Details

analyze3.2s (25.5%)

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 25 to 19 computations (24% saved)

sample68.0ms (0.5%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
9.0ms	103×	body	128	nan
3.0ms	38×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

645×	`distribute-neg-frac_binary64`
581×	`distribute-rgt-neg-in_binary64`
418×	`associate-/l*_binary64`
372×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	723	27
4	2855	27
5	4994	27

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

10.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 48 to 36 computations (25% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.6b	(/.f64 (.f64 M D) (.f64 2 d))
8.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite268.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

24×	`add-exp-log_binary64`
24×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
18×	`pow1_binary64`

Counts

4 → 169

Calls

4 calls:

19.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
18.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
15.0ms	(/.f64 (.f64 M D) (.f64 2 d))
15.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 4137 to 2444 computations (40.9% saved)

series359.0ms (2.9%)

Error

6.3b

Counts

4 → 73

Calls

4 calls:

144.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
91.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
82.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
21.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4634 to 3514 computations (24.2% saved)

simplify154.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-def_binary64`
326×	`unswap-sqr_binary64`
243×	`associate-r_binary64`
221×	`associate-l_binary64`
191×	`cancel-sign-sub-inv_binary64`

Counts

242 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4838
1	699	4629
2	2773	4563
3	4923	4563
4	5224	4563

prune156.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	141	14	155
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	14	156

Error

5.5b

Counts

156 → 14

Alt Table

Status	Error	Program
	10.9b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
▶	9.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2)) l))))
	14.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	36.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 (/.f64 h l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 (/.f64 h l)))))))
	36.3b	(.f64 (cbrt.f64 (.f64 w0 (.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))) w0))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) (neg.f64 (/.f64 l h))))))
	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (/.f64 h l) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2))))))
	10.9b	(.f64 w0 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 D -2) (/.f64 M d))) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	61.7b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))

Compiler

Compiled 3734 to 2197 computations (41.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) l)))
4.3b	(.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2))
4.3b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) l)
4.6b	(/.f64 (.f64 D M) (.f64 2 d))

rewrite371.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

27×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64`

Counts

4 → 167

Calls

4 calls:

19.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) l)
19.0ms	(/.f64 (.f64 D M) (.f64 2 d))
15.0ms	(.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2))
13.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) l)))

Compiler

Compiled 3728 to 2350 computations (37% saved)

series298.0ms (2.4%)

Error

5.5b

Counts

4 → 58

Calls

4 calls:

92.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) l)
79.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) l)))
66.0ms	(.f64 h (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2))
23.0ms	(/.f64 (.f64 D M) (.f64 2 d))

Compiler

Compiled 3440 to 2652 computations (22.9% saved)

simplify136.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary64`
289×	`unswap-sqr_binary64`
252×	`distribute-rgt-neg-in_binary64`
246×	`distribute-lft-neg-in_binary64`
216×	`times-frac_binary64`

Counts

225 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	3834
1	536	3670
2	2200	3636
3	4870	3631
4	5318	3631

prune211.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	144	13	157

Error

4.7b

Counts

157 → 13

Alt Table

Status	Error	Program
▶	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2)) l))))
	10.9b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 D (/.f64 2 (/.f64 M d))) 2)) l))))
	35.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (sqrt.f64 h))) l))))
	14.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (/.f64 h l) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2))))))
	9.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (cbrt.f64 h))) l))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) (neg.f64 (/.f64 l h))))))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 D -2) (/.f64 M d))) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	61.7b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))

Compiler

Compiled 3180 to 2009 computations (36.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.6b	(/.f64 (.f64 D M) (.f64 d 2))
4.6b	(/.f64 (.f64 D M) (.f64 d 2))
17.9b	(cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d)))
17.9b	(cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2)))

rewrite379.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

24×	`add-exp-log_binary64`
24×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`cbrt-div_binary64`

Counts

4 → 162

Calls

4 calls:

18.0ms	(/.f64 (.f64 D M) (.f64 d 2))
16.0ms	(/.f64 (.f64 D M) (.f64 d 2))
13.0ms	(cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2)))
12.0ms	(cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d)))

Compiler

Compiled 4905 to 2928 computations (40.3% saved)

series231.0ms (1.9%)

Error

4.7b

Counts

4 → 36

Calls

4 calls:

74.0ms	(cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d)))
68.0ms	(cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2)))
27.0ms	(/.f64 (.f64 D M) (.f64 d 2))
26.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 4092 to 2789 computations (31.8% saved)

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-/l*_binary64`
545×	`associate-l_binary64`
431×	`associate-r_binary64`
336×	`associate-*l/_binary64`
268×	`associate-*r/_binary64`

