Details

analyze632.0ms (15.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

prune2.0ms (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

Merged error: 37.3b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
34.6b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 28

Calls

2 calls:

11.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series174.0ms (4.2%)

Counts

2 → 6

Calls

2 calls:

133.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
41.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify166.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4924	598
1	4924	598

prune32.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	6	35

Merged error: 17.0b

Counts

35 → 6

Compiler

Compiled 629 to 152 computations (75.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
34.6b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
34.6b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite55.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
18×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`insert-posit16` `frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

28.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
8.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series459.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
136.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
136.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
44.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify128.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5247	3231

prune121.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Merged error: 17.0b

Counts

146 → 6

Compiler

Compiled 3933 to 488 computations (87.6% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
5.9b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
34.6b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `log-prod_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
5×	`add-log-exp_binary64`
4×	`sqrt-div_binary64`
3×	`flip3-+_binary64` `log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `log-div_binary64`
1×	`rem-exp-log_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 51

Calls

3 calls:

11.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

series314.0ms (7.7%)

Counts

3 → 9

Calls

3 calls:

139.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
135.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
40.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify207.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (180.0ms)

Iter	Nodes	Cost
0	4921	1136
1	4921	1136

prune54.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	57	9	66

Merged error: 17.0b

Counts

66 → 9

Compiler

Compiled 1175 to 266 computations (77.4% saved)

localize19.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
6.4b	(pow.f64 (exp.f64 1/2) (log.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
36.1b	(log.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`pow1_binary64` `log-prod_binary64`
5×	`add-log-exp_binary64`
4×	`pow-unpow_binary64` `pow-pow_binary64` `add-exp-log_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `unpow-prod-up_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `insert-posit16` `flip-+_binary64` `exp-prod_binary64`
2×	`log-pow_binary64` `pow-sub_binary64`
1×	`pow-to-exp_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 54

Calls

3 calls:

11.0ms	(pow.f64 (exp.f64 1/2) (log.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
8.0ms	(log.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

series255.0ms (6.2%)

Counts

3 → 9

Calls

3 calls:

130.0ms	(pow.f64 (exp.f64 1/2) (log.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))))
87.0ms	(log.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
37.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify187.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4900	1502
1	4900	1502

prune56.0ms (1.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	59	4	63
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	61	11	72

Merged error: 17.0b

Counts

72 → 11

Compiler

Compiled 1365 to 404 computations (70.4% saved)

regimes333.0ms (8.1%)

Compiler: Compiled 1336 to 1189 computations (11% saved)

bsearch37.0ms (0.9%)

Steps

Iters	Range		Point
8	5.925368333496744e+75	7.268934523160929e+79	6.48221010313292e+79
10	-5.757168685717274e+160	-1.375164455341625e+147	-4.269313514166145e+147

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms (0%)

sample717.0ms (17.5%)

Algorithm

1×

intervals

Results

328.0ms

8000×

body

valid

Compiler

Compiled 154 to 134 computations (13% saved)

Details

analyze632.0ms (15.4%)

sample18.0ms (0.4%)

simplify22.0ms (0.5%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite18.0ms (0.4%)

series174.0ms (4.2%)

simplify166.0ms (4.1%)

prune32.0ms (0.8%)

localize11.0ms (0.3%)

rewrite55.0ms (1.3%)

series459.0ms (11.2%)

simplify128.0ms (3.1%)

prune121.0ms (3%)

localize12.0ms (0.3%)

rewrite26.0ms (0.6%)

series314.0ms (7.7%)

simplify207.0ms (5.1%)

prune54.0ms (1.3%)

localize19.0ms (0.5%)

rewrite26.0ms (0.6%)

series255.0ms (6.2%)

simplify187.0ms (4.6%)

prune56.0ms (1.4%)

regimes333.0ms (8.1%)

bsearch37.0ms (0.9%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample717.0ms (17.5%)

Profiling