Details

analyze5.0ms (0.2%)

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)

sample26.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	68×	body	1024	valid
5.0ms	135×	body	128	valid
4.0ms	37×	body	512	valid
1.0ms	12×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify73.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

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: 29.1b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
1.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite68.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`distribute-lft-out--_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
4×	`associate-/r/_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 113

Calls

3 calls:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series313.0ms (10.9%)

Counts

3 → 9

Calls

3 calls:

210.0ms	(/.f64 x (+.f64 x 1))
76.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
26.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify74.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5940	2299

prune167.0ms (5.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

Compiler

Compiled 2515 to 1795 computations (28.6% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 x (+.f64 x 1))
1.4b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
4.4b	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

rewrite81.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64` `exp-prod_binary64`
31×	`add-cube-cbrt_binary64`
20×	`log-pow_binary64`
10×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
4×	`associate-/r*_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64` `associate--l+_binary64`
2×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64`

Counts

4 → 107

Calls

4 calls:

51.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))
7.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))
6.0ms	(/.f64 x (+.f64 x 1))

series188.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
37.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))
27.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))
25.0ms	(/.f64 x (+.f64 x 1))

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5061	1754

prune128.0ms (4.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	119	3	122

Merged error: 0.0b

Counts

122 → 3

Compiler

Compiled 2545 to 1800 computations (29.3% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 x (+.f64 x 3))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

1 → 23

Calls

1 calls:

7.0ms

(*.f64 x (+.f64 x 3))

series54.0ms (1.9%)

Counts

1 → 3

Calls

1 calls:

54.0ms

(*.f64 x (+.f64 x 3))

simplify80.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4875	233
1	4875	233

prune18.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Merged error: 0.0b

Counts

29 → 3

Compiler

Compiled 302 to 219 computations (27.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.3b	(/.f64 -1 (*.f64 x x))
0.4b	(/.f64 3 (pow.f64 x 3))
6.6b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite96.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
9×	`unpow3_binary64`
6×	`distribute-lft-out_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`pow1_binary64` `distribute-rgt-out_binary64` `sqr-pow_binary64` `div-inv_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt1-in_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 128

Calls

4 calls:

41.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
33.0ms	(+.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))

series226.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
43.0ms	(/.f64 3 (pow.f64 x 3))
40.0ms	(/.f64 -1 (*.f64 x x))
30.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify48.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5229	2228

prune153.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	4	143

Merged error: 0b

Counts

143 → 4

Compiler

Compiled 2890 to 1997 computations (30.9% saved)

regimes23.0ms (0.8%)

Compiler: Compiled 57 to 47 computations (17.5% saved)

bsearch37.0ms (1.3%)

Steps

Iters	Range		Point
9	0.00019631484427225273	375132.5995195478	9530.965198687854
9	-4012917671.3003016	-5.907094254255359	-13923.55108423105

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	59
1	90	59

end0.0ms (0%)

sample897.0ms (31.3%)

Algorithm

1×

intervals

Results

294.0ms	1965×	body	1024	valid
167.0ms	4289×	body	128	valid
116.0ms	1013×	body	512	valid
41.0ms	528×	body	256	valid
38.0ms	205×	body	2048	valid

Compiler

Compiled 108 to 87 computations (19.4% saved)

Details

analyze5.0ms (0.2%)

sample26.0ms (0.9%)

simplify73.0ms (2.5%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite68.0ms (2.4%)

series313.0ms (10.9%)

simplify74.0ms (2.6%)

prune167.0ms (5.8%)

localize10.0ms (0.4%)

rewrite81.0ms (2.8%)

series188.0ms (6.5%)

simplify66.0ms (2.3%)

prune128.0ms (4.5%)

localize7.0ms (0.2%)

rewrite8.0ms (0.3%)

series54.0ms (1.9%)

simplify80.0ms (2.8%)

prune18.0ms (0.6%)

localize10.0ms (0.4%)

rewrite96.0ms (3.4%)

series226.0ms (7.9%)

simplify48.0ms (1.7%)

prune153.0ms (5.3%)

regimes23.0ms (0.8%)

bsearch37.0ms (1.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample897.0ms (31.3%)

Profiling