Counts

198 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	2304
1	309	2122
2	862	2004
3	4564	2000
4	5256	2000

prune240.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	131	13	144

Error

4.6b

Counts

144 → 13

Alt Table

Status	Error	Program
✓	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2)) l))))
	10.9b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 D (/.f64 2 (/.f64 M d))) 2)) l))))
	35.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (sqrt.f64 h))) l))))
	14.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	26.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (.f64 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (/.f64 D d))) M)) (cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2)) l))))
	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (/.f64 h l) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2))))))
▶	9.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (cbrt.f64 h))) l))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) (neg.f64 (/.f64 l h))))))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 D -2) (/.f64 M d))) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))

Compiler

Compiled 4507 to 2780 computations (38.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h)))
3.5b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h))) l)))
4.3b	(/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h))) l)
4.6b	(/.f64 (.f64 D M) (.f64 d 2))

rewrite448.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

4.6b

Rules

30×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64`

Counts

4 → 167

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h)))
21.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h))) l)
18.0ms	(/.f64 (.f64 D M) (.f64 d 2))
12.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h))) l)))

Compiler

Compiled 5034 to 2538 computations (49.6% saved)

series330.0ms (2.7%)

Error

4.6b

Counts

4 → 58

Calls

4 calls:

107.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h))) l)
94.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h))) l)))
74.0ms	(.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 d 2)) 2) (cbrt.f64 h)))
28.0ms	(/.f64 (.f64 D M) (.f64 d 2))

Compiler

Compiled 3662 to 2786 computations (23.9% saved)

simplify151.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

399×	`unswap-sqr_binary64`
303×	`fma-def_binary64`
274×	`times-frac_binary64`
201×	`associate-r_binary64`
199×	`associate-/l*_binary64`

Counts

225 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	5154
1	614	3784
2	2677	3718
3	4908	3718
4	5087	3718

prune219.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	131	13	144

Error

4.6b

Counts

144 → 13

Alt Table

Status	Error	Program
	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2)) l))))
	10.9b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 D (/.f64 2 (/.f64 M d))) 2)) l))))
	35.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 d 2)) (sqrt.f64 h))) l))))
	14.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	26.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (.f64 (log.f64 (pow.f64 (sqrt.f64 (exp.f64 (/.f64 D d))) M)) (cbrt.f64 (/.f64 (.f64 D M) (.f64 d 2))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2)) l))))
	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (/.f64 h l) (pow.f64 (cbrt.f64 (/.f64 (.f64 D M) (.f64 2 d))) 2))))))
	9.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 d 2)) 2) (cbrt.f64 h))) l))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2)) (neg.f64 (/.f64 l h))))))
	61.5b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 D -2) (/.f64 M d))) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
	61.4b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))

Compiler

Compiled 2705 to 1623 computations (40% saved)

regimes2.5s (19.9%)

Accuracy

Total 3.9b remaining (40.4%)

Threshold costs 0b (0%)

Compiler

Compiled 72294 to 51267 computations (29.1% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	106
1	54	106
2	60	106
3	70	106
4	83	106
5	98	106
6	110	106
7	124	106
8	132	106
9	137	106
10	139	106
11	138	106

end10.0ms (0.1%)

Compiler: Compiled 228 to 144 computations (36.8% saved)

sample2.5s (20.3%)

Algorithm

1×

intervals

Results

791.0ms	8000×	body	128	valid
292.0ms	3211×	body	128	nan
131.0ms	1344×	body	128	invalid

Compiler

Compiled 586 to 403 computations (31.2% saved)

Iter	Nodes	Cost
0	43	106
1	54	106
2	60	106
3	70	106
4	83	106
5	98	106
6	110	106
7	124	106
8	132	106
9	137	106
10	139	106
11	138	106

Iter	Nodes	Cost
0	43	106
1	54	106
2	60	106
3	70	106
4	83	106
5	98	106
6	110	106
7	124	106
8	132	106
9	137	106
10	139	106
11	138	106

Details

analyze3.2s (25.5%)

sample68.0ms (0.5%)

simplify32.0ms (0.3%)

prune2.0ms (0%)

localize13.0ms (0.1%)

rewrite268.0ms (2.2%)

series359.0ms (2.9%)

simplify154.0ms (1.2%)

prune156.0ms (1.3%)

localize13.0ms (0.1%)

rewrite371.0ms (3%)

series298.0ms (2.4%)

simplify136.0ms (1.1%)

prune211.0ms (1.7%)

localize21.0ms (0.2%)

rewrite379.0ms (3.1%)

series231.0ms (1.9%)

simplify97.0ms (0.8%)

prune240.0ms (1.9%)

localize18.0ms (0.1%)

rewrite448.0ms (3.6%)

series330.0ms (2.7%)

simplify151.0ms (1.2%)

prune219.0ms (1.8%)

regimes2.5s (19.9%)

bsearch7.0ms (0.1%)

simplify9.0ms (0.1%)

end10.0ms (0.1%)

sample2.5s (20.3%)

Profiling

Iter	Nodes	Cost
0	43	106
1	54	106
2	60	106
3	70	106
4	83	106
5	98	106
6	110	106
7	124	106
8	132	106
9	137	106
10	139	106
11	138	106