Details

analyze277.0ms (7.5%)

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
31.2%	68.6%	0.1%	9
43.3%	49.9%	6.8%	10
49.7%	40.8%	9.5%	11
55.7%	34%	10.3%	12
61.3%	24.4%	14.3%	13
65%	19.8%	15.3%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	13×	body	128	invalid

Compiler

Compiled 15 to 16 computations (-6.7% saved)

simplify108.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	301	10
1	301	10

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 y x) z)
0.0b	(+.f64 x (*.f64 (-.f64 y x) z))
0.0b	(+.f64 x (*.f64 (-.f64 y x) z))
0.0b	(*.f64 (-.f64 y x) z)

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_6920`
6×	`*-un-lft-identity_binary64_6898`
5×	`associate-l_binary64_6839`
4×	`add-cube-cbrt_binary64_6933` `pow1_binary64_6959` `add-exp-log_binary64_6936` `add-log-exp_binary64_6937` `add-cbrt-cube_binary64_6934`
3×	`associate-r_binary64_6838`
2×	`associate-*l/_binary64_6841`
1×	`flip-+_binary64_6872` `prod-exp_binary64_6947` `+-commutative_binary64_6828` `distribute-lft-out--_binary64_6850` `flip3-+_binary64_6901` `flip--_binary64_6873` `unswap-sqr_binary64_6866` `cbrt-unprod_binary64_6931` `*-commutative_binary64_6829` `flip3--_binary64_6902` `sum-log_binary64_6989` `pow-prod-down_binary64_6969` `difference-of-squares_binary64_6867`

Counts

2 → 33

Calls

4 calls:

7.0ms	(*.f64 (-.f64 y x) z)
4.0ms	(+.f64 x (*.f64 (-.f64 y x) z))
0.0ms	(+.f64 x (*.f64 (-.f64 y x) z))
0.0ms	(*.f64 (-.f64 y x) z)

series218.0ms (5.9%)

Counts

2 → 33

Calls

2 calls:

122.0ms	(+.f64 x (*.f64 (-.f64 y x) z))
96.0ms	(*.f64 (-.f64 y x) z)

Compiler

Compiled 387 to 328 computations (15.2% saved)

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5343	634

prune44.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	3	67

Error

Counts

67 → 3

Compiler

Compiled 650 to 145 computations (77.7% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

21.4b	(/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x))
7.6b	(.f64 z (-.f64 (.f64 y y) (*.f64 x x)))
2.1b	(-.f64 (.f64 y y) (.f64 x x))
0.0b	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))
0.0b	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))
2.1b	(-.f64 (.f64 y y) (.f64 x x))
7.6b	(.f64 z (-.f64 (.f64 y y) (*.f64 x x)))
21.4b	(/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_6898`
11×	`add-exp-log_binary64_6936` `add-cbrt-cube_binary64_6934`
10×	`add-sqr-sqrt_binary64_6920`
8×	`add-cube-cbrt_binary64_6933` `add-log-exp_binary64_6937`
6×	`pow1_binary64_6959`
4×	`associate-r_binary64_6838` `associate-r/_binary64_6840` `associate-/r_binary64_6842` `times-frac_binary64_6904`
3×	`sub-neg_binary64_6891` `distribute-lft-out_binary64_6849` `flip--_binary64_6873` `cancel-sign-sub-inv_binary64_6864` `flip3--_binary64_6902` `associate-l_binary64_6839`
2×	`flip-+_binary64_6872` `prod-exp_binary64_6947` `div-exp_binary64_6949` `flip3-+_binary64_6901` `cbrt-undiv_binary64_6932` `associate-/r/_binary64_6844` `distribute-lft-in_binary64_6847` `cbrt-unprod_binary64_6931` `difference-of-squares_binary64_6867` `associate-/l/_binary64_6845` `distribute-rgt-in_binary64_6848`
1×	`+-commutative_binary64_6828` `unswap-sqr_binary64_6866` `-commutative_binary64_6829` `clear-num_binary64_6897` `sum-log_binary64_6989` `pow-prod-down_binary64_6969` `frac-2neg_binary64_6909` `div-inv_binary64_6895` `diff-log_binary64_6990` `associate-/l_binary64_6843`

