Details

analyze95.0ms (1.4%)

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
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample13.0ms (0.2%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify241.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	5248	10

prune3.0ms (0%)

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_17128`
3×	`add-log-exp_binary64_17167`
2×	`times-frac_binary64_17134` `distribute-lft-out_binary64_17079`
1×	`add-cube-cbrt_binary64_17163` `add-sqr-sqrt_binary64_17150` `flip-+_binary64_17102` `add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166` `pow1_binary64_17189` `+-commutative_binary64_17058` `sum-log_binary64_17219` `frac-add_binary64_17136` `flip3-+_binary64_17131`

Counts

1 → 14

Calls

1 calls:

12.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

series18.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

18.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4854	239
1	4854	239

prune13.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	2	18

Error

0.0b

Counts

18 → 2

Compiler

Compiled 222 to 168 computations (24.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/4 (*.f64 y y))
0.4b	(/.f64 1/4 (*.f64 x x))
3.8b	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
30.9b	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

rewrite70.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`add-sqr-sqrt_binary64_17150`
194×	`times-frac_binary64_17134`
112×	`*-un-lft-identity_binary64_17128`
84×	`difference-of-squares_binary64_17097`
42×	`distribute-lft-out--_binary64_17080`
30×	`add-cube-cbrt_binary64_17163`
26×	`div-inv_binary64_17125`
16×	`add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166`
15×	`associate-/l*_binary64_17073`
11×	`associate-/r*_binary64_17072`
7×	`cancel-sign-sub-inv_binary64_17094`
6×	`add-log-exp_binary64_17167`
5×	`cbrt-undiv_binary64_17162` `div-exp_binary64_17179`
4×	`pow1_binary64_17189`
3×	`clear-num_binary64_17127` `associate-/r/_binary64_17074` `flip--_binary64_17103` `frac-2neg_binary64_17139` `associate-/l/_binary64_17075` `frac-sub_binary64_17137` `flip3--_binary64_17132`
2×	`cbrt-unprod_binary64_17161` `prod-exp_binary64_17177`
1×	`diff-log_binary64_17220` `div-sub_binary64_17133` `sub-neg_binary64_17121`

Counts

4 → 185

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
10.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
4.0ms	(/.f64 1/4 (*.f64 x x))
4.0ms	(/.f64 1/4 (*.f64 y y))

series116.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
26.0ms	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
17.0ms	(/.f64 1/4 (*.f64 y y))
16.0ms	(/.f64 1/4 (*.f64 x x))

simplify124.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4908	6428
1	4908	6428

prune319.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Error

Counts

199 → 4

Compiler

Compiled 5799 to 3823 computations (34.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
0.6b	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

rewrite100.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64_17150`
71×	`cbrt-prod_binary64_17159`
63×	`*-un-lft-identity_binary64_17128`
42×	`times-frac_binary64_17134`
33×	`cbrt-div_binary64_17160`
28×	`difference-of-squares_binary64_17097`
16×	`distribute-lft-out--_binary64_17080`
15×	`add-cube-cbrt_binary64_17163`
14×	`swap-sqr_binary64_17095`
12×	`associate-r_binary64_17068` `associate-l_binary64_17069`
11×	`flip--_binary64_17103` `pow1_binary64_17189` `frac-sub_binary64_17137` `flip3--_binary64_17132`
9×	`pow1/3_binary64_17210` `frac-times_binary64_17138`
6×	`add-exp-log_binary64_17166`
4×	`add-cbrt-cube_binary64_17164` `add-log-exp_binary64_17167` `unswap-sqr_binary64_17096`
3×	`associate-r/_binary64_17070` `associate-l/_binary64_17071`
2×	`pow-sqr_binary64_17101` `pow-prod-down_binary64_17199` `pow-prod-up_binary64_17198`
1×	`cbrt-unprod_binary64_17161` `prod-exp_binary64_17177` `*-commutative_binary64_17059` `pow2_binary64_17209` `pow-plus_binary64_17191`

Counts

4 → 135

Calls

4 calls:

