Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	67×	body	1024	valid
4.0ms	129×	body	128	valid
3.0ms	36×	body	512	valid
2.0ms	10×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify242.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

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: 31.4b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite77.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_1455`
88×	`times-frac_binary64_1461`
85×	`add-sqr-sqrt_binary64_1477`
37×	`add-cube-cbrt_binary64_1490`
34×	`cancel-sign-sub-inv_binary64_1421`
27×	`distribute-lft-out_binary64_1406`
22×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
11×	`associate-/r*_binary64_1399`
9×	`difference-of-sqr-1_binary64_1425`
7×	`add-cbrt-cube_binary64_1491` `associate-/l*_binary64_1400` `add-exp-log_binary64_1493`
6×	`associate-/r/_binary64_1401`
5×	`add-log-exp_binary64_1494`
3×	`pow1_binary64_1516` `flip--_binary64_1430` `div-inv_binary64_1452` `flip3--_binary64_1459`
2×	`flip-+_binary64_1429` `associate-/l/_binary64_1402` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `flip3-+_binary64_1458`
1×	`diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448`

Counts

3 → 147

Calls

3 calls:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series124.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

75.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
26.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
24.0ms	(/.f64 x (+.f64 x 1))

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5369	2774

prune581.0ms (10.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	4	157

Merged error: 0.0b

Counts

157 → 4

Compiler

Compiled 10435 to 7756 computations (25.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.1b	(/.f64 -1 (*.f64 x x))
0.3b	(/.f64 3 (pow.f64 x 3))
4.8b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite100.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64_1455`
68×	`times-frac_binary64_1461`
44×	`add-sqr-sqrt_binary64_1477`
40×	`add-cube-cbrt_binary64_1490`
14×	`unpow3_binary64_1521` `add-exp-log_binary64_1493`
13×	`associate-/r*_binary64_1399` `cancel-sign-sub-inv_binary64_1421`
12×	`unpow-prod-down_binary64_1534` `cube-prod_binary64_1483`
11×	`distribute-lft-out_binary64_1406` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491`
8×	`distribute-rgt-out_binary64_1408`
6×	`associate-/l*_binary64_1400` `div-inv_binary64_1452`
5×	`div-exp_binary64_1506`
4×	`cube-mult_binary64_1485` `pow1_binary64_1516` `sqr-pow_binary64_1427`
3×	`cbrt-undiv_binary64_1489` `frac-sub_binary64_1464`
2×	`distribute-lft-out--_binary64_1407` `flip-+_binary64_1429` `difference-of-squares_binary64_1424` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `flip3-+_binary64_1458` `distribute-rgt1-in_binary64_1411` `sum-log_binary64_1546` `frac-add_binary64_1463`
1×	`prod-exp_binary64_1504` `associate--r+_binary64_1391` `pow-to-exp_binary64_1524` `flip--_binary64_1430` `cbrt-unprod_binary64_1488` `sub-neg_binary64_1448` `pow-exp_binary64_1523` `+-commutative_binary64_1385` `flip3--_binary64_1459`

Counts

4 → 141

Calls

4 calls:

40.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
34.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))

series215.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
45.0ms	(/.f64 3 (pow.f64 x 3))
32.0ms	(/.f64 -1 (*.f64 x x))
32.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4952	2429
1	4952	2429

prune404.0ms (7.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	152	5	157

Merged error: 0.0b

Counts

157 → 5

Compiler

Compiled 4061 to 2904 computations (28.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 -1 (*.f64 x x))
0.2b	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
0.2b	(/.f64 1 (pow.f64 x 3))
4.8b	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

rewrite73.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1461` `*-un-lft-identity_binary64_1455`
39×	`add-sqr-sqrt_binary64_1477`
37×	`add-cube-cbrt_binary64_1490`
20×	`add-exp-log_binary64_1493`
16×	`associate-r_binary64_1395`
13×	`associate-/r*_binary64_1399` `add-cbrt-cube_binary64_1491`
12×	`unpow-prod-down_binary64_1534` `cube-prod_binary64_1483`
10×	`unpow3_binary64_1521`
8×	`div-exp_binary64_1506`
7×	`distribute-lft-out_binary64_1406` `div-inv_binary64_1452`
6×	`associate-r/_binary64_1397` `pow1_binary64_1516` `add-log-exp_binary64_1494` `associate-/l_binary64_1400`
5×	`distribute-rgt-out_binary64_1408`
4×	`cube-mult_binary64_1485` `sqr-pow_binary64_1427`
3×	`1-exp_binary64_1499` `pow-to-exp_binary64_1524` `cbrt-undiv_binary64_1489` `frac-sub_binary64_1464` `pow-exp_binary64_1523` `rec-exp_binary64_1505` `associate-l_binary64_1396`
2×	`prod-exp_binary64_1504` `distribute-rgt-in_binary64_1405` `flip-+_binary64_1429` `associate--r+_binary64_1391` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `distribute-lft-in_binary64_1404` `cbrt-unprod_binary64_1488` `flip3-+_binary64_1458` `frac-add_binary64_1463`
1×	`inv-pow_binary64_1540` `pow-flip_binary64_1529` `*-commutative_binary64_1386` `flip--_binary64_1430` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `distribute-rgt1-in_binary64_1411` `flip3--_binary64_1459` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 147

