Details

analyze1.6s (19.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample50.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
11.0ms	96×	body	128	invalid
3.0ms	46×	body	128	nan

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify297.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	5019	19

prune13.0ms (0.2%)

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

Error

2.8b

Counts

2 → 2

Compiler

Compiled 41 to 34 computations (17.1% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(*.f64 a (pow.f64 k m))
2.8b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64_1480`
17×	`add-sqr-sqrt_binary64_1464`
12×	`add-cbrt-cube_binary64_1478` `*-un-lft-identity_binary64_1442`
11×	`associate-r_binary64_1382`
10×	`add-cube-cbrt_binary64_1477`
7×	`prod-exp_binary64_1491`
6×	`associate-l_binary64_1383`
5×	`pow1_binary64_1503`
4×	`div-exp_binary64_1493` `unpow-prod-down_binary64_1521` `unswap-sqr_binary64_1410`
3×	`associate-/r*_binary64_1386` `cbrt-unprod_binary64_1475` `times-frac_binary64_1448` `add-log-exp_binary64_1481`
2×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `pow-exp_binary64_1510` `associate-/r/_binary64_1388` `-commutative_binary64_1373` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`
1×	`div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l*_binary64_1387` `pow-prod-down_binary64_1513` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`

Counts

3 → 73

Calls

3 calls:

14.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
13.0ms	(*.f64 k (+.f64 k 10))
11.0ms	(*.f64 a (pow.f64 k m))

series279.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

160.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
82.0ms	(*.f64 a (pow.f64 k m))
36.0ms	(*.f64 k (+.f64 k 10))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4956	1226
1	4956	1226

prune155.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Error

2.8b

Counts

84 → 4

Compiler

Compiled 1596 to 862 computations (46% saved)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
2.8b	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_1464`
45×	`times-frac_binary64_1448`
38×	`*-un-lft-identity_binary64_1442`
36×	`add-cube-cbrt_binary64_1477`
31×	`associate-r_binary64_1382`
22×	`unpow-prod-down_binary64_1521`
20×	`add-exp-log_binary64_1480`
12×	`add-cbrt-cube_binary64_1478`
8×	`sqr-pow_binary64_1414`
7×	`associate-/l*_binary64_1387` `pow1_binary64_1503`
6×	`associate-l_binary64_1383` `div-exp_binary64_1493`
5×	`prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
4×	`associate-/r/_binary64_1388`
3×	`associate-r/_binary64_1384` `associate-/r_binary64_1386` `cbrt-unprod_binary64_1475` `add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`cbrt-undiv_binary64_1476` `pow-exp_binary64_1510` `div-inv_binary64_1439` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `pow-to-exp_binary64_1511`
1×	`clear-num_binary64_1441` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`

Counts

3 → 120

Calls

3 calls:

17.0ms	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
6.0ms	(*.f64 k (+.f64 k 10))
6.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))

series346.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

214.0ms	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
83.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
49.0ms	(*.f64 k (+.f64 k 10))

simplify133.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4981	2966
1	4981	2966

prune236.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	129	4	133

Error

2.8b

Counts

133 → 4

Compiler

Compiled 3015 to 1762 computations (41.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
0.0b	(pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10)))) 3)
2.8b	(.f64 a (cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))) 3)))
5.2b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10)))) 3))

rewrite123.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary64_1448` `unpow-prod-down_binary64_1521`
134×	`add-sqr-sqrt_binary64_1464`
130×	`cbrt-prod_binary64_1473`
109×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
85×	`cube-prod_binary64_1470`
63×	`associate-r_binary64_1382`
28×	`sqr-pow_binary64_1414`
17×	`add-exp-log_binary64_1480`
14×	`associate-/r/_binary64_1388`
11×	`unswap-sqr_binary64_1410`
10×	`add-cbrt-cube_binary64_1478`
7×	`div-inv_binary64_1439` `associate-/l*_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503`
6×	`pow-exp_binary64_1510` `div-exp_binary64_1493`
4×	`add-log-exp_binary64_1481`
3×	`associate-/r_binary64_1386` `cube-mult_binary64_1472` `associate-l*_binary64_1383` `pow-unpow_binary64_1519` `unpow3_binary64_1508` `cube-div_binary64_1471` `pow-to-exp_binary64_1511`
2×	`cbrt-undiv_binary64_1476` `cbrt-div_binary64_1474` `rem-cube-cbrt_binary64_1465`
1×	`associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `pow1/3_binary64_1524` `prod-exp_binary64_1491` `rem-cbrt-cube_binary64_1466` `pow-pow_binary64_1514`

