Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample27.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	30×	body	1024	valid
7.0ms	64×	body	512	valid
5.0ms	138×	body	128	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify173.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 8.2b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite101.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1455`
74×	`times-frac_binary64_1461`
72×	`add-sqr-sqrt_binary64_1477`
39×	`add-cube-cbrt_binary64_1490`
26×	`cancel-sign-sub-inv_binary64_1421`
18×	`distribute-lft-out--_binary64_1407`
17×	`distribute-lft-out_binary64_1406`
14×	`difference-of-squares_binary64_1424` `associate-+l+_binary64_1388`
12×	`add-exp-log_binary64_1493`
11×	`associate-/r*_binary64_1399` `add-log-exp_binary64_1494`
10×	`div-inv_binary64_1452`
8×	`add-cbrt-cube_binary64_1491`
6×	`pow1_binary64_1516` `associate-/l*_binary64_1400`
4×	`associate-/r/_binary64_1401` `div-exp_binary64_1506` `difference-of-sqr-1_binary64_1425`
3×	`flip--_binary64_1430` `frac-add_binary64_1463` `flip3--_binary64_1459`
2×	`inv-pow_binary64_1540` `flip-+_binary64_1429` `1-exp_binary64_1499` `clear-num_binary64_1454` `pow-flip_binary64_1529` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `sum-log_binary64_1546` `rec-exp_binary64_1505`
1×	`associate-+l-_binary64_1390` `+-commutative_binary64_1385`

Counts

4 → 161

Calls

4 calls:

47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
21.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series161.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
29.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
19.0ms	(/.f64 1 (-.f64 x 1))
18.0ms	(/.f64 1 (+.f64 x 1))

simplify78.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4911	2799
1	4911	2799

prune462.0ms (12.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	4	174

Merged error: 0.1b

Counts

174 → 4

Compiler

Compiled 8808 to 7159 computations (18.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
0.1b	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
6.3b	(+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)
14.2b	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))

rewrite168.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_1455`
16×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
13×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
12×	`frac-times_binary64_1465`
11×	`associate-/r/_binary64_1401` `associate-/l/_binary64_1402`
10×	`distribute-lft-out_binary64_1406` `add-log-exp_binary64_1494`
9×	`times-frac_binary64_1461`
8×	`associate-+l+_binary64_1388` `frac-add_binary64_1463`
6×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `cancel-sign-sub-inv_binary64_1421`
5×	`associate-r/_binary64_1397` `associate-l/_binary64_1398`
4×	`prod-exp_binary64_1504` `distribute-rgt-in_binary64_1405` `pow1_binary64_1516` `div-exp_binary64_1506` `flip--_binary64_1430` `cbrt-undiv_binary64_1489` `distribute-lft-in_binary64_1404` `cbrt-unprod_binary64_1488` `flip3--_binary64_1459`
3×	`div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385`
2×	`sub-neg_binary64_1448`
1×	`clear-num_binary64_1454` `associate-/r_binary64_1399` `frac-2neg_binary64_1466` `associate-/l_binary64_1400`

Counts

4 → 94

Calls

4 calls:

80.0ms	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
34.0ms	(+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)
20.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
19.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))

series282.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
62.0ms	(+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)
26.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
26.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5355	3222

