Details

analyze2.4s (28.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
7.0ms	93×	body	128	nan
4.0ms	45×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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: 13.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
10.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64` `div-exp_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`times-frac_binary64`
13×	`associate-l_binary64`
10×	`unswap-sqr_binary64` `pow-exp_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 116

Calls

4 calls:

18.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.0s (12.1%)

Counts

4 → 12

Calls

4 calls:

517.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
305.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
162.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5598	2845

prune303.0ms (3.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 7.2b

Counts

129 → 8

Compiler

Compiled 5776 to 4001 computations (30.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
3.8b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
4.6b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
26×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64` `div-exp_binary64`
13×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64` `add-cube-cbrt_binary64` `pow-exp_binary64`
6×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64` `times-frac_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-l_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series978.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

586.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
183.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
165.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5309	2178

prune172.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	112	7	119

Merged error: 7.2b

Counts

119 → 7

Compiler

Compiled 3345 to 2287 computations (31.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.8b	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
4.5b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite72.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
116×	`cbrt-unprod_binary64` `prod-exp_binary64`
87×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `times-frac_binary64`
5×	`associate-/r_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `associate-*l/_binary64`
3×	`associate-/l/_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 153

Calls

4 calls:

20.0ms	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
9.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series354.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
98.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))
41.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify87.0ms (1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5237	3130

prune233.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	164	8	172

Merged error: 7.0b

Counts

172 → 8

Compiler

Compiled 4760 to 2886 computations (39.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.5b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
5.1b	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
21×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`div-inv_binary64`
7×	`associate-/l*_binary64`
6×	`pow1_binary64`
5×	`associate-/r_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `unswap-sqr_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

9.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
9.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series254.0ms (3%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
79.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
43.0ms	(/.f64 (.f64 M D) (.f64 2 d))
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4949	1882
1	4949	1882

prune149.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	127	8	135

Merged error: 7.0b

Counts

135 → 8

Compiler

Compiled 3565 to 1959 computations (45% saved)

regimes300.0ms (3.5%)

Compiler: Compiled 2320 to 2174 computations (6.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 10 computations (-42.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	93	52
1	93	52

end0.0ms (0%)

sample1.7s (19.9%)

Algorithm

1×

intervals

Results

620.0ms	8000×	body	128	valid
257.0ms	3086×	body	128	nan
118.0ms	1388×	body	128	invalid

Compiler

Compiled 241 to 216 computations (10.4% saved)

Details

analyze2.4s (28.2%)

sample48.0ms (0.6%)

simplify44.0ms (0.5%)

prune3.0ms (0%)

localize18.0ms (0.2%)

rewrite50.0ms (0.6%)

series1.0s (12.1%)

simplify56.0ms (0.7%)

prune303.0ms (3.6%)

localize13.0ms (0.2%)

rewrite40.0ms (0.5%)

series978.0ms (11.5%)

simplify61.0ms (0.7%)

prune172.0ms (2%)

localize13.0ms (0.2%)

rewrite72.0ms (0.8%)

series354.0ms (4.2%)

simplify87.0ms (1%)

prune233.0ms (2.7%)

localize17.0ms (0.2%)

rewrite44.0ms (0.5%)

series254.0ms (3%)

simplify73.0ms (0.9%)

prune149.0ms (1.7%)

regimes300.0ms (3.5%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.7s (19.9%)

Profiling