Details

analyze2.2s (14.6%)

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)

sample5.6s (37.6%)

Symmetry

(sort M D)

Results

3.3s	13662×	body	128	invalid
2.1s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify36.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-def_binary64`
437×	`*-commutative_binary64`
425×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	188	39
3	1071	39
4	3610	39
5	5106	39

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

24.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.5b	(.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))))

Compiler

Compiled 146 to 106 computations (27.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.5b	(.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))))
✓	9.4b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
✓	11.2b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	11.4b	(pow.f64 (/.f64 d h) (/.f64 1 2))

series1.2s (8.4%)

Counts

4 → 144

Calls

4 calls:

417.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
396.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
236.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
195.0ms	(.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))))

rewrite79.0ms (0.5%)

Algorithm

1×	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 → 67

Calls

4 calls:

78.0ms	(.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))))
78.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
78.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
78.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))

Iterations

Useful iterations: 1 (0.0ms)

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

simplify86.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-/r/_binary64`
631×	`associate-/l/_binary64`
227×	`associate-/l*_binary64`
225×	`times-frac_binary64`
149×	`associate-r_binary64`

Counts

211 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	3502
1	197	3448
2	524	3384
3	2323	3112
4	5136	3112

prune146.0ms (1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	72	20	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	20	93

Error

10.3b

Counts

93 → 20

Alt Table

Status	Error	Program
	24.5b	(.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 d 2)) 2)) h) l)))
	41.3b	(.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))))
	24.6b	(.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))))
▶	24.5b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 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)) (/.f64 h l))))
	58.9b	(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 d 2)) 2)) (/.f64 h l)))))
	43.0b	(.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)) (/.f64 h l))))
	40.2b	(.f64 (.f64 (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 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))))
	24.6b	(.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))))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	33.7b	(.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	38.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 l (pow.f64 d 2))))))
	38.6b	(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))))
	34.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (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))))
	40.2b	(.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))))
	26.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (exp.f64 (log.f64 (sqrt.f64 (/.f64 d l))))) (-.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)) (/.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))))
	24.5b	(.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))))
	24.8b	(.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)) (/.f64 h l))))
	59.6b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	24.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (pow.f64 (cbrt.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))) 3)))

Compiler

Compiled 4560 to 2983 computations (34.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.5b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 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)) (/.f64 h l))))
	9.4b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
	11.2b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	11.4b	(sqrt.f64 (*.f64 (/.f64 -1 h) (neg.f64 d)))

series510.0ms (3.4%)

Counts

2 → 32

Calls

2 calls:

496.0ms

(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 -1 h) (neg.f64 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)) (/.f64 h l))))

13.0ms

(sqrt.f64 (*.f64 (/.f64 -1 h) (neg.f64 d)))

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

269×	`add-sqr-sqrt_binary64`
253×	`log1p-expm1-u_binary64`
253×	`expm1-log1p-u_binary64`
250×	`add-cbrt-cube_binary64`
250×	`add-log-exp_binary64`

Counts

2 → 37

Calls

2 calls:

70.0ms

(*.f64 (*.f64 (sqrt.f64 (*.f64 (/.f64 -1 h) (neg.f64 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)) (/.f64 h l))))

70.0ms

(sqrt.f64 (*.f64 (/.f64 -1 h) (neg.f64 d)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	57
1	562	56
2	5070	56

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

569×	`associate-/l/_binary64`
540×	`distribute-rgt-neg-in_binary64`
500×	`distribute-lft-neg-in_binary64`
492×	`associate-r_binary64`
429×	`associate-l_binary64`

Counts

69 → 43

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	1155
1	63	1107
2	150	1107
3	508	1107
4	2397	1107
5	4746	1107
6	4996	1107
7	4949	1107

prune178.0ms (1.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	1	18	19
Picked	1	0	1
Done	0	0	0
Total	86	22	108

