Details

analyze40.0ms (1%)

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)

sample37.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	43×	body	2048	valid
9.0ms	61×	body	1024	valid
3.0ms	101×	body	128	valid
3.0ms	26×	body	512	valid
1.0ms	25×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify226.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5029	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: 30.4b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
6.2b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1464`
6×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `difference-of-squares_binary64_1411`
1×	`sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `exp-prod_binary64_1494` `flip--_binary64_1417` `diff-log_binary64_1534` `exp-to-pow_binary64_1504` `distribute-lft-out--_binary64_1394`

Counts

2 → 28

Calls

2 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

series69.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

46.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
23.0ms	(exp.f64 (*.f64 a x))

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5005	377

prune37.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Merged error: 4.6b

Counts

35 → 5

Compiler

Compiled 426 to 214 computations (49.8% saved)

localize13.0ms (0.3%)

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)))))))
5.9b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.7b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.9b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite42.0ms (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:

11.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
7.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

series519.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
172.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
91.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
82.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4991	1832
1	4991	1832

prune104.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 1.5b

Counts

91 → 6

Compiler

Compiled 2256 to 1335 computations (40.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
0.3b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
1.2b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
6.7b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
15×	`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`
8×	`associate-*r/_binary64_1384`
6×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
4×	`*-commutative_binary64_1373` `add-log-exp_binary64_1481`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`

Counts

4 → 90

Calls

4 calls:

11.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
7.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
4.0ms	(*.f64 x 1/6)

series418.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
159.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
71.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
23.0ms	(*.f64 x 1/6)

simplify49.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5686	1933

prune108.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	101	7	108

Merged error: 1.5b

Counts

108 → 7

Compiler

Compiled 2442 to 1416 computations (42% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 a (.f64 (.f64 1/2 (*.f64 a a)) x))
1.2b	(.f64 x (+.f64 a (.f64 (.f64 1/2 (.f64 a a)) x)))
7.5b	(.f64 (.f64 1/2 (*.f64 a a)) x)

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

9.0ms	(.f64 x (+.f64 a (.f64 (.f64 1/2 (.f64 a a)) x)))
9.0ms	(.f64 (.f64 1/2 (*.f64 a a)) x)
4.0ms	(+.f64 a (.f64 (.f64 1/2 (*.f64 a a)) x))

series207.0ms (5.2%)

Counts

3 → 9

Calls

3 calls:

107.0ms	(.f64 x (+.f64 a (.f64 (.f64 1/2 (.f64 a a)) x)))
67.0ms	(+.f64 a (.f64 (.f64 1/2 (*.f64 a a)) x))
32.0ms	(.f64 (.f64 1/2 (*.f64 a a)) x)

simplify79.0ms (2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4932	992
1	4932	992

prune49.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	63	7	70

Merged error: 0.1b

Counts

70 → 7

Compiler

Compiled 1017 to 515 computations (49.4% saved)

regimes289.0ms (7.3%)

Compiler: Compiled 1520 to 1156 computations (23.9% 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	26	50
1	26	50

end0.0ms (0%)

sample1.5s (36.8%)

Algorithm

1×

intervals

Results

466.0ms	1480×	body	2048	valid
259.0ms	1667×	body	1024	valid
107.0ms	1148×	body	512	valid
81.0ms	3043×	body	128	valid
42.0ms	662×	body	256	valid
4.0ms	140×	body	128	invalid

Compiler

Compiled 336 to 244 computations (27.4% saved)

Details

analyze40.0ms (1%)

sample37.0ms (0.9%)

simplify226.0ms (5.7%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite8.0ms (0.2%)

series69.0ms (1.7%)

simplify50.0ms (1.3%)

prune37.0ms (0.9%)

localize13.0ms (0.3%)

rewrite42.0ms (1.1%)

series519.0ms (13.1%)

simplify62.0ms (1.6%)

prune104.0ms (2.6%)

localize11.0ms (0.3%)

rewrite41.0ms (1%)

series418.0ms (10.6%)

simplify49.0ms (1.2%)

prune108.0ms (2.7%)

localize7.0ms (0.2%)

rewrite26.0ms (0.7%)

series207.0ms (5.2%)

simplify79.0ms (2%)

prune49.0ms (1.2%)

regimes289.0ms (7.3%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (36.8%)

Profiling