Details

analyze2.3s (23.5%)

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)

sample54.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	80	valid
9.0ms	112×	body	80	nan
5.0ms	55×	body	80	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5038	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: 14.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
12.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite42.0ms (0.4%)

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` `insert-posit16` `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 → 120

Calls

4 calls:

13.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
10.0ms	(.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 (10.7%)

Counts

4 → 12

Calls

4 calls:

524.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
304.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
170.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
49.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5856	2933

prune207.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Merged error: 6.7b

Counts

133 → 9

Compiler

Compiled 3422 to 1996 computations (41.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
4.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
7.6b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`add-exp-log_binary64`
121×	`prod-exp_binary64`
43×	`div-exp_binary64`
33×	`add-cbrt-cube_binary64`
30×	`pow-exp_binary64`
23×	`associate-r_binary64` `add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
19×	`cbrt-unprod_binary64`
11×	`associate-l_binary64`
9×	`cbrt-prod_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64`
6×	`pow-to-exp_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`div-inv_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `unpow2_binary64` `sqr-pow_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 149

Calls

4 calls:

21.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
14.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

series888.0ms (9%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
309.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
197.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
48.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify174.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4966	3572
1	4966	3572

prune213.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	159	11	170

Merged error: 6.7b

Counts

170 → 11

Compiler

Compiled 4506 to 2376 computations (47.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
11.9b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`cbrt-unprod_binary64` `prod-exp_binary64`
21×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`add-sqr-sqrt_binary64`
13×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
7×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `insert-posit16`
3×	`sqrt-prod_binary64`
2×	`associate-/r_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 113

Calls

4 calls:

15.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

series527.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
123.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
48.0ms	(/.f64 (.f64 M D) (.f64 2 d))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify112.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5088	2223

prune180.0ms (1.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	121	15	136

Merged error: 5.8b

Counts

136 → 15

Compiler

Compiled 3848 to 2046 computations (46.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
7.8b	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-exp-log_binary64`
118×	`add-cbrt-cube_binary64`
73×	`cbrt-unprod_binary64` `prod-exp_binary64`
48×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
5×	`associate-r_binary64` `associate-l_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `insert-posit16`
3×	`sqrt-prod_binary64`
2×	`associate-/r_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

24.0ms	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
15.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series745.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
318.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify133.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5075	3302

prune371.0ms (3.8%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	1	11	12
Picked	0	1	1
Done	0	2	2
Total	146	16	162

Merged error: 5.8b

Counts

162 → 16

Compiler

Compiled 5740 to 2286 computations (60.2% saved)

regimes457.0ms (4.7%)

Compiler: Compiled 5379 to 4499 computations (16.4% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	122	60
1	122	60

end0.0ms (0%)

sample1.9s (19.6%)

Algorithm

1×

intervals

Results

665.0ms	8000×	body	80	valid
260.0ms	3079×	body	80	nan
112.0ms	1289×	body	80	invalid

Compiler

Compiled 509 to 417 computations (18.1% saved)

Details

analyze2.3s (23.5%)

sample54.0ms (0.6%)

simplify106.0ms (1.1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite42.0ms (0.4%)

series1.0s (10.7%)

simplify83.0ms (0.8%)

prune207.0ms (2.1%)

localize18.0ms (0.2%)

rewrite59.0ms (0.6%)

series888.0ms (9%)

simplify174.0ms (1.8%)

prune213.0ms (2.2%)

localize16.0ms (0.2%)

rewrite42.0ms (0.4%)

series527.0ms (5.4%)

simplify112.0ms (1.1%)

prune180.0ms (1.8%)

localize23.0ms (0.2%)

rewrite63.0ms (0.6%)

series745.0ms (7.6%)

simplify133.0ms (1.4%)

prune371.0ms (3.8%)

regimes457.0ms (4.7%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample1.9s (19.6%)

Profiling