Details

analyze372.0ms (6.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4931	40
1	4931	40
0	2	2
1	2	2

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%	62.4%	12.6%	6
31.2%	50%	18.8%	7
40.6%	37.5%	22%	8
45.3%	26.5%	28.2%	9
46.8%	19.5%	33.7%	10
48.8%	14%	37.2%	11
51.7%	10.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	5.1%	41.6%	14

Symmetry

Compiler

Compiled 20 to 12 computations (40% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 39 to 25 computations (35.9% saved)

simplify145.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4956	20
1	4956	20

prune7.0ms (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

6.1b

Counts

2 → 2

Compiler

Compiled 41 to 29 computations (29.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
0.2b	(.f64 (.f64 x.im x.im) -3)
6.7b	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))

rewrite79.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

6.0b

Rules

17×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
9×	`pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
6×	`add-sqr-sqrt_binary64_2828`
5×	`add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
4×	`associate-l_binary64_2747` `associate-r_binary64_2746`
2×	`*-commutative_binary64_2737`
1×	`unswap-sqr_binary64_2774` `sum-log_binary64_2897` `flip3-+_binary64_2809` `flip-+_binary64_2780` `cube-mult_binary64_2836` `distribute-lft-out_binary64_2757` `+-commutative_binary64_2736`

Counts

3 → 52

Calls

3 calls:

10.0ms	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
7.0ms	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))
6.0ms	(.f64 (.f64 x.im x.im) -3)

Compiler

Compiled 947 to 550 computations (41.9% saved)

series274.0ms (5%)

Error

5.9b

Counts

3 → 21

Calls

3 calls:

155.0ms	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
76.0ms	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))
28.0ms	(.f64 (.f64 x.im x.im) -3)

Compiler

Compiled 555 to 476 computations (14.2% saved)

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4951	1038
1	4951	1038

prune77.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Error

5.9b

Counts

75 → 7

Compiler

Compiled 1116 to 835 computations (25.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))
0.1b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
5.8b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

rewrite92.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64_2828` `associate-*l/_binary64_2749`
8×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-log-exp_binary64_2845` `add-cbrt-cube_binary64_2842` `add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
7×	`associate-l_binary64_2747`
6×	`associate-r_binary64_2746`
4×	`flip3--_binary64_2810` `flip--_binary64_2781` `flip3-+_binary64_2809` `flip-+_binary64_2780` `frac-sub_binary64_2815`
2×	`pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `*-commutative_binary64_2737`
1×	`difference-of-squares_binary64_2775` `diff-log_binary64_2898` `sub-neg_binary64_2799` `cancel-sign-sub-inv_binary64_2772` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 68

Calls

4 calls:

8.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
7.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
6.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
4.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

Compiler

Compiled 2304 to 309 computations (86.6% saved)

series444.0ms (8.1%)

Error

4.8b

Counts

4 → 36

Calls

4 calls:

159.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
130.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
78.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
52.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

Compiler

Compiled 1392 to 856 computations (38.5% saved)

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4691	2004
1	4691	2004

prune99.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	105	6	111

Error

0.0b

Counts

111 → 6

Compiler

Compiled 2336 to 942 computations (59.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x.re (-.f64 x.re x.im))
0.1b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.2b	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))

rewrite184.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

36×	`distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755`
31×	`cancel-sign-sub-inv_binary64_2772`
26×	`associate-*r/_binary64_2748`
25×	`add-sqr-sqrt_binary64_2828`
24×	`associate-*l/_binary64_2749`
23×	`*-un-lft-identity_binary64_2806`
19×	`add-cube-cbrt_binary64_2841`
18×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
16×	`frac-sub_binary64_2815` `associate--l+_binary64_2743`
13×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
12×	`frac-times_binary64_2816`
11×	`flip3--_binary64_2810` `flip--_binary64_2781` `sub-neg_binary64_2799`
10×	`associate-l_binary64_2747`
9×	`associate-r_binary64_2746`
6×	`add-log-exp_binary64_2845`
5×	`pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
3×	`*-commutative_binary64_2737`
2×	`unswap-sqr_binary64_2774`
1×	`distribute-lft-out_binary64_2757` `diff-log_binary64_2898` `difference-of-squares_binary64_2775` `distribute-lft-out--_binary64_2758`

