Details

analyze2.2s (10.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 41 to 32 computations (22% saved)

sample5.8s (28.6%)

Alt Table

Status	Error	Program
▶	25.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))

Symmetry

(sort M D)

Results

3.5s	13402×	body	128	invalid
2.2s	8256×	body	128	valid

Compiler

Compiled 202 to 157 computations (22.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
✓	10.4b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	10.9b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	11.8b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

series1.3s (6.6%)

Counts

4 → 144

Calls

4 calls:

400.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
381.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
331.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
219.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

rewrite72.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

427×	`log1p-udef_binary64`
242×	`add-sqr-sqrt_binary64`
232×	`log1p-expm1-u_binary64`
232×	`expm1-log1p-u_binary64`
227×	`add-cbrt-cube_binary64`

Counts

4 → 65

Calls

4 calls:

69.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
69.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
69.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
69.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	74
1	507	73
2	4698	73
3	5555	73
0	0	0
1	0	0

prune306.0ms (1.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	193	16	209
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	16	210

Error

9.3b

Counts

210 → 16

Alt Table

Status	Error	Program
	25.3b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	61.2b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l)))))
	34.2b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l)))) 1)
	25.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	25.3b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (/.f64 d l) 1/4) (pow.f64 (/.f64 d l) 1/4))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	42.1b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	45.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	39.5b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
▶	24.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	39.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 l) 1/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	39.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	25.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 d l)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 d l)) 1/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	25.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))) 2)))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	25.4b	(.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 1/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))

Compiler

Compiled 8220 to 5442 computations (33.8% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
✓	5.9b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)
✓	10.4b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	10.9b	(pow.f64 (/.f64 d h) (/.f64 1 2))

series1.4s (6.9%)

Counts

4 → 144

Calls

4 calls:

463.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
421.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
270.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
252.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)

rewrite71.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

241×	`add-sqr-sqrt_binary64`
231×	`log1p-expm1-u_binary64`
231×	`expm1-log1p-u_binary64`
226×	`add-cbrt-cube_binary64`
226×	`add-log-exp_binary64`

Counts

4 → 73

Calls

4 calls:

69.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
69.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)
69.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
69.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	74
1	505	73
2	4756	73
3	4884	73
0	0	0
1	0	0

prune313.0ms (1.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	206	11	217
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	216	17	233

Error

8.1b

Counts

233 → 17

Alt Table

Status	Error	Program
	24.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 l (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)))) -1)))
	25.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) h) l)))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
▶	24.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	45.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (exp.f64 (.f64 1/2 (+.f64 (log.f64 (/.f64 -1 l)) (log.f64 (neg.f64 d)))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) h) l)))
	24.9b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) h) l)))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	33.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l))) 1)
	25.4b	(.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 1/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	39.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) h) l)))
	39.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	61.2b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l)))))
	41.7b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	39.4b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	24.7b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	45.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))

Compiler

Compiled 8407 to 5608 computations (33.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h)))
✓	10.4b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	10.9b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	16.1b	(sqrt.f64 (/.f64 l h))

series1.0s (5%)

Counts

4 → 84

Calls

4 calls:

439.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
399.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
153.0ms	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h)))
18.0ms	(sqrt.f64 (/.f64 l h))

rewrite76.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
200×	`add-log-exp_binary64`
199×	`add-cbrt-cube_binary64`

Counts

4 → 101

Calls

4 calls:

74.0ms	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h)))
74.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
74.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
74.0ms	(sqrt.f64 (/.f64 l h))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	41
1	450	39
2	4865	39
3	5112	39
0	0	0
1	0	0

prune244.0ms (1.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	177	8	185
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	182	20	202

Error

6.3b

Counts

202 → 20

Alt Table

Status	Error	Program
	25.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) h) l)))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	41.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (sqrt.f64 1/2)) (.f64 (sqrt.f64 l) (sqrt.f64 (/.f64 1 h)))) 2)))
	61.2b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l)))))
▶	23.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 D M)) d) (sqrt.f64 (/.f64 h l)))) 2)))
	39.4b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	24.7b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	24.5b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (neg.f64 h)))) 2)))
	33.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l))) 1)
	25.4b	(.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 1/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	41.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 l) (sqrt.f64 h))) 2)))
	44.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	39.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	39.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	41.7b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	24.7b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	45.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)