Counts

4 → 77

Calls

8 calls:

10.0ms	(/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x))
7.0ms	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))
7.0ms	(.f64 z (-.f64 (.f64 y y) (*.f64 x x)))
4.0ms	(-.f64 (.f64 y y) (.f64 x x))
0.0ms	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))

series861.0ms (23.4%)

Counts

4 → 60

Calls

4 calls:

365.0ms	(+.f64 x (/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x)))
228.0ms	(/.f64 (.f64 z (-.f64 (.f64 y y) (*.f64 x x))) (+.f64 y x))
177.0ms	(.f64 z (-.f64 (.f64 y y) (*.f64 x x)))
90.0ms	(-.f64 (.f64 y y) (.f64 x x))

Compiler

Compiled 1149 to 912 computations (20.6% saved)

simplify47.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5154	1774

prune82.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	137	3	140

Error

Counts

140 → 3

Compiler

Compiled 2085 to 476 computations (77.2% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (sqrt.f64 (.f64 (-.f64 y x) z)) (sqrt.f64 (*.f64 (-.f64 y x) z)))
0.0b	(*.f64 (-.f64 y x) z)
0.0b	(*.f64 (-.f64 y x) z)
0.0b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y x) z)) (sqrt.f64 (*.f64 (-.f64 y x) z))))
0.0b	(*.f64 (-.f64 y x) z)
0.3b	(.f64 (sqrt.f64 (.f64 (-.f64 y x) z)) (sqrt.f64 (*.f64 (-.f64 y x) z)))
2.2b	(sqrt.f64 (*.f64 (-.f64 y x) z))
2.2b	(sqrt.f64 (*.f64 (-.f64 y x) z))

rewrite43.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64_6959`
32×	`sqrt-pow1_binary64_6916`
23×	`pow-prod-down_binary64_6969`
20×	`associate-*l/_binary64_6841`
16×	`add-sqr-sqrt_binary64_6920` `sqrt-div_binary64_6915`
12×	`*-un-lft-identity_binary64_6898` `pow1/2_binary64_6978`
10×	`add-cube-cbrt_binary64_6933` `pow-prod-up_binary64_6968`
9×	`flip--_binary64_6873` `flip3--_binary64_6902` `associate-l_binary64_6839`
8×	`add-exp-log_binary64_6936` `add-cbrt-cube_binary64_6934`
7×	`associate-r_binary64_6838`
6×	`pow-sqr_binary64_6871` `sqrt-prod_binary64_6914`
4×	`swap-sqr_binary64_6865` `add-log-exp_binary64_6937` `frac-times_binary64_6908`
2×	`prod-exp_binary64_6947` `unswap-sqr_binary64_6866` `cbrt-unprod_binary64_6931` `associate-r/_binary64_6840` `-commutative_binary64_6829`
1×	`pow2_binary64_6979` `sqrt-unprod_binary64_6918` `distribute-lft-out--_binary64_6850` `pow-plus_binary64_6961` `difference-of-squares_binary64_6867` `rem-square-sqrt_binary64_6910`

Counts

4 → 105

Calls

8 calls:

16.0ms	(.f64 (sqrt.f64 (.f64 (-.f64 y x) z)) (sqrt.f64 (*.f64 (-.f64 y x) z)))
7.0ms	(*.f64 (-.f64 y x) z)
5.0ms	(sqrt.f64 (*.f64 (-.f64 y x) z))
5.0ms	(sqrt.f64 (*.f64 (-.f64 y x) z))
0.0ms	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y x) z)) (sqrt.f64 (*.f64 (-.f64 y x) z))))

series370.0ms (10.1%)

Counts

4 → 51

Calls

4 calls:

