Details

analyze4.0ms (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)

sample23.0ms (1%)

Algorithm

1×

intervals

Results

7.0ms	47×	body	1280	valid
5.0ms	47×	body	640	valid
4.0ms	128×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify87.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	682	19
1	682	19

prune3.0ms (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: 30.1b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite53.0ms (2.2%)

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:

34.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series13.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

7.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(/.f64 x (+.f64 x 1))

simplify119.0ms (5%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4913	2299
1	4913	2299

prune131.0ms (5.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

Compiler

Compiled 2547 to 1818 computations (28.6% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.1b	(*.f64 x (/.f64 1 (+.f64 x 1)))
7.9b	(-.f64 (*.f64 x (/.f64 1 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite50.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
19×	`add-exp-log_binary64`
18×	`associate-r_binary64`
15×	`distribute-lft-out_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-/r*_binary64`
10×	`difference-of-squares_binary64`
7×	`pow1_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
4×	`prod-exp_binary64`
3×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `un-div-inv_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 146

Calls

4 calls:

17.0ms	(-.f64 (*.f64 x (/.f64 1 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
10.0ms	(*.f64 x (/.f64 1 (+.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
8.0ms	(/.f64 1 (+.f64 x 1))

series15.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (*.f64 x (/.f64 1 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(*.f64 x (/.f64 1 (+.f64 x 1)))
2.0ms	(/.f64 1 (+.f64 x 1))

simplify100.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5912	2411

prune131.0ms (5.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Merged error: 0.0b

Counts

162 → 4

Compiler

Compiled 3361 to 2501 computations (25.6% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.1b	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
7.9b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

rewrite46.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
69×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
27×	`associate-r_binary64`
19×	`add-exp-log_binary64`
14×	`difference-of-squares_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-/r*_binary64`
7×	`pow1_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `frac-sub_binary64`
5×	`flip3-+_binary64` `distribute-lft-out_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`associate-l_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `un-div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

15.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
11.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
7.0ms	(/.f64 x (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))

series15.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
3.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
3.0ms	(/.f64 x (+.f64 x 1))
2.0ms	(/.f64 1 (-.f64 x 1))

simplify88.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5181	2533

prune134.0ms (5.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	166	4	170

Merged error: 0.0b

Counts

170 → 4

Compiler

Compiled 3513 to 2551 computations (27.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 x 1))
0.2b	(cbrt.f64 (+.f64 x 1))
0.3b	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
22.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))

rewrite77.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64` `cbrt-prod_binary64`
16×	`cbrt-div_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
11×	`pow1_binary64`
9×	`swap-sqr_binary64`
8×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `difference-of-squares_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

55.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))
11.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))

series27.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
8.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))
6.0ms	(cbrt.f64 (+.f64 x 1))
5.0ms	(cbrt.f64 (+.f64 x 1))

simplify127.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4890	2265
1	4890	2265

prune126.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	114	4	118

Merged error: 0.0b

Counts

118 → 4

Compiler

Compiled 3326 to 2527 computations (24% saved)

regimes28.0ms (1.2%)

Compiler: Compiled 71 to 57 computations (19.7% saved)

bsearch24.0ms (1%)

Steps

Iters	Range		Point
8	5.151418838250441	38625.96836589602	13458.95778492134
11	-1.457145943166892e+17	-0.0017045774885850432	-13944.835699645984

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	75	58
1	75	58

end0.0ms (0%)

sample916.0ms (38.5%)

Algorithm

1×

intervals

Results

277.0ms	1841×	body	1280	valid
139.0ms	1232×	body	640	valid
122.0ms	4003×	body	80	valid
54.0ms	623×	body	320	valid
17.0ms	301×	body	160	valid

Compiler

Compiled 122 to 97 computations (20.5% saved)

Details

analyze4.0ms (0.2%)

sample23.0ms (1%)

simplify87.0ms (3.7%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

rewrite53.0ms (2.2%)

series13.0ms (0.5%)

simplify119.0ms (5%)

prune131.0ms (5.5%)

localize7.0ms (0.3%)

rewrite50.0ms (2.1%)

series15.0ms (0.6%)

simplify100.0ms (4.2%)

prune131.0ms (5.5%)

localize7.0ms (0.3%)

rewrite46.0ms (1.9%)

series15.0ms (0.6%)

simplify88.0ms (3.7%)

prune134.0ms (5.6%)

localize10.0ms (0.4%)

rewrite77.0ms (3.2%)

series27.0ms (1.2%)

simplify127.0ms (5.3%)

prune126.0ms (5.3%)

regimes28.0ms (1.2%)

bsearch24.0ms (1%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample916.0ms (38.5%)

Profiling