37.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
12.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
12.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

series441.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
108.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
106.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
104.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))

simplify100.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4870	4157
1	4870	4157

prune539.0ms (7.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	147	4	151

Error

Counts

151 → 4

Compiler

Compiled 7895 to 6142 computations (22.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 -1/2 x))
0.1b	(*.f64 (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))) (/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))))
0.1b	(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
0.1b	(/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))

rewrite493.0ms (7.1%)

Algorithm

1×	rewrite-expression-head

Rules

591×	`*-un-lft-identity_binary64_17128`
538×	`times-frac_binary64_17134`
522×	`add-sqr-sqrt_binary64_17150`
265×	`sqrt-prod_binary64_17144`
151×	`difference-of-squares_binary64_17097`
119×	`distribute-lft-out_binary64_17079`
87×	`add-cube-cbrt_binary64_17163`
82×	`associate-r_binary64_17068`
61×	`associate-l_binary64_17069`
59×	`distribute-lft-out--_binary64_17080`
21×	`associate-/r*_binary64_17072`
20×	`add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166`
14×	`associate-/l*_binary64_17073`
12×	`associate-/r/_binary64_17074`
9×	`sqrt-div_binary64_17145`
7×	`pow1_binary64_17189`
6×	`cbrt-undiv_binary64_17162` `associate-/l/_binary64_17075` `div-exp_binary64_17179`
5×	`div-inv_binary64_17125`
4×	`cbrt-unprod_binary64_17161` `prod-exp_binary64_17177` `add-log-exp_binary64_17167` `unswap-sqr_binary64_17096`
3×	`flip-+_binary64_17102` `flip--_binary64_17103` `frac-sub_binary64_17137` `flip3--_binary64_17132` `frac-add_binary64_17136` `flip3-+_binary64_17131`
2×	`clear-num_binary64_17127` `frac-2neg_binary64_17139` `rem-sqrt-square_binary64_17141`
1×	`associate-r/_binary64_17070` `associate-l/_binary64_17071` `frac-times_binary64_17138` `sqrt-pow1_binary64_17146` `div-sub_binary64_17133` `pow1/2_binary64_17208` `*-commutative_binary64_17059` `pow-prod-down_binary64_17199`

Counts

4 → 393

Calls

4 calls:

142.0ms	(*.f64 (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))) (/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))))
36.0ms	(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
33.0ms	(/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
3.0ms	(sqrt.f64 (/.f64 -1/2 x))

series1.2s (16.6%)

Counts

4 → 12

Calls

4 calls:

876.0ms	(*.f64 (/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))) (/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x)))))
141.0ms	(/.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (-.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
131.0ms	(/.f64 (-.f64 (/.f64 1/2 y) (/.f64 -1/2 x)) (+.f64 (sqrt.f64 (/.f64 1/2 y)) (sqrt.f64 (/.f64 -1/2 x))))
15.0ms	(sqrt.f64 (/.f64 -1/2 x))

simplify197.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5201	17477

prune2.0s (29.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	405	0	405
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	405	4	409

Error

Counts

409 → 4

Compiler

Compiled 19291 to 14989 computations (22.3% saved)

regimes83.0ms (1.2%)

Accuracy

Total 0.0b remaining (57.8%)

Threshold costs 0.0b (57.8%)

Compiler

Compiled 967 to 805 computations (16.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample677.0ms (9.7%)

Algorithm

1×

intervals

Results

233.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 339 to 285 computations (15.9% saved)

Details

analyze95.0ms (1.4%)

sample13.0ms (0.2%)

simplify241.0ms (3.4%)

prune3.0ms (0%)

localize5.0ms (0.1%)

rewrite13.0ms (0.2%)

series18.0ms (0.3%)

simplify81.0ms (1.2%)

prune13.0ms (0.2%)

localize12.0ms (0.2%)

rewrite70.0ms (1%)

series116.0ms (1.7%)

simplify124.0ms (1.8%)

prune319.0ms (4.6%)

localize16.0ms (0.2%)

rewrite100.0ms (1.4%)

series441.0ms (6.3%)

simplify100.0ms (1.4%)

prune539.0ms (7.7%)

localize14.0ms (0.2%)

rewrite493.0ms (7.1%)

series1.2s (16.6%)

simplify197.0ms (2.8%)

prune2.0s (29.2%)

regimes83.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample677.0ms (9.7%)

Profiling