prune262.0ms (7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	105	5	110

Merged error: 0.0b

Counts

110 → 5

Compiler

Compiled 5072 to 4026 computations (20.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
20.5b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite73.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*r/_binary64_1397`
40×	`*-un-lft-identity_binary64_1455`
32×	`frac-add_binary64_1463`
25×	`flip--_binary64_1430` `flip3--_binary64_1459`
21×	`times-frac_binary64_1461`
20×	`add-sqr-sqrt_binary64_1477` `flip-+_binary64_1429` `flip3-+_binary64_1458`
18×	`associate-/l/_binary64_1402` `add-cube-cbrt_binary64_1490`
16×	`frac-times_binary64_1465`
9×	`distribute-lft-out_binary64_1406`
8×	`unpow3_binary64_1521` `distribute-rgt-out_binary64_1408` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `associate-*l/_binary64_1398` `add-exp-log_binary64_1493`
7×	`associate-/r*_binary64_1399`
6×	`pow1_binary64_1516`
4×	`associate-r_binary64_1395` `distribute-rgt-in_binary64_1405` `neg-mul-1_binary64_1451` `distribute-rgt-neg-in_binary64_1413` `associate-+l+_binary64_1388` `distribute-lft-in_binary64_1404` `distribute-lft-neg-in_binary64_1412`
3×	`cancel-sign-sub-inv_binary64_1421` `associate-/l_binary64_1400` `sub-neg_binary64_1448` `associate-l*_binary64_1396`
2×	`associate-/r/_binary64_1401` `associate-+r+_binary64_1387`
1×	`prod-exp_binary64_1504` `div-exp_binary64_1506` `clear-num_binary64_1454` `*-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 131

Calls

4 calls:

25.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
13.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
7.0ms	(*.f64 x (+.f64 1 x))
4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series145.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
53.0ms	(*.f64 x (+.f64 1 x))
25.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
8.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify99.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4949	5492
1	4949	5492

prune372.0ms (10%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	0	2	2
Picked	1	0	1
Done	2	0	2
Total	143	5	148

Merged error: 0.0b

Counts

148 → 5

Compiler

Compiled 7344 to 5185 computations (29.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (pow.f64 x 3) (neg.f64 x))
0.1b	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_1455`
21×	`times-frac_binary64_1461`
14×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490`
10×	`distribute-lft-out_binary64_1406` `unpow3_binary64_1521` `distribute-rgt-out_binary64_1408`
7×	`associate-/r*_binary64_1399`
6×	`add-log-exp_binary64_1494`
5×	`neg-mul-1_binary64_1451` `distribute-rgt-neg-in_binary64_1413` `distribute-lft-neg-in_binary64_1412`
4×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`associate-/l*_binary64_1400`
2×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `pow1_binary64_1516` `flip3-+_binary64_1458` `sum-log_binary64_1546`
1×	`neg-log_binary64_1548` `neg-sub0_binary64_1450` `unsub-neg_binary64_1449` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `associate-+r-_binary64_1389` `div-inv_binary64_1452` `+-commutative_binary64_1385`

Counts

2 → 63

Calls

2 calls:

13.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))
11.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))

series136.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

88.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))
48.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4894	964
1	4894	964

prune148.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	68	6	74

Merged error: 0.0b

Counts

74 → 6

Compiler

Compiled 2396 to 1879 computations (21.6% saved)

regimes14.0ms (0.4%)

Compiler: Compiled 98 to 80 computations (18.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms (0%)

sample824.0ms (22.1%)

Algorithm

1×

intervals

Results

186.0ms	1320×	body	1024	valid
167.0ms	4372×	body	128	valid
158.0ms	1514×	body	512	valid
60.0ms	794×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 128 to 106 computations (17.2% saved)

Details

analyze6.0ms (0.2%)

sample27.0ms (0.7%)

simplify173.0ms (4.6%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite101.0ms (2.7%)

series161.0ms (4.3%)

simplify78.0ms (2.1%)

prune462.0ms (12.4%)

localize13.0ms (0.4%)

rewrite168.0ms (4.5%)

series282.0ms (7.6%)

simplify63.0ms (1.7%)

prune262.0ms (7%)

localize14.0ms (0.4%)

rewrite73.0ms (2%)

series145.0ms (3.9%)

simplify99.0ms (2.7%)

prune372.0ms (10%)

localize6.0ms (0.1%)

rewrite29.0ms (0.8%)

series136.0ms (3.6%)

simplify63.0ms (1.7%)

prune148.0ms (4%)

regimes14.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample824.0ms (22.1%)

Profiling