Counts

4 → 282

Calls

4 calls:

32.0ms	(.f64 a (cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))) 3)))
21.0ms	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10)))) 3))
9.0ms	(pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10)))) 3)
7.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))

series576.0ms (7%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(.f64 a (cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))) 3)))
194.0ms	(pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10)))) 3)
104.0ms	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10)))) 3))
75.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify162.0ms (2%)

Algorithm

1×	egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5418	8488

prune521.0ms (6.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	294	4	298

Error

2.8b

Counts

298 → 4

Compiler

Compiled 7942 to 5006 computations (37% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 a (pow.f64 (sqrt.f64 k) m))
0.0b	(*.f64 k (+.f64 k 10))
0.0b	(.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m))
2.8b	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1480`
46×	`prod-exp_binary64_1491`
24×	`associate-r_binary64_1382` `add-sqr-sqrt_binary64_1464`
22×	`add-cbrt-cube_binary64_1478`
17×	`*-un-lft-identity_binary64_1442`
15×	`pow-exp_binary64_1510` `add-cube-cbrt_binary64_1477` `pow-to-exp_binary64_1511`
14×	`unpow-prod-down_binary64_1521`
13×	`div-exp_binary64_1493`
8×	`cbrt-unprod_binary64_1475`
7×	`associate-l_binary64_1383` `sqrt-prod_binary64_1458`
6×	`pow1_binary64_1503`
5×	`unswap-sqr_binary64_1410`
4×	`add-log-exp_binary64_1481`
3×	`cbrt-undiv_binary64_1476` `associate-/r_binary64_1386` `times-frac_binary64_1448` `-commutative_binary64_1373` `sqr-pow_binary64_1414`
2×	`associate-*r/_binary64_1384` `associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l*_binary64_1387` `pow-prod-down_binary64_1513` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`

Counts

4 → 120

Calls

4 calls:

18.0ms	(.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m))
17.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (+.f64 1 (*.f64 k (+.f64 k 10))))
8.0ms	(*.f64 k (+.f64 k 10))
7.0ms	(*.f64 a (pow.f64 (sqrt.f64 k) m))

series813.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

387.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (+.f64 1 (*.f64 k (+.f64 k 10))))
276.0ms	(.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m))
120.0ms	(*.f64 a (pow.f64 (sqrt.f64 k) m))
30.0ms	(*.f64 k (+.f64 k 10))

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4965	2201
1	4965	2201

prune160.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	132	4	136

Error

2.8b

Counts

136 → 4

Compiler

Compiled 2942 to 1260 computations (57.2% saved)

regimes145.0ms (1.8%)

Accuracy

Total 0.0b remaining (1.5%)

Threshold costs 0.0b (1.5%)

Compiler

Compiled 1012 to 830 computations (18% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	19
1	17	19

end0.0ms (0%)

sample2.2s (26.7%)

Algorithm

1×

intervals

Results

758.0ms	8000×	body	128	valid
406.0ms	3273×	body	128	invalid
137.0ms	1986×	body	128	nan

Compiler

Compiled 273 to 224 computations (17.9% saved)

Details

analyze1.6s (19.5%)

sample50.0ms (0.6%)

simplify297.0ms (3.6%)

prune13.0ms (0.2%)

localize19.0ms (0.2%)

rewrite44.0ms (0.5%)

series279.0ms (3.4%)

simplify79.0ms (1%)

prune155.0ms (1.9%)

localize18.0ms (0.2%)

rewrite40.0ms (0.5%)

series346.0ms (4.2%)

simplify133.0ms (1.6%)

prune236.0ms (2.9%)

localize22.0ms (0.3%)

rewrite123.0ms (1.5%)

series576.0ms (7%)

simplify162.0ms (2%)

prune521.0ms (6.4%)

localize11.0ms (0.1%)

rewrite61.0ms (0.7%)

series813.0ms (9.9%)

simplify103.0ms (1.3%)

prune160.0ms (2%)

regimes145.0ms (1.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (26.7%)

Profiling