Details

analyze2.2s (21.4%)

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)

sample65.0ms (0.6%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
5.0ms	63×	body	128	nan
3.0ms	27×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify261.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	806	21
1	806	21

prune5.0ms (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: 24.5b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
4.6b	(.f64 (.f64 x y) z)
9.2b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite62.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
11×	`add-sqr-sqrt_binary64_9648`
10×	`add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626` `pow1_binary64_9687`
9×	`sqrt-prod_binary64_9642`
6×	`times-frac_binary64_9632` `add-log-exp_binary64_9665` `prod-exp_binary64_9675` `associate-/r*_binary64_9570` `cbrt-unprod_binary64_9659`
4×	`sqrt-div_binary64_9643`
3×	`flip3--_binary64_9630` `div-exp_binary64_9677` `pow-prod-down_binary64_9697` `flip--_binary64_9601` `cbrt-undiv_binary64_9660` `associate-r_binary64_9566`
2×	`associate-/r/_binary64_9572`
1×	`rem-sqrt-square_binary64_9639` `associate-l_binary64_9567` `sub-neg_binary64_9619` `diff-log_binary64_9718` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `-commutative_binary64_9557` `associate-/l_binary64_9571` `frac-2neg_binary64_9637` `cancel-sign-sub-inv_binary64_9592` `div-inv_binary64_9623` `clear-num_binary64_9625`

Counts

4 → 76

Calls

4 calls:

26.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
10.0ms	(.f64 (.f64 x y) z)
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
7.0ms	(-.f64 (.f64 z z) (.f64 t a))

series427.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
99.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
48.0ms	(-.f64 (.f64 z z) (.f64 t a))
47.0ms	(.f64 (.f64 x y) z)

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5138	1472

prune175.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Merged error: 4.1b

Counts

89 → 10

Compiler

Compiled 1775 to 366 computations (79.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
1.0b	(-.f64 (.f64 z z) (.f64 t a))
2.9b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite74.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_9632`
34×	`add-sqr-sqrt_binary64_9648`
33×	`add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
24×	`sqrt-prod_binary64_9642` `associate-r_binary64_9566`
18×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
10×	`pow1_binary64_9687`
6×	`add-log-exp_binary64_9665` `prod-exp_binary64_9675` `sqrt-div_binary64_9643` `associate-/r*_binary64_9570` `cbrt-unprod_binary64_9659`
4×	`flip3--_binary64_9630` `flip--_binary64_9601` `associate-/r/_binary64_9572`
3×	`div-exp_binary64_9677` `pow-prod-down_binary64_9697` `cbrt-undiv_binary64_9660` `associate-/l*_binary64_9571`
2×	`div-inv_binary64_9623`
1×	`rem-sqrt-square_binary64_9639` `associate-l_binary64_9567` `sub-neg_binary64_9619` `diff-log_binary64_9718` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `-commutative_binary64_9557` `frac-2neg_binary64_9637` `cancel-sign-sub-inv_binary64_9592` `clear-num_binary64_9625` `associate-r/_binary64_9568`

Counts

4 → 112

Calls

4 calls:

26.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
13.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
7.0ms	(-.f64 (.f64 z z) (.f64 t a))

series443.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
92.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
71.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
51.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify150.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5326	2521

prune181.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	8	8
Picked	1	0	1
Done	1	0	1
Total	122	12	134

Merged error: 3.6b

Counts

134 → 12

Compiler

Compiled 2872 to 543 computations (81.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 z z) (.f64 t a))
1.7b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
1.7b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite82.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_9648`
25×	`associate-r_binary64_9566`
20×	`times-frac_binary64_9632` `add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
18×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
13×	`sqrt-prod_binary64_9642`
12×	`pow1_binary64_9687`
7×	`prod-exp_binary64_9675` `cbrt-unprod_binary64_9659`
6×	`associate-l_binary64_9567` `add-log-exp_binary64_9665`
4×	`pow-prod-down_binary64_9697` `sqrt-div_binary64_9643`
3×	`flip3--_binary64_9630` `flip--_binary64_9601` `unswap-sqr_binary64_9594` `associate-*r/_binary64_9568`
2×	`div-exp_binary64_9677` `*-commutative_binary64_9557` `cbrt-undiv_binary64_9660` `associate-/r/_binary64_9572`
1×	`rem-sqrt-square_binary64_9639` `sub-neg_binary64_9619` `diff-log_binary64_9718` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706` `cancel-sign-sub-inv_binary64_9592` `div-inv_binary64_9623`

