Details

analyze2.2s (23.1%)

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)

sample46.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	82×	body	128	nan
3.0ms	40×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5037	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: 15.8b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
5.0b	(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))
10.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite47.0ms (0.5%)

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:

16.0ms	(.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)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.0s (10.6%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
297.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
165.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
43.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5528	2845

prune180.0ms (1.9%)

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: 8.3b

Counts

129 → 8

Compiler

Compiled 3325 to 1934 computations (41.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
5.5b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.8b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite43.0ms (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))

series989.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

584.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
205.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
159.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
41.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4996	2183
1	4996	2183

prune148.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Merged error: 7.8b

Counts

119 → 8

Compiler

Compiled 2763 to 1765 computations (36.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.5b	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
5.7b	(.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))

series337.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(/.f64 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) (/.f64 (.f64 M D) (.f64 2 d))) l)
87.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
45.0ms	(/.f64 (.f64 M D) (.f64 2 d))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5235	3130

prune209.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	165	8	173

Merged error: 7.8b

Counts

173 → 8

Compiler

Compiled 4376 to 2547 computations (41.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.8b	(/.f64 M (/.f64 2 (/.f64 D d)))
5.0b	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
5.5b	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
5.8b	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))

rewrite194.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

735×	`times-frac_binary64`
366×	`add-sqr-sqrt_binary64`
347×	`*-un-lft-identity_binary64`
344×	`add-cube-cbrt_binary64`
142×	`associate-r_binary64`
141×	`unpow-prod-down_binary64`
55×	`add-exp-log_binary64`
47×	`associate-/r*_binary64`
31×	`div-inv_binary64`
25×	`div-exp_binary64`
20×	`add-cbrt-cube_binary64`
12×	`prod-exp_binary64`
9×	`associate-/r/_binary64`
8×	`cbrt-undiv_binary64` `pow-exp_binary64`
7×	`unswap-sqr_binary64`
6×	`sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`associate-l_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_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 → 407

Calls

4 calls:

64.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
38.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
18.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))

series935.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

554.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
183.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
156.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
41.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

419 → 419

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5196	9905

prune713.0ms (7.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	417	2	419
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	419	8	427

Merged error: 7.8b

Counts

427 → 8

Compiler

Compiled 12348 to 6839 computations (44.6% saved)

regimes296.0ms (3.1%)

Compiler: Compiled 2670 to 2395 computations (10.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 12 computations (-33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	121
1	101	121

end0.0ms (0%)

sample1.7s (17.8%)

Algorithm

1×

intervals

Results

616.0ms	8000×	body	128	valid
259.0ms	3135×	body	128	nan
109.0ms	1330×	body	128	invalid

Compiler

Compiled 311 to 264 computations (15.1% saved)

Details

analyze2.2s (23.1%)

sample46.0ms (0.5%)

simplify45.0ms (0.5%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite47.0ms (0.5%)

series1.0s (10.6%)

simplify53.0ms (0.6%)

prune180.0ms (1.9%)

localize15.0ms (0.2%)

rewrite43.0ms (0.5%)

series989.0ms (10.4%)

simplify57.0ms (0.6%)

prune148.0ms (1.5%)

localize15.0ms (0.2%)

rewrite72.0ms (0.8%)

series337.0ms (3.5%)

simplify85.0ms (0.9%)

prune209.0ms (2.2%)

localize14.0ms (0.2%)

rewrite194.0ms (2%)

series935.0ms (9.8%)

simplify109.0ms (1.1%)

prune713.0ms (7.5%)

regimes296.0ms (3.1%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.7s (17.8%)

Profiling