Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample104.0ms (1.5%)

Algorithm

1×

intervals

Results

74.0ms	128×	body	2048	valid
17.0ms	71×	body	1024	valid
5.0ms	38×	body	512	valid
1.0ms	12×	body	256	valid
0.0ms	7×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify240.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5087	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
2.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1442`
9×	`add-log-exp_binary64_1481`
6×	`cancel-sign-sub-inv_binary64_1408` `add-sqr-sqrt_binary64_1464`
4×	`associate-+l+_binary64_1375` `frac-add_binary64_1450` `add-cube-cbrt_binary64_1477`
3×	`flip3--_binary64_1446` `flip--_binary64_1417`
2×	`add-cbrt-cube_binary64_1478` `sum-log_binary64_1533` `sub-neg_binary64_1435` `add-exp-log_binary64_1480` `distribute-lft-out_binary64_1393` `diff-log_binary64_1534` `exp-diff_binary64_1490` `pow1_binary64_1503` `neg-sub0_binary64_1437` `distribute-lft-out--_binary64_1394` `exp-neg_binary64_1489`
1×	`+-commutative_binary64_1372` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+l-_binary64_1377` `difference-of-squares_binary64_1411`

Counts

2 → 39

Calls

2 calls:

10.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
5.0ms	(-.f64 (exp.f64 x) 2)

series77.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

59.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
18.0ms	(-.f64 (exp.f64 x) 2)

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4904	654
1	4904	654

prune42.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	2	46

Merged error: 0.0b

Counts

46 → 2

Compiler

Compiled 621 to 325 computations (47.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1464`
14×	`associate-r_binary64_1382`
13×	`add-exp-log_binary64_1480`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-log-exp_binary64_1481` `unpow-prod-down_binary64_1521`
7×	`add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
4×	`sqr-pow_binary64_1414`
3×	`sum-log_binary64_1533` `pow1_binary64_1503`
2×	`cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `*-commutative_binary64_1373` `pow-to-exp_binary64_1511`
1×	`+-commutative_binary64_1372` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+r+_binary64_1374`

Counts

3 → 63

Calls

3 calls:

9.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
7.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/360 (pow.f64 x 6))

series190.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

68.0ms	(*.f64 1/360 (pow.f64 x 6))
63.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
58.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4910	967
1	4910	967

prune85.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Merged error: 0b

Counts

74 → 4

Compiler

Compiled 1540 to 1079 computations (29.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
27.7b	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
27.7b	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
27.7b	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

rewrite65.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1473`
23×	`add-sqr-sqrt_binary64_1464`
18×	`cbrt-div_binary64_1474`
15×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
11×	`pow1_binary64_1503`
9×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524`
6×	`associate-r_binary64_1382` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `unswap-sqr_binary64_1410`
2×	`associate-r/_binary64_1384` `pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512` `associate-l/_binary64_1385`
1×	`pow2_binary64_1523` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `*-commutative_binary64_1373` `prod-exp_binary64_1491`

Counts

4 → 87

Calls

4 calls:

22.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
10.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
8.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
8.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

series603.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6))))) (cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
145.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
144.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
143.0ms	(cbrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

simplify102.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4920	4267
1	4920	4267

prune358.0ms (5.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0b

Counts

103 → 4

Compiler

Compiled 6133 to 4442 computations (27.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) -2)
0.0b	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2))
0.0b	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
2.7b	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))

rewrite93.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_1442`
71×	`add-sqr-sqrt_binary64_1464`
36×	`times-frac_binary64_1448`
35×	`difference-of-squares_binary64_1411`
31×	`add-cube-cbrt_binary64_1477`
27×	`distribute-lft-out--_binary64_1394`
19×	`cancel-sign-sub-inv_binary64_1408`
14×	`unpow-prod-down_binary64_1521`
12×	`pow1_binary64_1503`
11×	`flip3--_binary64_1446` `flip--_binary64_1417`
10×	`sqr-pow_binary64_1414`
8×	`associate--l+_binary64_1379` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
7×	`swap-sqr_binary64_1409`
6×	`associate-/r_binary64_1386` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `add-log-exp_binary64_1481`
5×	`associate-r_binary64_1382` `sub-neg_binary64_1435` `associate-l_binary64_1383`
4×	`frac-sub_binary64_1451` `frac-times_binary64_1452` `pow-pow_binary64_1514`
3×	`pow-unpow_binary64_1519` `exp-prod_binary64_1494`
2×	`associate-r/_binary64_1384` `associate-/l/_binary64_1389` `exp-diff_binary64_1490` `neg-sub0_binary64_1437` `associate-l/_binary64_1385` `exp-neg_binary64_1489`
1×	`pow2_binary64_1523` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `div-inv_binary64_1439` `clear-num_binary64_1441` `pow-plus_binary64_1505` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `pow-sqr_binary64_1415` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `prod-exp_binary64_1491` `div-sub_binary64_1447` `pow-prod-up_binary64_1512` `div-exp_binary64_1493` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`

Counts

4 → 167

Calls

4 calls:

31.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
20.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))
14.0ms	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2))
4.0ms	(pow.f64 (exp.f64 x) -2)

series588.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
133.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2))
51.0ms	(pow.f64 (exp.f64 x) -2)
42.0ms	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2))

simplify122.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4918	4731
1	4918	4731

prune237.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	179	4	183

Merged error: 0b

Counts

183 → 4

Compiler

Compiled 5206 to 2879 computations (44.7% saved)

regimes57.0ms (0.8%)

Compiler: Compiled 648 to 484 computations (25.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.6s (52.9%)

Algorithm

1×

intervals

Results

2.4s	4195×	body	2048	valid
508.0ms	2010×	body	1024	valid
132.0ms	955×	body	512	valid
40.0ms	488×	body	256	valid
16.0ms	352×	body	128	valid

Compiler

Compiled 347 to 263 computations (24.2% saved)

Details

analyze4.0ms (0.1%)

sample104.0ms (1.5%)

simplify240.0ms (3.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite18.0ms (0.3%)

series77.0ms (1.1%)

simplify58.0ms (0.9%)

prune42.0ms (0.6%)

localize12.0ms (0.2%)

rewrite28.0ms (0.4%)

series190.0ms (2.8%)

simplify81.0ms (1.2%)

prune85.0ms (1.3%)

localize15.0ms (0.2%)

rewrite65.0ms (1%)

series603.0ms (8.9%)

simplify102.0ms (1.5%)

prune358.0ms (5.3%)

localize12.0ms (0.2%)

rewrite93.0ms (1.4%)

series588.0ms (8.6%)

simplify122.0ms (1.8%)

prune237.0ms (3.5%)

regimes57.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.6s (52.9%)

Profiling