Details

analyze603.0ms (11.3%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample37.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	175×	body	128	valid
7.0ms	34×	body	2048	valid
4.0ms	20×	body	1024	valid
3.0ms	13×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	22×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify175.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune4.0ms (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

Error

31.6b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.1b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series224.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
63.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
56.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
28.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4941	2578
1	4941	2578

prune114.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Error

5.6b

Counts

109 → 7

Compiler

Compiled 2344 to 436 computations (81.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.1b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite58.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
19×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 182

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series243.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
61.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5030	5933

prune168.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	193	8	201

Error

5.6b

Counts

201 → 8

Compiler

Compiled 4981 to 981 computations (80.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
13.3b	(.f64 (.f64 a c) (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) a))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
4×	`cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

10.0ms	(.f64 (.f64 a c) (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series146.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
49.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
30.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(.f64 (.f64 a c) (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) a))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4949	1250
1	4949	1250

prune108.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	86	9	95

Error

5.6b

Counts

95 → 9

Compiler

Compiled 2549 to 1247 computations (51.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 c (/.f64 (cbrt.f64 1) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64`
42×	`associate-r_binary64`
41×	`*-un-lft-identity_binary64`
39×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
20×	`cbrt-prod_binary64`
14×	`difference-of-squares_binary64`
10×	`sqrt-prod_binary64`
9×	`add-exp-log_binary64`
8×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `flip--_binary64`
3×	`associate-l_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

20.0ms	(.f64 c (/.f64 (cbrt.f64 1) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series317.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(.f64 c (/.f64 (cbrt.f64 1) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
59.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
28.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5120	2545

prune115.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Error

5.6b

Counts

128 → 9

Compiler

Compiled 2895 to 946 computations (67.3% saved)

regimes611.0ms (11.5%)

Accuracy

Total 1.3b remaining (18.6%)

Threshold costs 0b (0%)

Compiler

Compiled 4066 to 2605 computations (35.9% saved)

bsearch92.0ms (1.7%)

Steps

Iters	Range	Point
10	5.6409200446738983e+48	6.680819182205816e+58	5.943737817038774e+58
5	2.077023047695624e-252	7.940550091717544e-252	5.980743311430165e-252
9	-2.2860812834988032e+125	-1.0222164280511116e+117	-3.4695905252840837e+123

Iters

Range

Point

5.6409200446738983e+48

6.680819182205816e+58

5.943737817038774e+58

2.077023047695624e-252

7.940550091717544e-252

5.980743311430165e-252

-2.2860812834988032e+125

-1.0222164280511116e+117

-3.4695905252840837e+123

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	75
1	93	75

end0.0ms (0%)

sample1.8s (33.7%)

Algorithm

1×

intervals

Results

247.0ms	1175×	body	2048	valid
231.0ms	5214×	body	128	valid
114.0ms	695×	body	1024	valid
95.0ms	366×	body	4096	valid
44.0ms	371×	body	512	valid
31.0ms	749×	body	128	nan
15.0ms	179×	body	256	valid
13.0ms	250×	body	128	invalid

Compiler

Compiled 1044 to 666 computations (36.2% saved)

Details

analyze603.0ms (11.3%)

sample37.0ms (0.7%)

simplify175.0ms (3.3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite47.0ms (0.9%)

series224.0ms (4.2%)

simplify71.0ms (1.3%)

prune114.0ms (2.1%)

localize11.0ms (0.2%)

rewrite58.0ms (1.1%)

series243.0ms (4.6%)

simplify98.0ms (1.8%)

prune168.0ms (3.1%)

localize15.0ms (0.3%)

rewrite33.0ms (0.6%)

series146.0ms (2.7%)

simplify93.0ms (1.7%)

prune108.0ms (2%)

localize11.0ms (0.2%)

rewrite46.0ms (0.9%)

series317.0ms (5.9%)

simplify80.0ms (1.5%)

prune115.0ms (2.2%)

regimes611.0ms (11.5%)

bsearch92.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.8s (33.7%)

Profiling