Details

analyze2.2s (29.3%)

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)

sample55.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	80	valid
12.0ms	100×	body	80	nan
5.0ms	61×	body	80	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5466	27

prune7.0ms (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

Merged error: 13.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.7b	(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))
8.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite36.0ms (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:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
9.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series203.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
63.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
31.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4985	2845
1	4985	2845

prune167.0ms (2.2%)

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: 8.0b

Counts

129 → 8

Compiler

Compiled 3291 to 1911 computations (41.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.2b	(/.f64 (.f64 M D) (.f64 2 d))
16.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
16.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
16.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `times-frac_binary64` `div-inv_binary64` `div-exp_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64`
1×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 63

Calls

4 calls:

7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
4.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
4.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

series84.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
26.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
24.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4972	1120
1	4972	1120

prune123.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 8.0b

Counts

83 → 9

Compiler

Compiled 3422 to 2113 computations (38.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.1b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
4.7b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
5.4b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
40×	`div-exp_binary64`
30×	`add-cbrt-cube_binary64`
25×	`pow-exp_binary64`
23×	`associate-r_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`cbrt-unprod_binary64` `times-frac_binary64`
8×	`1-exp_binary64` `rec-exp_binary64`
7×	`pow1_binary64`
6×	`cbrt-undiv_binary64` `unpow-prod-down_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64`
3×	`div-inv_binary64` `sqrt-prod_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `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` `un-div-inv_binary64` `flip--_binary64`

Counts

4 → 130

Calls

4 calls:

11.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))

series201.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
55.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
35.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5194	2770

prune168.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	141	10	151

Merged error: 7.5b

Counts

151 → 10

Compiler

Compiled 3547 to 2352 computations (33.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.2b	(/.f64 (.f64 M D) (.f64 2 d))
16.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
16.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
16.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `times-frac_binary64` `div-inv_binary64` `div-exp_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64`
1×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 63

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

series82.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
24.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
24.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4972	1120
1	4972	1120

prune107.0ms (1.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	75	10	85

Merged error: 7.5b

Counts

85 → 10

Compiler

Compiled 3398 to 2177 computations (35.9% saved)

regimes961.0ms (12.6%)

Compiler: Compiled 2921 to 2729 computations (6.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	81	70
1	81	70

end0.0ms (0%)

sample2.6s (34.2%)

Algorithm

1×

intervals

Results

609.0ms	8000×	body	80	valid
245.0ms	3127×	body	80	nan
110.0ms	1358×	body	80	invalid

Compiler

Compiled 319 to 286 computations (10.3% saved)

Details

analyze2.2s (29.3%)

sample55.0ms (0.7%)

simplify47.0ms (0.6%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

rewrite36.0ms (0.5%)

series203.0ms (2.7%)

simplify108.0ms (1.4%)

prune167.0ms (2.2%)

localize20.0ms (0.3%)

rewrite22.0ms (0.3%)

series84.0ms (1.1%)

simplify102.0ms (1.3%)

prune123.0ms (1.6%)

localize14.0ms (0.2%)

rewrite37.0ms (0.5%)

series201.0ms (2.6%)

simplify83.0ms (1.1%)

prune168.0ms (2.2%)

localize21.0ms (0.3%)

rewrite22.0ms (0.3%)

series82.0ms (1.1%)

simplify101.0ms (1.3%)

prune107.0ms (1.4%)

regimes961.0ms (12.6%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.6s (34.2%)

Profiling