Counts

4 → 92

Calls

4 calls:

29.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
22.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
8.0ms	(-.f64 (.f64 z z) (.f64 t a))
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series488.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
125.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
87.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
51.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5059	1897

prune162.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	103	13	116

Merged error: 3.6b

Counts

116 → 13

Compiler

Compiled 2323 to 540 computations (76.8% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.6b	(cbrt.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_9657`
23×	`add-sqr-sqrt_binary64_9648`
20×	`add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
18×	`times-frac_binary64_9632` `sqrt-prod_binary64_9642`
8×	`sqrt-div_binary64_9643`
7×	`pow1_binary64_9687`
4×	`flip3--_binary64_9630` `add-log-exp_binary64_9665` `flip--_binary64_9601` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
3×	`rem-sqrt-square_binary64_9639` `sqrt-pow1_binary64_9644` `pow1/2_binary64_9706`
2×	`associate-/r/_binary64_9572`
1×	`pow1/3_binary64_9708` `cbrt-div_binary64_9658` `div-inv_binary64_9623`

Counts

4 → 78

Calls

4 calls:

13.0ms	(cbrt.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series490.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
106.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
85.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
85.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify173.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4847	1998
1	4847	1998

prune180.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	90	13	103

Merged error: 3.6b

Counts

103 → 13

Compiler

Compiled 4204 to 535 computations (87.3% saved)

regimes1.3s (13%)

Compiler: Compiled 5396 to 3548 computations (34.2% saved)

bsearch172.0ms (1.7%)

Steps

Iters	Range	Point
6	4.5616761800950534e+117	4.534677235688088e+118	2.456100249180412e+118
9	-8.494172414618244e-307	2.968296435483714e-303	6.724224666826136e-307
10	-3.588302038806949e+99	-1.8294345800465724e+85	-1.1701128116145023e+88

Iters

Range

Point

4.5616761800950534e+117

4.534677235688088e+118

2.456100249180412e+118

-8.494172414618244e-307

2.968296435483714e-303

6.724224666826136e-307

-3.588302038806949e+99

-1.8294345800465724e+85

-1.1701128116145023e+88

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	81	88
1	81	88

end0.0ms (0%)

sample2.7s (26.8%)

Algorithm

1×

intervals

Results

767.0ms	8000×	body	128	valid
202.0ms	2157×	body	128	nan
84.0ms	840×	body	128	invalid

Compiler

Compiled 698 to 448 computations (35.8% saved)

Details

analyze2.2s (21.4%)

sample65.0ms (0.6%)

simplify261.0ms (2.6%)

prune5.0ms (0%)

localize20.0ms (0.2%)

rewrite62.0ms (0.6%)

series427.0ms (4.2%)

simplify101.0ms (1%)

prune175.0ms (1.7%)

localize20.0ms (0.2%)

rewrite74.0ms (0.7%)

series443.0ms (4.3%)

simplify150.0ms (1.5%)

prune181.0ms (1.8%)

localize20.0ms (0.2%)

rewrite82.0ms (0.8%)

series488.0ms (4.8%)

simplify102.0ms (1%)

prune162.0ms (1.6%)

localize29.0ms (0.3%)

rewrite57.0ms (0.6%)

series490.0ms (4.8%)

simplify173.0ms (1.7%)

prune180.0ms (1.8%)

regimes1.3s (13%)

bsearch172.0ms (1.7%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.7s (26.8%)

Profiling