Error

10.3b

Counts

108 → 22

Alt Table

Status	Error	Program
	24.5b	(.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 d 2)) 2)) h) l)))
	41.3b	(.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))))
	58.9b	(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 d 2)) 2)) (/.f64 h l)))))
	43.0b	(.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)) (/.f64 h l))))
	40.2b	(.f64 (.f64 (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 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))))
	24.6b	(.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))))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	24.8b	(.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)) (/.f64 h l))))
	38.7b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 d))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (*.f64 (pow.f64 d 2) l)))))
	59.6b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	35.8b	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 (/.f64 -1 h) (neg.f64 d)) 3/2) 1/3) (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))))
	33.7b	(.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	38.7b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (.f64 l (pow.f64 d 2))))))
	41.3b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 -1 h)) (sqrt.f64 (neg.f64 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)) (/.f64 h l))))
	38.6b	(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))))
	34.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (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))))
	43.0b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 d))) (/.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))))
	40.2b	(.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))))
	26.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (exp.f64 (log.f64 (sqrt.f64 (/.f64 d l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	24.6b	(.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))))
	41.4b	(.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))))
▶	24.5b	(.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))))

Compiler

Compiled 4703 to 3180 computations (32.4% saved)

localize131.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.5b	(.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))))
	9.4b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
✓	11.1b	(sqrt.f64 (/.f64 l d))
	11.4b	(pow.f64 (/.f64 d h) (/.f64 1 2))

series213.0ms (1.4%)

Counts

2 → 33

Calls

2 calls:

200.0ms	(.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))))
14.0ms	(sqrt.f64 (/.f64 l d))

rewrite36.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`add-sqr-sqrt_binary64`
243×	`log1p-expm1-u_binary64`
243×	`expm1-log1p-u_binary64`
240×	`add-log-exp_binary64`
239×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

35.0ms	(.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))))
35.0ms	(sqrt.f64 (/.f64 l d))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	47
1	532	47
2	4880	47

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-/l/_binary64`
540×	`distribute-rgt-neg-in_binary64`
500×	`distribute-lft-neg-in_binary64`
492×	`associate-r_binary64`
429×	`associate-l_binary64`

Counts

70 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	1164
1	72	1116
2	179	1116
3	563	1116
4	2480	1116
5	4834	1116
6	4971	1116

prune139.0ms (0.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	8	13	21
Picked	1	0	1
Done	0	0	0
Total	91	21	112

Error

10.0b

Counts

112 → 21

Alt Table

Status	Error	Program
	40.2b	(.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))))
	25.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (expm1.f64 (log1p.f64 (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))))
	43.0b	(.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)) (/.f64 h l))))
	40.2b	(.f64 (.f64 (.f64 (sqrt.f64 d) (pow.f64 (/.f64 1 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))))
	24.6b	(.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))))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	33.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (log.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
	59.6b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	35.8b	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 (/.f64 -1 h) (neg.f64 d)) 3/2) 1/3) (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))))
▶	24.4b	(.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 d 2)) 2)) h) l)))
	33.7b	(.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	41.3b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 -1 h)) (sqrt.f64 (neg.f64 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)) (/.f64 h l))))
	34.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (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))))
	43.0b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 d))) (/.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))))
	24.5b	(.f64 (/.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 l d))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
	41.2b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 l d))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l)))) 3))
	41.4b	(.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))))
	31.1b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 l d))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))) 2)
	38.7b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 d))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (*.f64 (pow.f64 d 2) l)))))
	59.9b	(neg.f64 (/.f64 d (*.f64 h l)))
	41.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (/.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))))

Compiler

Compiled 4438 to 2840 computations (36% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.5b	(.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 d 2)) 2)) h) l)))
✓	6.0b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
	11.1b	(sqrt.f64 (/.f64 l d))
	11.4b	(pow.f64 (/.f64 d h) (/.f64 1 2))

series534.0ms (3.6%)

Counts

2 → 93

Calls

2 calls:

326.0ms

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

207.0ms

(*.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 d 2)) 2)) h) l)))

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`add-sqr-sqrt_binary64`
242×	`log1p-expm1-u_binary64`
242×	`expm1-log1p-u_binary64`
239×	`add-log-exp_binary64`
238×	`add-cbrt-cube_binary64`