Counts

4 → 137

Calls

4 calls:

15.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
11.0ms	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))
7.0ms	(*.f64 x.re (-.f64 x.re x.im))
7.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)

Compiler

Compiled 4904 to 737 computations (85% saved)

series479.0ms (8.7%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

166.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
140.0ms	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))
75.0ms	(*.f64 x.re (-.f64 x.re x.im))
72.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)

Compiler

Compiled 1680 to 964 computations (42.6% saved)

simplify109.0ms (2%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4716	4129
1	4716	4129

prune163.0ms (3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	177	8	185

Error

Counts

185 → 8

Compiler

Compiled 4315 to 1516 computations (64.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x.re (+.f64 x.im x.re))
0.1b	(+.f64 (.f64 x.re (+.f64 x.im x.re)) (.f64 2 (*.f64 x.im x.re)))
0.1b	(.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.im x.re)) (.f64 2 (.f64 x.im x.re))))
3.1b	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))

rewrite124.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`add-sqr-sqrt_binary64_2828`
15×	`*-un-lft-identity_binary64_2806`
14×	`associate-l_binary64_2747`
13×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
11×	`add-cube-cbrt_binary64_2841` `associate-r_binary64_2746`
6×	`add-log-exp_binary64_2845` `associate-*r/_binary64_2748`
5×	`pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
4×	`distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `flip3-+_binary64_2809` `flip-+_binary64_2780`
3×	`unswap-sqr_binary64_2774` `*-commutative_binary64_2737` `distribute-rgt-neg-in_binary64_2764` `distribute-lft-neg-in_binary64_2763`
2×	`distribute-lft-out_binary64_2757` `associate-+l+_binary64_2739`
1×	`distribute-lft-neg-out_binary64_2765` `neg-mul-1_binary64_2802` `sum-log_binary64_2897` `+-commutative_binary64_2736`

Counts

4 → 90

Calls

4 calls:

11.0ms	(.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.im x.re)) (.f64 2 (.f64 x.im x.re))))
8.0ms	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))
8.0ms	(+.f64 (.f64 x.re (+.f64 x.im x.re)) (.f64 2 (*.f64 x.im x.re)))
6.0ms	(*.f64 x.re (+.f64 x.im x.re))

Compiler

Compiled 2717 to 790 computations (70.9% saved)

series468.0ms (8.5%)

Error

Counts

4 → 48

Calls

4 calls:

160.0ms	(.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.im x.re)) (.f64 2 (.f64 x.im x.re))))
108.0ms	(+.f64 (.f64 x.re (+.f64 x.im x.re)) (.f64 2 (*.f64 x.im x.re)))
97.0ms	(.f64 (.f64 x.re x.re) (+.f64 x.re x.im))
68.0ms	(*.f64 x.re (+.f64 x.im x.re))

Compiler

Compiled 2448 to 1404 computations (42.6% saved)

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4964	2119
1	4964	2119

prune117.0ms (2.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	138	8	146

Error

Counts

146 → 8

Compiler

Compiled 3269 to 1167 computations (64.3% saved)

regimes331.0ms (6%)

Accuracy

Total 0.2b remaining (99.1%)

Threshold costs 0.2b (99.1%)

Compiler

Compiled 4560 to 2781 computations (39% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	104	41
1	104	41

Removed

()

end0.0ms (0%)

sample1.7s (30.3%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
17.0ms	418×	body	128	invalid

Compiler

Compiled 1564 to 954 computations (39% saved)

Details

analyze372.0ms (6.8%)

sample19.0ms (0.4%)

simplify145.0ms (2.6%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite79.0ms (1.4%)

series274.0ms (5%)

simplify74.0ms (1.3%)

prune77.0ms (1.4%)

localize11.0ms (0.2%)

rewrite92.0ms (1.7%)

series444.0ms (8.1%)

simplify53.0ms (1%)

prune99.0ms (1.8%)

localize11.0ms (0.2%)

rewrite184.0ms (3.3%)

series479.0ms (8.7%)

simplify109.0ms (2%)

prune163.0ms (3%)

localize15.0ms (0.3%)

rewrite124.0ms (2.3%)

series468.0ms (8.5%)

simplify76.0ms (1.4%)

prune117.0ms (2.1%)

regimes331.0ms (6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (30.3%)

Profiling