102.0ms	(.f64 (sqrt.f64 (.f64 (-.f64 y x) z)) (sqrt.f64 (*.f64 (-.f64 y x) z)))
97.0ms	(*.f64 (-.f64 y x) z)
86.0ms	(sqrt.f64 (*.f64 (-.f64 y x) z))
84.0ms	(sqrt.f64 (*.f64 (-.f64 y x) z))

Compiler

Compiled 1713 to 1268 computations (26% saved)

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4994	1514
1	4994	1514

prune96.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	156	3	159

Error

Counts

159 → 3

Compiler

Compiled 2410 to 507 computations (79% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	136
1	84	136

regimes85.0ms (2.3%)

Compiler: Compiled 384 to 362 computations (5.7% saved)

bsearch0.0ms (0%)

regimes104.0ms (2.8%)

Compiler: Compiled 72 to 120 computations (-66.7% saved)

bsearch29.0ms (0.8%)

Steps

Iters	Range		Point
8	0.0008356622548412558	1.915248178685038	1.018067930420241
10	-1.3151073853382249e+36	-8.865335787368739e+24	-8.953042990058884e+24

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes114.0ms (3.1%)

Compiler: Compiled 57 to 105 computations (-84.2% saved)

bsearch23.0ms (0.6%)

Steps

Iters	Range		Point
9	6.8460523085683435e-65	1.1387647867507897e-57	1.3690179349825641e-58
6	-9.750173532991806e-09	-7.693910810081602e-10	-2.1722713831908392e-09

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes97.0ms (2.6%)

Compiler: Compiled 42 to 90 computations (-114.3% saved)

bsearch22.0ms (0.6%)

Steps

Iters	Range		Point
9	6.8460523085683435e-65	1.1387647867507897e-57	1.3690179349825641e-58
6	-9.750173532991806e-09	-7.693910810081602e-10	-7.82692955336557e-10

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes91.0ms (2.5%)

Compiler: Compiled 27 to 75 computations (-177.8% saved)

bsearch24.0ms (0.7%)

Steps

Iters	Range		Point
9	6.8460523085683435e-65	1.1387647867507897e-57	3.581400428508114e-58
6	-9.750173532991806e-09	-7.693910810081602e-10	-7.82692955336557e-10

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes29.0ms (0.8%)

Compiler: Compiled 18 to 63 computations (-250% saved)

bsearch0.0ms (0%)

regimes24.0ms (0.7%)

Accuracy

Total 0.0b remaining (44.7%)

Threshold costs 0.0b (44.7%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 89 to 60 computations (32.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	77	109
1	77	109

end0.0ms (0%)

sample688.0ms (18.7%)

Algorithm

1×

intervals

Results

203.0ms	8000×	body	128	valid
17.0ms	576×	body	128	invalid

Compiler

Compiled 174 to 157 computations (9.8% saved)

Pareto

0.2062379192755784

Details

analyze277.0ms (7.5%)

sample15.0ms (0.4%)

simplify108.0ms (2.9%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite14.0ms (0.4%)

series218.0ms (5.9%)

simplify40.0ms (1.1%)

prune44.0ms (1.2%)

localize10.0ms (0.3%)

rewrite37.0ms (1%)

series861.0ms (23.4%)

simplify47.0ms (1.3%)

prune82.0ms (2.2%)

localize8.0ms (0.2%)

rewrite43.0ms (1.2%)

series370.0ms (10.1%)

simplify61.0ms (1.7%)

prune96.0ms (2.6%)

simplify4.0ms (0.1%)

regimes85.0ms (2.3%)

bsearch0.0ms (0%)

regimes104.0ms (2.8%)

bsearch29.0ms (0.8%)

regimes114.0ms (3.1%)

bsearch23.0ms (0.6%)

regimes97.0ms (2.6%)

bsearch22.0ms (0.6%)

regimes91.0ms (2.5%)

bsearch24.0ms (0.7%)

regimes29.0ms (0.8%)

bsearch0.0ms (0%)

regimes24.0ms (0.7%)

bsearch5.0ms (0.1%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample688.0ms (18.7%)

Profiling