Details

analyze459.0ms (6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	44×	body	2560	valid
9.0ms	170×	body	80	valid
4.0ms	18×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	21×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	15×	body	80	invalid
0.0ms	3×	body	160	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify405.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (389.0ms)

Iter	Nodes	Cost
0	1708	24
1	1708	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series523.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
73.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify166.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	4889	2045
1	4889	2045

prune131.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	76	10	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	11	87

Merged error: 5.7b

Counts

87 → 11

Compiler

Compiled 2226 to 1350 computations (39.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite89.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64`
438×	`add-sqr-sqrt_binary64`
363×	`*-un-lft-identity_binary64`
289×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`
71×	`associate-/r*_binary64`
40×	`sqrt-prod_binary64`
37×	`distribute-lft-out--_binary64`
25×	`add-exp-log_binary64`
17×	`div-inv_binary64`
15×	`div-exp_binary64`
13×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64`
5×	`associate-/r/_binary64`
4×	`insert-posit16`
3×	`flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 356

Calls

4 calls:

28.0ms	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series530.0ms (7%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify244.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4942	16375
1	4942	16375

prune764.0ms (10.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	366	2	368
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	369	10	379

Merged error: 5.7b

Counts

379 → 10

Compiler

Compiled 12811 to 7869 computations (38.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a) (cbrt.f64 3))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite58.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`times-frac_binary64`
210×	`add-sqr-sqrt_binary64`
165×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
69×	`cbrt-prod_binary64`
44×	`difference-of-squares_binary64`
25×	`sqrt-prod_binary64`
22×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
9×	`add-exp-log_binary64`
8×	`add-log-exp_binary64` `div-inv_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`pow1_binary64`
4×	`insert-posit16`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 220

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a) (cbrt.f64 3))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series594.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

277.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a) (cbrt.f64 3))
131.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify169.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5481	10291

prune553.0ms (7.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	229	3	232
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	230	12	242

Merged error: 5.7b

Counts

242 → 12

Compiler

Compiled 9644 to 6631 computations (31.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 62

Calls

4 calls:

10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series502.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)

simplify132.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4998	1616
1	4998	1616

prune116.0ms (1.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	74	12	86

Merged error: 5.7b

Counts

86 → 12

Compiler

Compiled 2780 to 1648 computations (40.7% saved)

regimes282.0ms (3.7%)

Compiler: Compiled 942 to 832 computations (11.7% saved)

bsearch101.0ms (1.3%)

Steps

Iters	Range	Point
8	4.326838733471441e+64	1.2058980158258533e+67	1.1308364602898941e+67
7	4.171215766268283e-139	1.5383360139223542e-137	4.2393047293392074e-139
8	-9.266086035849809e+107	-2.9115369684660863e+103	-6.350987509722503e+107

Iters

Range

Point

4.326838733471441e+64

1.2058980158258533e+67

1.1308364602898941e+67

4.171215766268283e-139

1.5383360139223542e-137

4.2393047293392074e-139

-9.266086035849809e+107

-2.9115369684660863e+103

-6.350987509722503e+107

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	99	107
1	99	107

end0.0ms (0%)

sample1.6s (20.9%)

Algorithm

1×

intervals

Results

343.0ms	1118×	body	2560	valid
288.0ms	5119×	body	80	valid
222.0ms	896×	body	1280	valid
80.0ms	415×	body	640	valid
44.0ms	115×	body	5120	valid
35.0ms	642×	body	80	nan
30.0ms	205×	body	320	valid
24.0ms	394×	body	80	invalid
13.0ms	132×	body	160	valid

Compiler

Compiled 308 to 257 computations (16.6% saved)

Details

analyze459.0ms (6%)

sample43.0ms (0.6%)

simplify405.0ms (5.3%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite38.0ms (0.5%)

series523.0ms (6.9%)

simplify166.0ms (2.2%)

prune131.0ms (1.7%)

localize12.0ms (0.2%)

rewrite89.0ms (1.2%)

series530.0ms (7%)

simplify244.0ms (3.2%)

prune764.0ms (10.1%)

localize18.0ms (0.2%)

rewrite58.0ms (0.8%)

series594.0ms (7.8%)

simplify169.0ms (2.2%)

prune553.0ms (7.3%)

localize17.0ms (0.2%)

rewrite33.0ms (0.4%)

series502.0ms (6.6%)

simplify132.0ms (1.7%)

prune116.0ms (1.5%)

regimes282.0ms (3.7%)

bsearch101.0ms (1.3%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample1.6s (20.9%)

Profiling