Details

analyze7.0ms (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)

sample28.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	39×	body	1024	valid
6.0ms	152×	body	128	valid
5.0ms	46×	body	512	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify100.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (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: 10.1b

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 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (-.f64 x 1))
2.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite94.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1442`
74×	`times-frac_binary64_1448`
72×	`add-sqr-sqrt_binary64_1464`
39×	`add-cube-cbrt_binary64_1477`
26×	`cancel-sign-sub-inv_binary64_1408`
18×	`distribute-lft-out--_binary64_1394`
17×	`distribute-lft-out_binary64_1393`
14×	`associate-+l+_binary64_1375` `difference-of-squares_binary64_1411`
12×	`add-exp-log_binary64_1480`
11×	`associate-/r*_binary64_1386` `add-log-exp_binary64_1481`
10×	`div-inv_binary64_1439`
8×	`add-cbrt-cube_binary64_1478`
6×	`associate-/l*_binary64_1387` `pow1_binary64_1503`
4×	`associate-/r/_binary64_1388` `difference-of-sqr-1_binary64_1412` `div-exp_binary64_1493`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `frac-add_binary64_1450`
2×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `sub-neg_binary64_1435` `clear-num_binary64_1441` `1-exp_binary64_1486` `frac-sub_binary64_1451` `rec-exp_binary64_1492` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`+-commutative_binary64_1372` `associate-+l-_binary64_1377`

Counts

4 → 161

Calls

4 calls:

47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series55.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
9.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

simplify75.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4971	2704
1	4971	2704

prune228.0ms (5.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Merged error: 0.2b

Counts

174 → 3

Compiler

Compiled 3553 to 2853 computations (19.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))
15.3b	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite144.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1442`
21×	`times-frac_binary64_1448`
14×	`associate-+l+_binary64_1375` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
13×	`cancel-sign-sub-inv_binary64_1408`
12×	`cbrt-prod_binary64_1473`
11×	`distribute-lft-out_binary64_1393`
9×	`add-log-exp_binary64_1481`
8×	`distribute-lft-out--_binary64_1394`
6×	`cbrt-div_binary64_1474`
5×	`div-inv_binary64_1439`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503`
3×	`pow1/3_binary64_1524` `frac-add_binary64_1450`
2×	`sum-log_binary64_1533`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `flip--_binary64_1417` `diff-log_binary64_1534` `associate-+l-_binary64_1377`

Counts

4 → 80

Calls

4 calls:

125.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
4.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 x 1))

series84.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
22.0ms	(cbrt.f64 (+.f64 1 x))
14.0ms	(cbrt.f64 (+.f64 1 x))
14.0ms	(cbrt.f64 (+.f64 x 1))

simplify98.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4884	1600
1	4884	1600

prune140.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	92	3	95

Merged error: 0.2b

Counts

95 → 3

Compiler

Compiled 2678 to 2152 computations (19.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
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) x))
15.0b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite70.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_1464`
42×	`associate-*r/_binary64_1384`
35×	`*-un-lft-identity_binary64_1442`
32×	`flip3--_binary64_1446` `flip--_binary64_1417` `frac-add_binary64_1450`
27×	`times-frac_binary64_1448`
20×	`frac-times_binary64_1452` `add-cube-cbrt_binary64_1477`
18×	`associate-/l/_binary64_1389` `flip3-+_binary64_1445` `flip-+_binary64_1416` `difference-of-squares_binary64_1411`
10×	`associate-*l/_binary64_1385`
9×	`associate-/r*_binary64_1386`
8×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
7×	`associate-l_binary64_1383`
6×	`pow1_binary64_1503`
5×	`cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `distribute-lft-out--_binary64_1394`
4×	`associate-+l+_binary64_1375` `cube-prod_binary64_1470` `distribute-rgt-out--_binary64_1396` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `unpow-prod-down_binary64_1521`
3×	`associate-r_binary64_1382` `associate-/l*_binary64_1387`
2×	`associate-/r/_binary64_1388` `associate-+r+_binary64_1374`
1×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `difference-of-sqr-1_binary64_1412` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `prod-exp_binary64_1491` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 150

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
15.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
10.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series33.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
8.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
4.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

simplify110.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5009	6628

prune363.0ms (9.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	162	3	165

Merged error: 0.2b

Counts

165 → 3

Compiler

Compiled 6879 to 4787 computations (30.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.2b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1464`
27×	`times-frac_binary64_1448` `*-un-lft-identity_binary64_1442`
16×	`difference-of-squares_binary64_1411`
15×	`add-cube-cbrt_binary64_1477`
9×	`associate-/r*_binary64_1386`
4×	`cube-prod_binary64_1470` `distribute-rgt-out--_binary64_1396` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `distribute-lft-out--_binary64_1394` `unpow-prod-down_binary64_1521`
3×	`add-cbrt-cube_binary64_1478` `associate-/l*_binary64_1387` `add-exp-log_binary64_1480`
2×	`associate-/r/_binary64_1388`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `flip3--_binary64_1446` `add-log-exp_binary64_1481` `flip--_binary64_1417` `frac-2neg_binary64_1453` `pow1_binary64_1503` `div-exp_binary64_1493`

Counts

1 → 53

Calls

1 calls:

12.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

series13.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

13.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4899	1047
1	4899	1047

prune59.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	56	3	59

Merged error: 0.0b

Counts

59 → 3

Compiler

Compiled 847 to 623 computations (26.4% saved)

regimes211.0ms (5.4%)

Compiler: Compiled 2672 to 2194 computations (17.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	13
1	18	13

end0.0ms (0%)

sample1.9s (48.2%)

Algorithm

1×

intervals

Results

197.0ms	1356×	body	1024	valid
170.0ms	1526×	body	512	valid
165.0ms	4346×	body	128	valid
55.0ms	772×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 1354 to 1112 computations (17.9% saved)

Details

analyze7.0ms (0.2%)

sample28.0ms (0.7%)

simplify100.0ms (2.5%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite94.0ms (2.4%)

series55.0ms (1.4%)

simplify75.0ms (1.9%)

prune228.0ms (5.8%)

localize14.0ms (0.4%)

rewrite144.0ms (3.7%)

series84.0ms (2.1%)

simplify98.0ms (2.5%)

prune140.0ms (3.6%)

localize12.0ms (0.3%)

rewrite70.0ms (1.8%)

series33.0ms (0.8%)

simplify110.0ms (2.8%)

prune363.0ms (9.2%)

localize4.0ms (0.1%)

rewrite16.0ms (0.4%)

series13.0ms (0.3%)

simplify70.0ms (1.8%)

prune59.0ms (1.5%)

regimes211.0ms (5.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.9s (48.2%)

Profiling