Details

analyze458.0ms (8.3%)

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
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)

sample17.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 25 to 22 computations (12% saved)

simplify167.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	18
1	20	18

prune2.0ms (0%)

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: 41.3b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
38.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_15462`
5×	`add-sqr-sqrt_binary64_15445`
4×	`add-cube-cbrt_binary64_15458` `pow1_binary64_15484` `*-un-lft-identity_binary64_15423` `sum-log_binary64_15514`
3×	`flip3-+_binary64_15426` `flip-+_binary64_15397` `add-exp-log_binary64_15461` `add-cbrt-cube_binary64_15459` `sqrt-prod_binary64_15439`
2×	`sqrt-div_binary64_15440` `+-commutative_binary64_15353`
1×	`rem-sqrt-square_binary64_15436` `sqrt-pow1_binary64_15441` `pow1/2_binary64_15503` `associate-+l+_binary64_15356`

Counts

3 → 39

Calls

3 calls:

7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series249.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

153.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
59.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
37.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4984	904
1	4984	904

prune39.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Merged error: 20.0b

Counts

49 → 5

Compiler

Compiled 868 to 176 computations (79.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
6.3b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
38.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_15462`
9×	`add-sqr-sqrt_binary64_15445`
8×	`add-cube-cbrt_binary64_15458` `*-un-lft-identity_binary64_15423`
7×	`pow1_binary64_15484`
6×	`log-prod_binary64_15509` `exp-prod_binary64_15475` `sqrt-prod_binary64_15439` `exp-sum_binary64_15469`
4×	`flip3-+_binary64_15426` `sqrt-div_binary64_15440` `flip-+_binary64_15397` `sum-log_binary64_15514` `add-exp-log_binary64_15461` `add-cbrt-cube_binary64_15459`
3×	`log-pow_binary64_15512`
2×	`sqrt-pow1_binary64_15441` `exp-diff_binary64_15471` `+-commutative_binary64_15353` `pow1/2_binary64_15503` `log-div_binary64_15510`
1×	`rem-sqrt-square_binary64_15436` `associate-+l+_binary64_15356` `rem-exp-log_binary64_15463`

Counts

4 → 61

Calls

4 calls:

9.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series415.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(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)))
56.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
36.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4867	1422
1	4867	1422

prune60.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	70	8	78

Merged error: 20.0b

Counts

78 → 8

Compiler

Compiled 1455 to 318 computations (78.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.5b	(pow.f64 E.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
38.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_15462`
10×	`add-sqr-sqrt_binary64_15445`
9×	`add-cube-cbrt_binary64_15458` `*-un-lft-identity_binary64_15423`
8×	`pow1_binary64_15484`
6×	`log-prod_binary64_15509` `pow-unpow_binary64_15500` `sqrt-prod_binary64_15439` `unpow-prod-up_binary64_15501`
5×	`add-exp-log_binary64_15461`
4×	`flip3-+_binary64_15426` `sqrt-div_binary64_15440` `flip-+_binary64_15397` `sum-log_binary64_15514` `add-cbrt-cube_binary64_15459`
3×	`log-pow_binary64_15512` `unpow-prod-down_binary64_15502`
2×	`sqrt-pow1_binary64_15441` `pow-sub_binary64_15499` `+-commutative_binary64_15353` `pow1/2_binary64_15503` `log-div_binary64_15510` `pow-exp_binary64_15491`
1×	`rem-sqrt-square_binary64_15436` `pow-pow_binary64_15495` `pow-to-exp_binary64_15492` `e-exp-1_binary64_15468` `sqr-pow_binary64_15395` `associate-+l+_binary64_15356`

Counts

4 → 68

Calls

4 calls:

10.0ms	(pow.f64 E.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series386.0ms (7%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow.f64 E.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))))
143.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
56.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
35.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify116.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4915	1869
1	4915	1869

prune70.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	77	11	88

Merged error: 20.0b

Counts

88 → 11

Compiler

Compiled 1808 to 378 computations (79.1% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

6.1b	(pow.f64 (pow.f64 E.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))
38.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
38.4b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_15445`
11×	`add-cube-cbrt_binary64_15458` `*-un-lft-identity_binary64_15423`
10×	`unpow-prod-down_binary64_15502`
9×	`pow1_binary64_15484` `pow-unpow_binary64_15500` `sqrt-prod_binary64_15439`
6×	`sqrt-div_binary64_15440` `add-exp-log_binary64_15461` `cbrt-prod_binary64_15454` `pow-exp_binary64_15491`
4×	`sqrt-pow1_binary64_15441` `pow1/2_binary64_15503` `add-cbrt-cube_binary64_15459` `add-log-exp_binary64_15462`
3×	`flip3-+_binary64_15426` `rem-sqrt-square_binary64_15436` `log-pow_binary64_15512` `flip-+_binary64_15397`
2×	`pow-to-exp_binary64_15492` `sqr-pow_binary64_15395`
1×	`pow-pow_binary64_15495` `e-exp-1_binary64_15468`

Counts

4 → 75

Calls

4 calls:

7.0ms	(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)))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
5.0ms	(pow.f64 (pow.f64 E.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))

series1.7s (31%)

Counts

4 → 12

Calls

4 calls:

1.3s	(pow.f64 (pow.f64 E.f64 (.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))))))
134.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
123.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
123.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4922	3605
1	4922	3605

prune114.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	85	13	98

Merged error: 20.0b

Counts

98 → 13

Compiler

Compiled 4597 to 413 computations (91% saved)

regimes445.0ms (8.1%)

Compiler: Compiled 3352 to 1870 computations (44.2% saved)

bsearch13.0ms (0.2%)

Steps

Iters	Range		Point
1	2.44705323363674e+86	2.6934912059401883e+86	2.6219909757612777e+86
5	-3.560209948911124e+98	-9.277146381273524e+97	-3.477124351905511e+98

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	34
1	27	34

end0.0ms (0%)

sample806.0ms (14.6%)

Algorithm

1×

intervals

Results

323.0ms

8000×

body

128

valid

Compiler

Compiled 304 to 189 computations (37.8% saved)

Details

analyze458.0ms (8.3%)

sample17.0ms (0.3%)

simplify167.0ms (3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite21.0ms (0.4%)

series249.0ms (4.5%)

simplify69.0ms (1.2%)

prune39.0ms (0.7%)

localize12.0ms (0.2%)

rewrite34.0ms (0.6%)

series415.0ms (7.5%)

simplify94.0ms (1.7%)

prune60.0ms (1.1%)

localize18.0ms (0.3%)

rewrite35.0ms (0.6%)

series386.0ms (7%)

simplify116.0ms (2.1%)

prune70.0ms (1.3%)

localize29.0ms (0.5%)

rewrite37.0ms (0.7%)

series1.7s (31%)

simplify96.0ms (1.7%)

prune114.0ms (2.1%)

regimes445.0ms (8.1%)

bsearch13.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample806.0ms (14.6%)

Profiling