Details

analyze38.0ms (1.3%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample34.0ms (1.1%)

Algorithm

1×

intervals

Results

13.0ms	49×	body	2048	valid
8.0ms	68×	body	1024	valid
3.0ms	33×	body	512	valid
2.0ms	85×	body	128	valid
1.0ms	21×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify155.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune2.0ms (0.1%)

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: 32.6b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

3.1b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1464`
5×	`*-un-lft-identity_binary64_1442`
3×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481`
2×	`difference-of-squares_binary64_1411` `add-cube-cbrt_binary64_1477`
1×	`add-cbrt-cube_binary64_1478` `sub-neg_binary64_1435` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `add-exp-log_binary64_1480` `flip--_binary64_1417` `diff-log_binary64_1534` `pow1_binary64_1503` `distribute-lft-out--_binary64_1394`

Counts

1 → 18

Calls

1 calls:

4.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1)

series25.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

25.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1)

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4929	280
1	4929	280

prune25.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	3	22

Merged error: 5.4b

Counts

22 → 3

Compiler

Compiled 288 to 146 computations (49.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.8b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.0b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.1b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite34.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_1480`
13×	`add-cbrt-cube_binary64_1478` `add-sqr-sqrt_binary64_1464`
10×	`pow1_binary64_1503`
9×	`associate-l_binary64_1383` `prod-exp_binary64_1491` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
7×	`associate-r_binary64_1382`
6×	`add-log-exp_binary64_1481`
5×	`cbrt-unprod_binary64_1475`
4×	`associate-*r/_binary64_1384`
3×	`pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `unswap-sqr_binary64_1410`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `+-commutative_binary64_1372` `pow-to-exp_binary64_1511`

Counts

4 → 74

Calls

4 calls:

10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
6.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
5.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

series261.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
83.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
41.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
40.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5442	1832

prune101.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.1b

Counts

89 → 4

Compiler

Compiled 2247 to 1328 computations (40.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 1/6) a)
0.3b	(*.f64 x 1/6)
1.2b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
6.0b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite31.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
14×	`add-sqr-sqrt_binary64_1464`
11×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
10×	`associate-r_binary64_1382` `associate-l_binary64_1383` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-*r/_binary64_1384`
5×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
4×	`*-commutative_binary64_1373` `add-log-exp_binary64_1481`
2×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`

Counts

4 → 85

Calls

4 calls:

10.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
6.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
5.0ms	(.f64 (.f64 x 1/6) a)
4.0ms	(*.f64 x 1/6)

series183.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
73.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
14.0ms	(.f64 (.f64 x 1/6) a)
11.0ms	(*.f64 x 1/6)

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5964	1639

prune92.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	97	4	101

Merged error: 0.1b

Counts

101 → 4

Compiler

Compiled 2225 to 1271 computations (42.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.2b	(.f64 (.f64 x 1/6) a)
0.3b	(*.f64 x 1/6)
8.4b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64_1503`
16×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
13×	`add-sqr-sqrt_binary64_1464`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-r_binary64_1382`
7×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
5×	`associate-l_binary64_1383`
4×	`add-log-exp_binary64_1481` `pow-pow_binary64_1514`
3×	`*-commutative_binary64_1373` `exp-prod_binary64_1494` `unpow-prod-down_binary64_1521`
2×	`associate-*r/_binary64_1384` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `unpow-prod-up_binary64_1520` `unswap-sqr_binary64_1410`
1×	`pow-exp_binary64_1510` `pow-unpow_binary64_1519` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`

Counts

4 → 79

Calls

4 calls:

8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
5.0ms	(.f64 (.f64 x 1/6) a)
4.0ms	(*.f64 x 1/6)
4.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

series123.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
34.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
15.0ms	(.f64 (.f64 x 1/6) a)
11.0ms	(*.f64 x 1/6)

simplify68.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5128	1372

prune92.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	91	4	95

Merged error: 0.1b

Counts

95 → 4

Compiler

Compiled 2140 to 1209 computations (43.5% saved)

regimes180.0ms (6.1%)

Compiler: Compiled 1136 to 845 computations (25.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	131
1	69	131

end0.0ms (0%)

sample1.3s (43.7%)

Algorithm

1×

intervals

Results

419.0ms	1464×	body	2048	valid
256.0ms	1767×	body	1024	valid
91.0ms	1088×	body	512	valid
76.0ms	3022×	body	128	valid
34.0ms	659×	body	256	valid
4.0ms	153×	body	128	invalid

Compiler

Compiled 305 to 208 computations (31.8% saved)

Details

analyze38.0ms (1.3%)

sample34.0ms (1.1%)

simplify155.0ms (5.2%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite5.0ms (0.2%)

series25.0ms (0.8%)

simplify67.0ms (2.2%)

prune25.0ms (0.8%)

localize12.0ms (0.4%)

rewrite34.0ms (1.1%)

series261.0ms (8.8%)

simplify44.0ms (1.5%)

prune101.0ms (3.4%)

localize10.0ms (0.3%)

rewrite31.0ms (1.1%)

series183.0ms (6.2%)

simplify44.0ms (1.5%)

prune92.0ms (3.1%)

localize12.0ms (0.4%)

rewrite27.0ms (0.9%)

series123.0ms (4.1%)

simplify68.0ms (2.3%)

prune92.0ms (3.1%)

regimes180.0ms (6.1%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (43.7%)

Profiling