Compiler

Compiled 8475 to 5425 computations (36% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 D M)) d) (sqrt.f64 (/.f64 h l)))
✓	10.4b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	10.9b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	15.2b	(sqrt.f64 (/.f64 h l))

series890.0ms (4.4%)

Counts

4 → 64

Calls

4 calls:

397.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
389.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
86.0ms	(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 D M)) d) (sqrt.f64 (/.f64 h l)))
18.0ms	(sqrt.f64 (/.f64 h l))

rewrite87.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

195×	`add-sqr-sqrt_binary64`
185×	`log1p-expm1-u_binary64`
185×	`expm1-log1p-u_binary64`
183×	`add-log-exp_binary64`
182×	`add-cbrt-cube_binary64`

Counts

4 → 113

Calls

4 calls:

82.0ms	(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 D M)) d) (sqrt.f64 (/.f64 h l)))
82.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
82.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
82.0ms	(sqrt.f64 (/.f64 h l))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	418	38
2	4882	38
3	4968	38
0	0	0
1	0	0

prune219.0ms (1.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	177	20	197

Error

5.9b

Counts

197 → 20

Alt Table

Status	Error	Program
	39.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 d) (sqrt.f64 l))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	24.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (cbrt.f64 (/.f64 d l)) (cbrt.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (pow.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 D M)) d) (sqrt.f64 (/.f64 h l)))) 2)))
	41.7b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	38.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (sqrt.f64 d) (sqrt.f64 (/.f64 1 l)))) (-.f64 1 (pow.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 D M)) d) (sqrt.f64 (/.f64 h l)))) 2)))
	35.3b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 1/2 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 h l))) (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 D M)) d)))) 2)))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	45.2b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 l)))) (-.f64 1 (pow.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 D M)) d) (sqrt.f64 (/.f64 h l)))) 2)))
	24.5b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 d h) 1/4) (pow.f64 (/.f64 d h) 1/4)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 l h))) 2)))
	44.0b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 (neg.f64 l)) (sqrt.f64 (neg.f64 h)))) 2)))
	24.1b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 1/2 (.f64 (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 D M)) d) (sqrt.f64 (/.f64 h l)))) 2)))
	33.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2))) l))) 1)
	25.4b	(.f64 (.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 d h)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 d h)) 1/2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
	41.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 l) (sqrt.f64 h))) 2)))
	61.0b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	61.2b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l)))))
	41.4b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 h) (.f64 (/.f64 d (.f64 (sqrt.f64 1/2) (.f64 D M))) (sqrt.f64 l)))) 2)))
	39.4b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	24.7b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (/.f64 h d))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) h) l)))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)

Compiler

Compiled 7340 to 4603 computations (37.3% saved)

regimes3.6s (17.6%)

Accuracy

Total 6.8b remaining (43.9%)

Threshold costs 0b (0%)

Counts

169 → 6

Compiler

Compiled 51767 to 39529 computations (23.6% saved)

bsearch2.0s (10%)

Steps

Iters	Range		Point
9	1.622865278006966e+247	1.645179643507673e+252	1.6302922045807467e+252
6	2.923164361140824e+178	2.4767195465292648e+179	2.962503803557255e+178
11	4.313123919949746e-121	2.4463303372999564e-100	2.7669274764063216e-116
10	-9.321270622984603e-302	1.0199301877728507e-297	-5.3271081112533e-310
9	-3.165679778567944e-42	-1.291320244133197e-48	-1.4693568850199418e-48

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`*-commutative_binary64`
13×	`+-commutative_binary64`
13×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	314
1	106	314
2	135	314
3	157	314
4	167	314
5	170	314
6	167	314

end584.0ms (2.9%)

Remove: (sort M D)
Compiler: Compiled 1590 to 1079 computations (32.1% saved)

Details

analyze2.2s (10.7%)

sample5.8s (28.6%)

localize22.0ms (0.1%)

series1.3s (6.6%)

rewrite72.0ms (0.4%)

prune306.0ms (1.5%)

localize24.0ms (0.1%)

series1.4s (6.9%)

rewrite71.0ms (0.4%)

prune313.0ms (1.5%)

localize28.0ms (0.1%)

series1.0s (5%)

rewrite76.0ms (0.4%)

prune244.0ms (1.2%)

localize31.0ms (0.2%)

series890.0ms (4.4%)

rewrite87.0ms (0.4%)

prune219.0ms (1.1%)

regimes3.6s (17.6%)

bsearch2.0s (10%)

simplify13.0ms (0.1%)

end584.0ms (2.9%)

Profiling