Details

analyze6.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample25.0ms (1%)

Algorithm

1×

intervals

Results

8.0ms	62×	body	640	valid
4.0ms	127×	body	80	valid
3.0ms	34×	body	320	valid
3.0ms	17×	body	1280	valid
1.0ms	16×	body	160	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	193	22
1	193	22

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.2b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite74.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

37.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series15.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

simplify103.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4989	2576
1	4989	2576

prune161.0ms (6.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	4	148

Merged error: 0.0b

Counts

148 → 4

Compiler

Compiled 3249 to 2610 computations (19.7% saved)

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
19.2b	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite131.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
32×	`cbrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`cbrt-div_binary64` `distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `add-log-exp_binary64` `swap-sqr_binary64` `flip-+_binary64`
8×	`pow1/3_binary64` `distribute-lft-out--_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `div-inv_binary64` `frac-times_binary64`
3×	`frac-add_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `pow-plus_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `frac-sub_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

110.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
11.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series26.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
6.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
5.0ms	(cbrt.f64 (+.f64 1 x))
5.0ms	(cbrt.f64 (+.f64 1 x))

simplify106.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4905	2222
1	4905	2222

prune155.0ms (6.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

Compiler

Compiled 3623 to 2938 computations (18.9% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(*.f64 x (+.f64 1 x))
17.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite35.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-*r/_binary64`
19×	`flip3--_binary64` `flip--_binary64`
16×	`frac-add_binary64` `add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
12×	`frac-times_binary64`
10×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-r_binary64`
6×	`associate-*l/_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-+l+_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 97

Calls

4 calls:

12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
9.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
6.0ms	(*.f64 x (+.f64 1 x))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series11.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 x (+.f64 1 x))
3.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
2.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
1.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify92.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4980	3152
1	4980	3152

prune318.0ms (13.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	112	1	113

Merged error: 0.0b

Counts

113 → 1

Compiler

Compiled 3814 to 2650 computations (30.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `times-frac_binary64`
16×	`difference-of-squares_binary64`
15×	`add-cube-cbrt_binary64`
9×	`associate-/r*_binary64`
4×	`distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `distribute-lft-out--_binary64` `unpow3_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`

Counts

1 → 53

Calls

1 calls:

9.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

series5.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

5.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify69.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5059	1071

prune42.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Merged error: 0b

Counts

57 → 3

Compiler

Compiled 863 to 636 computations (26.3% saved)

regimes16.0ms (0.7%)

Compiler: Compiled 29 to 25 computations (13.8% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms (0%)

sample902.0ms (37.9%)

Algorithm

1×

intervals

Results

260.0ms	1921×	body	640	valid
147.0ms	4108×	body	80	valid
97.0ms	577×	body	1280	valid
91.0ms	911×	body	320	valid
32.0ms	483×	body	160	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 59 to 51 computations (13.6% saved)

Details

analyze6.0ms (0.3%)

sample25.0ms (1%)

simplify24.0ms (1%)

prune3.0ms (0.1%)

localize9.0ms (0.4%)

rewrite74.0ms (3.1%)

series15.0ms (0.6%)

simplify103.0ms (4.3%)

prune161.0ms (6.7%)

localize16.0ms (0.7%)

rewrite131.0ms (5.5%)

series26.0ms (1.1%)

simplify106.0ms (4.5%)

prune155.0ms (6.5%)

localize13.0ms (0.5%)

rewrite35.0ms (1.5%)

series11.0ms (0.5%)

simplify92.0ms (3.9%)

prune318.0ms (13.4%)

localize5.0ms (0.2%)

rewrite11.0ms (0.5%)

series5.0ms (0.2%)

simplify69.0ms (2.9%)

prune42.0ms (1.7%)

regimes16.0ms (0.7%)

bsearch0.0ms (0%)

simplify6.0ms (0.3%)

end0.0ms (0%)

sample902.0ms (37.9%)

Profiling