Calls

4 calls:

39.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
8.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))
6.0ms	(/.f64 1 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))

series207.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
43.0ms	(/.f64 1 (pow.f64 x 3))
40.0ms	(/.f64 -1 (*.f64 x x))
30.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4934	2063
1	4934	2063

prune217.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	159	5	164

Merged error: 0.0b

Counts

164 → 5

Compiler

Compiled 3573 to 2567 computations (28.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1)))
0.0b	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
0.0b	(pow.f64 (/.f64 x (+.f64 x 1)) 3)
2.5b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))

rewrite270.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Rules

373×	`*-un-lft-identity_binary64_1455`
224×	`times-frac_binary64_1461`
219×	`add-sqr-sqrt_binary64_1477`
146×	`unpow-prod-down_binary64_1534` `cube-prod_binary64_1483`
74×	`cancel-sign-sub-inv_binary64_1421`
71×	`add-cube-cbrt_binary64_1490`
69×	`distribute-lft-out--_binary64_1407`
68×	`difference-of-squares_binary64_1424`
66×	`distribute-lft-out_binary64_1406`
16×	`difference-of-sqr-1_binary64_1425`
15×	`sqr-pow_binary64_1427`
12×	`associate-/r/_binary64_1401`
10×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
8×	`add-log-exp_binary64_1494`
6×	`pow1_binary64_1516` `div-inv_binary64_1452` `pow-unpow_binary64_1532`
5×	`flip--_binary64_1430` `flip3--_binary64_1459`
4×	`cube-div_binary64_1484` `rem-cube-cbrt_binary64_1478` `pow-exp_binary64_1523`
3×	`cube-mult_binary64_1485` `unpow3_binary64_1521` `flip-+_binary64_1429` `flip3-+_binary64_1458` `frac-add_binary64_1463`
2×	`div-exp_binary64_1506` `pow-pow_binary64_1527` `pow-to-exp_binary64_1524` `cbrt-undiv_binary64_1489`
1×	`difference-cubes_binary64_1457` `associate-r/_binary64_1397` `frac-times_binary64_1465` `diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448` `sum-log_binary64_1546` `+-commutative_binary64_1385` `associate-l/_binary64_1398`

Counts

4 → 318

Calls

4 calls:

148.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
24.0ms	(+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1)))
13.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
12.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

series298.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
95.0ms	(+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (/.f64 (+.f64 x (.f64 (+.f64 x 1) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (-.f64 x 1)))
35.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
28.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

330 → 330

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5016	9297

prune1.4s (24.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	329	1	330
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	330	5	335

Merged error: 0.0b

Counts

335 → 5

Compiler

Compiled 18670 to 13681 computations (26.7% saved)

regimes28.0ms (0.5%)

Compiler: Compiled 114 to 87 computations (23.7% saved)

bsearch50.0ms (0.9%)

Steps

Iters	Range		Point
9	2082.790261631103	31785431694.52961	13111.01440601656
10	-57867379.025228694	-8.453621939525379e-09	-14614.459261386228

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	115
1	90	115

end0.0ms (0%)

sample832.0ms (15%)

Algorithm

1×

intervals

Results

244.0ms	1969×	body	1024	valid
141.0ms	4278×	body	128	valid
94.0ms	1018×	body	512	valid
35.0ms	227×	body	2048	valid
32.0ms	508×	body	256	valid

Compiler

Compiled 203 to 154 computations (24.1% saved)

Details

analyze4.0ms (0.1%)

sample23.0ms (0.4%)

simplify242.0ms (4.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite77.0ms (1.4%)

series124.0ms (2.2%)

simplify76.0ms (1.4%)

prune581.0ms (10.5%)

localize9.0ms (0.2%)

rewrite100.0ms (1.8%)

series215.0ms (3.9%)

simplify93.0ms (1.7%)

prune404.0ms (7.3%)

localize11.0ms (0.2%)

rewrite73.0ms (1.3%)

series207.0ms (3.7%)

simplify70.0ms (1.3%)

prune217.0ms (3.9%)

localize17.0ms (0.3%)

rewrite270.0ms (4.9%)

series298.0ms (5.4%)

simplify121.0ms (2.2%)

prune1.4s (24.9%)

regimes28.0ms (0.5%)

bsearch50.0ms (0.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample832.0ms (15%)

Profiling