Details

analyze1.1s (17.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample32.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	72×	body	128	nan
1.0ms	26×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify171.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	175	21
1	175	21

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: 25.4b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
6.2b	(.f64 (.f64 x y) z)
8.6b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
25.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_8198` `add-exp-log_binary64_8200`
11×	`add-sqr-sqrt_binary64_8186`
10×	`*-un-lft-identity_binary64_8165` `pow1_binary64_8223` `add-cube-cbrt_binary64_8197`
9×	`sqrt-prod_binary64_8180`
6×	`times-frac_binary64_8171` `associate-/r*_binary64_8111` `prod-exp_binary64_8211` `cbrt-unprod_binary64_8195` `add-log-exp_binary64_8201`
4×	`sqrt-div_binary64_8181`
3×	`pow-prod-down_binary64_8233` `cbrt-undiv_binary64_8196` `associate-r_binary64_8107` `flip--_binary64_8140` `flip3--_binary64_8169` `div-exp_binary64_8213`
2×	`associate-/r/_binary64_8113`
1×	`associate-l_binary64_8108` `diff-log_binary64_8254` `sub-neg_binary64_8158` `rem-sqrt-square_binary64_8178` `-commutative_binary64_8098` `frac-2neg_binary64_8176` `clear-num_binary64_8164` `associate-/l_binary64_8112` `div-inv_binary64_8162` `sqrt-pow1_binary64_8182` `pow1/2_binary64_8242`

Counts

4 → 75

Calls

4 calls:

13.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
6.0ms	(.f64 (.f64 x y) z)
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series450.0ms (7%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
110.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
52.0ms	(-.f64 (.f64 z z) (.f64 t a))
49.0ms	(.f64 (.f64 x y) z)

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5153	1466

prune100.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	10	88

Merged error: 3.3b

Counts

88 → 10

Compiler

Compiled 1824 to 376 computations (79.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
5.0b	(.f64 x (.f64 z y))
8.6b	(/.f64 (.f64 x (.f64 z y)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
25.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_8198` `add-exp-log_binary64_8200`
11×	`add-sqr-sqrt_binary64_8186`
10×	`*-un-lft-identity_binary64_8165` `pow1_binary64_8223` `add-cube-cbrt_binary64_8197`
9×	`sqrt-prod_binary64_8180`
6×	`times-frac_binary64_8171` `associate-/r*_binary64_8111` `prod-exp_binary64_8211` `cbrt-unprod_binary64_8195` `add-log-exp_binary64_8201`
4×	`sqrt-div_binary64_8181`
3×	`associate-l_binary64_8108` `pow-prod-down_binary64_8233` `cbrt-undiv_binary64_8196` `flip--_binary64_8140` `flip3--_binary64_8169` `div-exp_binary64_8213`
2×	`associate-/r/_binary64_8113`
1×	`diff-log_binary64_8254` `sub-neg_binary64_8158` `rem-sqrt-square_binary64_8178` `-commutative_binary64_8098` `frac-2neg_binary64_8176` `clear-num_binary64_8164` `associate-/l_binary64_8112` `div-inv_binary64_8162` `associate-r_binary64_8107` `sqrt-pow1_binary64_8182` `pow1/2_binary64_8242`

Counts

4 → 75

Calls

4 calls:

13.0ms	(/.f64 (.f64 x (.f64 z y)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 x (.f64 z y))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series436.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(/.f64 (.f64 x (.f64 z y)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
108.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
52.0ms	(.f64 x (.f64 z y))
51.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4980	1467
1	4980	1467

prune78.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	86	11	97

Merged error: 3.3b

Counts

97 → 11

Compiler

Compiled 1867 to 403 computations (78.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
1.1b	(.f64 x (/.f64 (.f64 z y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
9.2b	(/.f64 (.f64 z y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
25.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_8198` `add-exp-log_binary64_8200`
16×	`add-sqr-sqrt_binary64_8186`
13×	`*-un-lft-identity_binary64_8165` `add-cube-cbrt_binary64_8197`
12×	`sqrt-prod_binary64_8180` `times-frac_binary64_8171` `associate-r_binary64_8107`
7×	`pow1_binary64_8223`
6×	`associate-/r*_binary64_8111` `sqrt-div_binary64_8181` `add-log-exp_binary64_8201`
5×	`prod-exp_binary64_8211` `cbrt-unprod_binary64_8195`
4×	`cbrt-undiv_binary64_8196` `associate-/r/_binary64_8113` `flip--_binary64_8140` `flip3--_binary64_8169` `div-exp_binary64_8213`
3×	`associate-l_binary64_8108`
2×	`div-inv_binary64_8162`
1×	`diff-log_binary64_8254` `pow-prod-down_binary64_8233` `sub-neg_binary64_8158` `rem-sqrt-square_binary64_8178` `-commutative_binary64_8098` `frac-2neg_binary64_8176` `associate-r/_binary64_8109` `clear-num_binary64_8164` `associate-/l*_binary64_8112` `sqrt-pow1_binary64_8182` `pow1/2_binary64_8242` `unswap-sqr_binary64_8133`

