Details

analyze46.0ms (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)

sample40.0ms (1.1%)

Algorithm

1×

intervals

Results

17.0ms	46×	body	2048	valid
9.0ms	55×	body	1024	valid
3.0ms	34×	body	512	valid
3.0ms	100×	body	128	valid
1.0ms	21×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify62.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4815	9
1	4815	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: 29.6b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
4.6b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

2 → 25

Calls

2 calls:

4.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

series74.0ms (2%)

Counts

2 → 6

Calls

2 calls:

49.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
25.0ms	(exp.f64 (*.f64 a x))

simplify48.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4985	374
1	4985	374

prune35.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	6	32

Merged error: 5.3b

Counts

32 → 6

Compiler

Compiled 406 to 208 computations (48.8% saved)

localize14.0ms (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)))))))
6.7b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
7.5b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
10.4b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`pow-to-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

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)))))
7.0ms	(+.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)))))))

series505.0ms (13.7%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
156.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
82.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
81.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4975	1832
1	4975	1832

prune104.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 0.1b

Counts

92 → 7

Compiler

Compiled 2285 to 1354 computations (40.7% 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)))
2.6b	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
7.5b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite48.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
17×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
12×	`associate-*r/_binary64` `add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-r_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`unswap-sqr_binary64`

Counts

4 → 102

Calls

4 calls:

13.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
13.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
4.0ms	(*.f64 x 1/6)

series388.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
146.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
69.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
22.0ms	(*.f64 x 1/6)

simplify44.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5095	2104

prune111.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	114	7	121

Merged error: 0.1b

Counts

121 → 7

Compiler

Compiled 2798 to 1507 computations (46.1% saved)

localize10.0ms (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))))))
7.5b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite36.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
10×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`associate-*r/_binary64`
6×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`

Counts

4 → 90

Calls

4 calls:

10.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
8.0ms	(.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))))))
4.0ms	(*.f64 x 1/6)

series404.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
150.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
72.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
20.0ms	(*.f64 x 1/6)

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5618	1933

prune100.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	102	7	109

Merged error: 0.1b

Counts

109 → 7

Compiler

Compiled 2337 to 1342 computations (42.6% saved)

regimes154.0ms (4.2%)

Compiler: Compiled 708 to 509 computations (28.1% saved)

bsearch1.0ms (0%)

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

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	60
1	37	60

end0.0ms (0%)

sample1.3s (35.8%)

Algorithm

1×

intervals

Results

481.0ms	1458×	body	2048	valid
270.0ms	1705×	body	1024	valid
100.0ms	1109×	body	512	valid
83.0ms	3080×	body	128	valid
40.0ms	648×	body	256	valid
4.0ms	139×	body	128	invalid

Compiler

Compiled 195 to 134 computations (31.3% saved)

Details

analyze46.0ms (1.3%)

sample40.0ms (1.1%)

simplify62.0ms (1.7%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite7.0ms (0.2%)

series74.0ms (2%)

simplify48.0ms (1.3%)

prune35.0ms (0.9%)

localize14.0ms (0.4%)

rewrite38.0ms (1%)

series505.0ms (13.7%)

simplify40.0ms (1.1%)

prune104.0ms (2.8%)

localize11.0ms (0.3%)

rewrite48.0ms (1.3%)

series388.0ms (10.5%)

simplify44.0ms (1.2%)

prune111.0ms (3%)

localize10.0ms (0.3%)

rewrite36.0ms (1%)

series404.0ms (10.9%)

simplify43.0ms (1.2%)

prune100.0ms (2.7%)

regimes154.0ms (4.2%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (35.8%)

Profiling