Details

analyze123.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample45.0ms

Algorithm

intervals

Results

12.0ms	208×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	19×	body	1280	valid
3.0ms	13×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	7×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5203	43

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 25.3b

Counts

2 → 1

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.8b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

21.9b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
5×	`add-log-exp_binary64`
4×	`frac-times_binary64`
3×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

3 → 111

Calls

3 calls:

23.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

37.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

15.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series682.0ms

Counts

3 → 9

Calls

3 calls:

280.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

334.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

68.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify82.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5105	5316

prune755.0ms

Filtered

91 candidates to 120 candidates (-31.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 5.7b

Counts

121 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.1b	(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.3b	(/.f64 1 (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
1.8b	(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
42×	`add-exp-log_binary64`
38×	`add-cube-cbrt_binary64`
32×	`add-cbrt-cube_binary64`
28×	`associate-/r/_binary64`
21×	`associate-r_binary64`
17×	`div-exp_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
14×	`associate-/r*_binary64`
13×	`cbrt-undiv_binary64`
12×	`frac-times_binary64` `associate-*l/_binary64`
9×	`distribute-lft-out_binary64`
8×	`prod-exp_binary64` `div-inv_binary64`
7×	`pow1_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64`
4×	`associate-l_binary64` `rec-exp_binary64`
3×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 170

Calls

4 calls:

19.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
23.0ms	(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
25.0ms	(/.f64 1 (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
38.0ms	(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

series797.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
118.0ms	(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
284.0ms	(/.f64 1 (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
333.0ms	(+.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

simplify122.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5736	7127

prune661.0ms

Filtered

118 candidates to 182 candidates (-54.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	182	10	192

Merged error: 5.7b

Counts

192 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.1b	(.f64 (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.3b	(+.f64 (.f64 (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 1)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
42×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
32×	`add-cbrt-cube_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64` `associate-l_binary64`
17×	`prod-exp_binary64`
12×	`pow1_binary64` `cbrt-unprod_binary64`
11×	`frac-times_binary64`
10×	`flip3-+_binary64` `flip-+_binary64`
8×	`distribute-lft-out_binary64` `associate-*r/_binary64` `div-exp_binary64`
7×	`cbrt-undiv_binary64` `associate-*l/_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64` `rec-exp_binary64`
3×	`difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 147

Calls

4 calls:

14.0ms	(/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
18.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
26.0ms	(.f64 (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
28.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 1)

series727.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
68.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
281.0ms	(.f64 (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
331.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 1)

simplify79.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5004	4879

prune575.0ms

Filtered

102 candidates to 159 candidates (-55.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	160	9	169

Merged error: 5.7b

Counts

169 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
0.3b	(/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.4b	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
6.2b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
62×	`add-exp-log_binary64`
60×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
47×	`add-cbrt-cube_binary64`
42×	`sqrt-prod_binary64`
41×	`add-cube-cbrt_binary64`
27×	`associate-l_binary64`
21×	`div-exp_binary64`
20×	`prod-exp_binary64`
17×	`cbrt-undiv_binary64`
14×	`associate-/r*_binary64` `cbrt-unprod_binary64`
13×	`associate-r_binary64`
10×	`distribute-lft-out_binary64`
8×	`pow1_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64`
5×	`associate-/l/_binary64` `unswap-sqr_binary64` `rec-exp_binary64`
4×	`associate-/l*_binary64` `div-inv_binary64`
3×	`pow-flip_binary64` `frac-times_binary64` `associate-*l/_binary64`
2×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 176

Calls

4 calls:

45.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
23.0ms	(/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
37.0ms	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

series1.0s

Counts

4 → 12

Calls

4 calls:

283.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
302.0ms	(/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
118.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
332.0ms	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))) 1)

simplify109.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5427	7632

prune139.0ms

Filtered: 107 candidates to 188 candidates (-75.7%)

Details

analyze123.0ms

sample45.0ms

simplify57.0ms

prune12.0ms

localize20.0ms

rewrite79.0ms

series682.0ms

simplify82.0ms

prune755.0ms

localize22.0ms

rewrite112.0ms

series797.0ms

simplify122.0ms

prune661.0ms

localize31.0ms

rewrite92.0ms

series727.0ms

simplify79.0ms

prune575.0ms

localize33.0ms

rewrite122.0ms

series1.0s

simplify109.0ms

prune139.0ms

Profiling