Counts

4 → 87

Calls

4 calls:

12.0ms	(.f64 x (/.f64 (.f64 z y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
9.0ms	(/.f64 (.f64 z y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series493.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(.f64 x (/.f64 (.f64 z y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
111.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
109.0ms	(/.f64 (.f64 z y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
52.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4965	1871
1	4965	1871

prune83.0ms (1.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	99	11	110

Merged error: 3.3b

Counts

110 → 11

Compiler

Compiled 2135 to 446 computations (79.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
1.1b	(.f64 x (.f64 z (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
12.6b	(.f64 z (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
25.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_8186`
25×	`associate-r_binary64_8107`
20×	`*-un-lft-identity_binary64_8165` `times-frac_binary64_8171` `add-cube-cbrt_binary64_8197`
18×	`add-cbrt-cube_binary64_8198` `add-exp-log_binary64_8200`
13×	`sqrt-prod_binary64_8180`
12×	`pow1_binary64_8223`
7×	`prod-exp_binary64_8211` `cbrt-unprod_binary64_8195`
6×	`associate-l_binary64_8108` `add-log-exp_binary64_8201`
4×	`pow-prod-down_binary64_8233` `sqrt-div_binary64_8181`
3×	`associate-*r/_binary64_8109` `flip--_binary64_8140` `flip3--_binary64_8169` `unswap-sqr_binary64_8133`
2×	`*-commutative_binary64_8098` `cbrt-undiv_binary64_8196` `associate-/r/_binary64_8113` `div-exp_binary64_8213`
1×	`diff-log_binary64_8254` `sub-neg_binary64_8158` `rem-sqrt-square_binary64_8178` `div-inv_binary64_8162` `sqrt-pow1_binary64_8182` `pow1/2_binary64_8242`

Counts

4 → 91

Calls

4 calls:

13.0ms	(.f64 z (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
11.0ms	(.f64 x (.f64 z (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series482.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(.f64 x (.f64 z (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
115.0ms	(.f64 z (/.f64 y (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
106.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
51.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4929	1891
1	4929	1891

prune82.0ms (1.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	103	11	114

Merged error: 3.3b

Counts

114 → 11

Compiler

Compiled 2092 to 387 computations (81.5% saved)

regimes842.0ms (13%)

Compiler: Compiled 6475 to 4244 computations (34.5% saved)

bsearch35.0ms (0.5%)

Steps

Iters	Range		Point
4	8.441302553760846e+48	1.5709125518766296e+49	1.4065604657845695e+49
6	-3.090535010143132e+123	-2.5522747836066967e+122	-2.599070637400722e+122

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	73	43
1	73	43

end0.0ms (0%)

sample1.6s (24.5%)

Algorithm

1×

intervals

Results

416.0ms	8000×	body	128	valid
107.0ms	2293×	body	128	nan
42.0ms	859×	body	128	invalid

Compiler

Compiled 807 to 529 computations (34.4% saved)

Details

analyze1.1s (17.5%)

sample32.0ms (0.5%)

simplify171.0ms (2.7%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite37.0ms (0.6%)

series450.0ms (7%)

simplify56.0ms (0.9%)

prune100.0ms (1.5%)

localize11.0ms (0.2%)

rewrite33.0ms (0.5%)

series436.0ms (6.8%)

simplify54.0ms (0.8%)

prune78.0ms (1.2%)

localize10.0ms (0.2%)

rewrite38.0ms (0.6%)

series493.0ms (7.6%)

simplify71.0ms (1.1%)

prune83.0ms (1.3%)

localize11.0ms (0.2%)

rewrite43.0ms (0.7%)

series482.0ms (7.5%)

simplify82.0ms (1.3%)

prune82.0ms (1.3%)

regimes842.0ms (13%)

bsearch35.0ms (0.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (24.5%)

Profiling