Details

analyze265.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

Compiler

Compiled 32 to 28 computations (12.5% saved)

sample120.0ms (1.4%)

Algorithm

1×

intervals

Results

41.0ms	146×	body	512	valid
32.0ms	292×	body	128	nan
21.0ms	55×	body	1024	valid
6.0ms	29×	body	256	valid
2.0ms	26×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5168	50

prune4.0ms (0%)

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: 4.7b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.9b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
40×	`*-un-lft-identity_binary64`
24×	`cancel-sign-sub-inv_binary64`
16×	`difference-of-squares_binary64`
12×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`

Counts

4 → 96

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series289.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
73.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
72.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
70.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4912	2211
1	4912	2211

prune510.0ms (6.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 0.9b

Counts

109 → 8

Compiler

Compiled 9746 to 7284 computations (25.3% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
2.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64`
49×	`sqrt-prod_binary64`
45×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
19×	`distribute-lft-out_binary64`
18×	`cancel-sign-sub-inv_binary64` `times-frac_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
9×	`distribute-lft-out--_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`associate-/r/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 116

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series258.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
67.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
63.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5122	2607

prune371.0ms (4.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	129	7	136

Merged error: 0.4b

Counts

136 → 7

Compiler

Compiled 6863 to 4791 computations (30.2% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite65.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64`
54×	`sqrt-prod_binary64`
46×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
34×	`distribute-lft-out_binary64`
30×	`add-cube-cbrt_binary64`
12×	`associate-/r*_binary64` `cancel-sign-sub-inv_binary64`
10×	`add-exp-log_binary64`
8×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
6×	`pow1_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
4×	`associate-/r/_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series262.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
67.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

simplify94.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5735	3006

prune381.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Merged error: 0.2b

Counts

155 → 7

Compiler

Compiled 7485 to 5238 computations (30% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
3.1b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite67.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64`
59×	`sqrt-prod_binary64`
54×	`times-frac_binary64`
49×	`distribute-lft-out_binary64`
47×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
13×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64` `cancel-sign-sub-inv_binary64`
4×	`difference-of-squares_binary64`
3×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `pow-flip_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 156

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series243.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
53.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
53.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4921	3415
1	4921	3415

prune489.0ms (5.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	168	7	175

Merged error: 0.0b

Counts

175 → 7

Compiler

Compiled 8127 to 5698 computations (29.9% saved)

regimes332.0ms (4%)

Compiler: Compiled 4077 to 3542 computations (13.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	62
1	40	62

end0.0ms (0%)

sample4.1s (49%)

Algorithm

1×

intervals

Results

1.3s	4341×	body	512	valid
976.0ms	9767×	body	128	nan
737.0ms	1818×	body	1024	valid
196.0ms	1011×	body	256	valid
82.0ms	830×	body	128	valid

Compiler

Compiled 410 to 357 computations (12.9% saved)

Details

analyze265.0ms (3.2%)

sample120.0ms (1.4%)

simplify46.0ms (0.6%)

prune4.0ms (0%)

localize22.0ms (0.3%)

rewrite55.0ms (0.7%)

series289.0ms (3.4%)

simplify101.0ms (1.2%)

prune510.0ms (6.1%)

localize23.0ms (0.3%)

rewrite60.0ms (0.7%)

series258.0ms (3.1%)

simplify75.0ms (0.9%)

prune371.0ms (4.4%)

localize24.0ms (0.3%)

rewrite65.0ms (0.8%)

series262.0ms (3.1%)

simplify94.0ms (1.1%)

prune381.0ms (4.6%)

localize30.0ms (0.4%)

rewrite67.0ms (0.8%)

series243.0ms (2.9%)

simplify79.0ms (0.9%)

prune489.0ms (5.8%)

regimes332.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.1s (49%)

Profiling