Counts

2 → 33

Calls

2 calls:

39.0ms

(*.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 d 2)) 2)) h) l)))

39.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	63
1	530	63
2	4890	63

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

725×	`associate-/r/_binary64`
633×	`associate-/l/_binary64`
471×	`*-commutative_binary64`
452×	`fma-def_binary64`
305×	`distribute-rgt-neg-in_binary64`

Counts

126 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	2664
1	102	2616
2	346	2616
3	1787	2616
4	3851	2616
5	4885	2616
6	5045	2616

prune118.0ms (0.8%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	92	22	114

Error

9.5b

Counts

114 → 22

Alt Table

Status	Error	Program
	24.6b	(.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))))
	42.8b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	24.4b	(.f64 (/.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 l d))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) h) l)))
	33.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (log.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l)))))
	59.6b	(.f64 -1/8 (.f64 (/.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) d) (sqrt.f64 (/.f64 h (pow.f64 l 3)))))
	40.7b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
	35.8b	(.f64 (.f64 (pow.f64 (pow.f64 (.f64 (/.f64 -1 h) (neg.f64 d)) 3/2) 1/3) (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))))
	32.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 l d) 3/2)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
	33.7b	(.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
	41.3b	(.f64 (.f64 (.f64 (sqrt.f64 (/.f64 -1 h)) (sqrt.f64 (neg.f64 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)) (/.f64 h l))))
	34.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 d h) 3/2)) (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))))
	43.0b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 d))) (/.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))))
	41.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (/.f64 (sqrt.f64 l) (sqrt.f64 d)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
	30.8b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 l d))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) h) l)))))
	41.2b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 l d))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l)))) 3))
	25.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 l d)))))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
	43.0b	(.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)) (/.f64 h l))))
	41.4b	(.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))))
	40.3b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (/.f64 1 (sqrt.f64 (/.f64 l d)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
	31.1b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 l d))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))) 2)
	38.7b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 -1 h) (neg.f64 d))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (*.f64 (pow.f64 d 2) l)))))
	59.9b	(neg.f64 (/.f64 d (*.f64 h l)))

Compiler

Compiled 3767 to 2361 computations (37.3% saved)

regimes1.7s (11.7%)

Accuracy

Total 7.3b remaining (39.2%)

Threshold costs 0b (0%)

Counts

123 → 3

Compiler

Compiled 32671 to 24883 computations (23.8% saved)

bsearch786.0ms (5.3%)

Steps

Iters	Range		Point
7	1.4701407994876362e+23	4.238512840606073e+24	1.9115375279058692e+23
9	-1.0294624630244227e-287	-3.1024289247085445e-296	-3.170040707759249e-296

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	153
1	77	153
2	101	153
3	120	153
4	129	153
5	132	153
6	129	153

end674.0ms (4.5%)

Remove: (sort M D)
Compiler: Compiled 1186 to 872 computations (26.5% saved)

Details

analyze2.2s (14.6%)

sample5.6s (37.6%)

simplify36.0ms (0.2%)

prune5.0ms (0%)

localize25.0ms (0.2%)

series1.2s (8.4%)

rewrite79.0ms (0.5%)

simplify86.0ms (0.6%)

prune146.0ms (1%)

localize24.0ms (0.2%)

series510.0ms (3.4%)

rewrite71.0ms (0.5%)

simplify88.0ms (0.6%)

prune178.0ms (1.2%)

localize131.0ms (0.9%)

series213.0ms (1.4%)

rewrite36.0ms (0.2%)

simplify75.0ms (0.5%)

prune139.0ms (0.9%)

localize24.0ms (0.2%)

series534.0ms (3.6%)

rewrite40.0ms (0.3%)

simplify103.0ms (0.7%)

prune118.0ms (0.8%)

regimes1.7s (11.7%)

bsearch786.0ms (5.3%)

simplify10.0ms (0.1%)

end674.0ms (4.5%)

Profiling