prune173.0ms (2.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New71475
Fresh01212
Picked101
Done000
Total721688
Error
0.1b
Counts
88 → 16
Compiler

Compiled 4444 to 1968 computations (55.7% saved)

localize28.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
0.1b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1))))
0.5b
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.5b
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1)))))
2.7b
(+.f64 (cos.f64 eps) -1)
2.7b
(+.f64 (cos.f64 eps) -1)

rewrite25.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
10×*-un-lft-identity_binary64_1442
8×add-log-exp_binary64_1481 add-sqr-sqrt_binary64_1464
6×cbrt-prod_binary64_1473 add-cube-cbrt_binary64_1477
4×add-cbrt-cube_binary64_1478 cbrt-div_binary64_1474 add-exp-log_binary64_1480 flip3-+_binary64_1445 flip-+_binary64_1416 pow1_binary64_1503
2×sum-log_binary64_1533 +-commutative_binary64_1372 difference-of-sqr--1_binary64_1413 distribute-lft-out_binary64_1393 pow1/3_binary64_1524
Counts
4 → 52
Calls

8 calls:

5.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(+.f64 (cos.f64 eps) -1)
4.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1)))))
4.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.0ms
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1))))

series1.4s (17.5%)

Counts
4 → 30
Calls

4 calls:

763.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1)))))
633.0ms
(cbrt.f64 (+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
28.0ms
(+.f64 (cos.f64 eps) -1)
24.0ms
(+.f64 (cos.f64 eps) -1)
Compiler

Compiled 3043 to 1846 computations (39.3% saved)

simplify82.0ms (1%)

Algorithm
1×egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
051702559

prune186.0ms (2.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh31215
Picked101
Done000
Total831598
Error
0.1b
Counts
98 → 15
Compiler

Compiled 4922 to 2212 computations (55.1% saved)

simplify33.0ms (0.4%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (8.0ms)

IterNodesCost
04831897
14831897

regimes388.0ms (4.7%)

Compiler

Compiled 2292 to 1398 computations (39% saved)

bsearch0.0ms (0%)

regimes53.0ms (0.6%)

Compiler

Compiled 298 to 264 computations (11.4% saved)

bsearch0.0ms (0%)

regimes59.0ms (0.7%)

Compiler

Compiled 86 to 94 computations (-9.3% saved)

bsearch51.0ms (0.6%)

Steps
ItersRangePoint
6
4.005367464346597e-09
2.13199055564998e-08
2.1045680883946606e-08
7
-2.5070953418002607e-05
-9.594598602840287e-07
-2.4794567668379724e-05
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes54.0ms (0.7%)

Compiler

Compiled 64 to 76 computations (-18.8% saved)

bsearch47.0ms (0.6%)

Steps
ItersRangePoint
6
4.005367464346597e-09
2.13199055564998e-08
2.1045680883946606e-08
7
-2.5070953418002607e-05
-9.594598602840287e-07
-1.1182334377507595e-05
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes49.0ms (0.6%)

Compiler

Compiled 22 to 40 computations (-81.8% saved)

bsearch44.0ms (0.5%)

Steps
ItersRangePoint
6
4.005367464346597e-09
2.13199055564998e-08
2.1045680883946606e-08
7
-2.5070953418002607e-05
-9.594598602840287e-07
-1.1182334377507595e-05
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes20.0ms (0.2%)

Compiler

Compiled 14 to 32 computations (-128.6% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.2%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch0.0ms (0%)

regimes13.0ms (0.2%)

Accuracy

Total 0.3b remaining (76.4%)

Threshold costs 0.3b (76.4%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 99 to 74 computations (25.3% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
070139
170139

end0.0ms (0%)

sample3.5s (41.7%)

Algorithm
1×intervals
Results
1.0s3484×body1024valid
645.0ms1249×body2048valid
264.0ms1351×body512valid
83.0ms1308×body128valid
82.0ms606×body256valid
7.0ms2×body4096valid
Compiler

Compiled 1255 to 793 computations (36.8% saved)

Pareto

0.3853780139741782

Profiling

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