Details

analyze255.0ms (4.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample74.0ms (1.4%)

Algorithm

1×

intervals

Results

38.0ms	74×	body	1280	valid
12.0ms	42×	body	640	valid
8.0ms	24×	body	2560	valid
4.0ms	22×	body	320	valid
3.0ms	74×	body	80	valid
2.0ms	20×	body	160	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

prune5.0ms (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: 53.4b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
1.2b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.2b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
16.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
5×	`add-exp-log_binary64`
4×	`flip3-+_binary64` `log-prod_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`
3×	`sqrt-prod_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 57

Calls

4 calls:

8.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
8.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(+.f64 (*.f64 x x) 1)

series227.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
57.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
48.0ms	(+.f64 (*.f64 x x) 1)
39.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify100.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5131	1051

prune86.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 0.0b

Counts

70 → 5

Compiler

Compiled 1066 to 698 computations (34.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.0b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
19.6b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64` `insert-posit16`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `associate--l+_binary64` `cube-mult_binary64`

Counts

4 → 84

Calls

4 calls:

8.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))
4.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series339.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
65.0ms	(*.f64 3/40 (pow.f64 x 5))
56.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
56.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify101.0ms (2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4973	1252
1	4973	1252

prune105.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

Compiler

Compiled 1783 to 1380 computations (22.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.2b	(/.f64 1/8 (pow.f64 x 3))
9.5b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite96.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`
13×	`unpow-prod-down_binary64` `cube-prod_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `sum-log_binary64`
4×	`diff-log_binary64` `insert-posit16` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `log-div_binary64` `associate-+r+_binary64` `frac-sub_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 127

Calls

4 calls:

29.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
28.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
27.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
7.0ms	(/.f64 1/8 (pow.f64 x 3))

series211.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
51.0ms	(/.f64 1/8 (pow.f64 x 3))
43.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
38.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5541	2679

prune157.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	139	5	144

Merged error: 0.0b

Counts

144 → 5

Compiler

Compiled 2901 to 2081 computations (28.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.2b	(/.f64 1/8 (pow.f64 x 3))
11.4b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
18.6b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite114.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `insert-posit16` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 163

Calls

4 calls:

48.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
42.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
9.0ms	(/.f64 1/16 (pow.f64 x 5))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series245.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
62.0ms	(/.f64 1/16 (pow.f64 x 5))
53.0ms	(/.f64 1/8 (pow.f64 x 3))
51.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4935	3673
1	4935	3673

prune279.0ms (5.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	174	6	180

Merged error: 0.0b

Counts

180 → 6

Compiler

Compiled 4140 to 3295 computations (20.4% saved)

regimes69.0ms (1.3%)

Compiler: Compiled 351 to 280 computations (20.2% saved)

bsearch35.0ms (0.7%)

Steps

Iters	Range		Point
10	1.1382839578461993e-09	992.3880738714992	0.9561431325628968
7	-22.642665676168377	-0.4971138132094894	-1.0695579049787816

Compiler

Compiled 1 to 1 computations (0% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.4s (46%)

Algorithm

1×

intervals

Results

1.1s	2290×	body	1280	valid
426.0ms	1533×	body	640	valid
273.0ms	836×	body	2560	valid
126.0ms	765×	body	320	valid
96.0ms	2178×	body	80	valid
39.0ms	398×	body	160	valid

Compiler

Compiled 190 to 150 computations (21.1% saved)

Details

analyze255.0ms (4.9%)

sample74.0ms (1.4%)

simplify21.0ms (0.4%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite28.0ms (0.6%)

series227.0ms (4.4%)

simplify100.0ms (1.9%)

prune86.0ms (1.7%)

localize9.0ms (0.2%)

rewrite28.0ms (0.5%)

series339.0ms (6.6%)

simplify101.0ms (2%)

prune105.0ms (2%)

localize10.0ms (0.2%)

rewrite96.0ms (1.9%)

series211.0ms (4.1%)

simplify77.0ms (1.5%)

prune157.0ms (3%)

localize11.0ms (0.2%)

rewrite114.0ms (2.2%)

series245.0ms (4.8%)

simplify88.0ms (1.7%)

prune279.0ms (5.4%)

regimes69.0ms (1.3%)

bsearch35.0ms (0.7%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.4s (46%)

Profiling