Details

analyze2.2s (17.4%)

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)

sample5.9s (46.6%)

Symmetry

(sort M D)

Results

3.6s	13800×	body	128	invalid
2.2s	8256×	body	128	valid

Compiler

Compiled 122 to 95 computations (22.1% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

425×	`associate-/l*_binary64`
398×	`*-commutative_binary64`
236×	`associate-/l/_binary64`
214×	`associate-/r/_binary64`
203×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	195	39
3	1309	39

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

23.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	24.0b	(.f64 (sqrt.f64 (/.f64 d h)) (.f64 (sqrt.f64 (/.f64 d l)) (fma.f64 (/.f64 h l) (.f64 (pow.f64 (.f64 M (/.f64 (/.f64 D d) 2)) 2) -1/2) 1)))
▶	23.5b	(.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))))

Status

Error

Program

24.0b

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

▶

23.5b

(*.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 208 to 151 computations (27.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.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))))
✓	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	10.9b	(pow.f64 (/.f64 d l) (/.f64 1 2))
✓	13.0b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

series371.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

176.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
171.0ms	(.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))))
13.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
11.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

242×	`add-sqr-sqrt_binary64`
232×	`log1p-expm1-u_binary64`
232×	`expm1-log1p-u_binary64`
228×	`add-cbrt-cube_binary64`
226×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	74
1	510	73

Stop Event

1×	node limit

Counts

4 → 65

Calls

4 calls:

39.0ms	(.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))))
39.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
39.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
39.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-/r/_binary64`
609×	`associate-/l/_binary64`
434×	`*-commutative_binary64`
250×	`fma-def_binary64`
225×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	2790
1	122	2736
2	359	2736
3	2102	2736
4	4915	2736

Stop Event

1×	node limit

Counts

161 → 76

prune115.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	61	15	76
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	15	78

Error

12.8b

Counts

78 → 15

Alt Table

Status	Error	Program
	39.9b	(.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))))
	23.8b	(.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))))
	42.5b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))) 3))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	61.0b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))))
	39.8b	(.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))))
	35.1b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))) 1)
	33.5b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
	39.9b	(.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))))))
	44.5b	(.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))))
	44.1b	(.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))))
	23.6b	(.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))))
	23.7b	(.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 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
▶	22.6b	(.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 2) (/.f64 D d)) 2)) h) l)))
	23.8b	(.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))))

Compiler

Compiled 3629 to 2339 computations (35.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.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 2) (/.f64 D d)) 2)) h) l)))
	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
✓	8.0b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)
	10.9b	(pow.f64 (/.f64 d l) (/.f64 1 2))

series352.0ms (2.8%)

Counts

2 → 96

Calls

2 calls:

183.0ms

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

169.0ms

(*.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 2) (/.f64 D d)) 2)) h) l)))

rewrite31.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`add-sqr-sqrt_binary64`
235×	`log1p-expm1-u_binary64`
235×	`expm1-log1p-u_binary64`
231×	`add-cbrt-cube_binary64`
229×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	62
1	516	61

Stop Event

1×	node limit

Counts

2 → 31

Calls

2 calls:

30.0ms

(*.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 2) (/.f64 D d)) 2)) h) l)))

30.0ms

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

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-/r/_binary64`
609×	`associate-/l/_binary64`
434×	`*-commutative_binary64`
250×	`fma-def_binary64`
225×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	2790
1	122	2736
2	359	2736
3	2102	2736
4	4915	2736

Stop Event

1×	node limit

Counts

127 → 42

prune116.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	70	8	78
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	76	17	93

Error

11.2b

Counts

93 → 17

Alt Table

Status	Error	Program
	39.9b	(.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))))))
	60.0b	(.f64 (.f64 (log.f64 (exp.f64 (sqrt.f64 (/.f64 d h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	23.6b	(.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))))
	34.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 1/2 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 l h)))) 1)
	42.5b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))) 3))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	61.0b	(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l)))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))))
	39.8b	(.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))))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	23.8b	(.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))))
	40.4b	(.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 2) (/.f64 D d)) 2)) 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 2) (/.f64 D d)) 2)) h) l)))
	33.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (cbrt.f64 (pow.f64 (/.f64 d l) 3/2))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)))
	39.9b	(.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))))
	23.7b	(.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 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
▶	22.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	23.0b	(.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 2) (/.f64 D d)) 2)) h) l)))

Compiler

Compiled 3796 to 2469 computations (35% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.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 2) (/.f64 D d)) 2)) h) l)))
	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
	8.0b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)
✓	11.4b	(cbrt.f64 (/.f64 d l))

series235.0ms (1.9%)

Counts

2 → 36

Calls

2 calls:

209.0ms

(*.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 2) (/.f64 D d)) 2)) h) l)))

25.0ms

(cbrt.f64 (/.f64 d l))

rewrite29.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`log1p-expm1-u_binary64`
259×	`expm1-log1p-u_binary64`
252×	`add-cbrt-cube_binary64`
250×	`add-cube-cbrt_binary64`
246×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	48
1	589	46

Stop Event

1×	node limit

Counts

2 → 37

Calls

2 calls:

28.0ms

(*.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 2) (/.f64 D d)) 2)) h) l)))

28.0ms

(cbrt.f64 (/.f64 d l))

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-r_binary64`
447×	`cancel-sign-sub-inv_binary64`
425×	`associate-l_binary64`
264×	`unswap-sqr_binary64`
242×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	1292
1	75	1244
2	190	1244
3	669	1244
4	3515	1244

Stop Event

1×	node limit

Counts

73 → 47

prune144.0ms (1.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	109	18	127

Error

10.6b

Counts

127 → 18

Alt Table

Status	Error	Program
	39.9b	(.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))))
▶	22.9b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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 2) (/.f64 D d)) 2)) h) l)))
	23.6b	(.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))))
	34.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 1/2 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 l h)))) 1)
	42.5b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))) 3))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	23.1b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (.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 2) (/.f64 D d)) 2)) h) l)))
	39.8b	(.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))))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.5b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (.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 2) (/.f64 D d)) 2)) h) l)))
	23.8b	(.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))))
	40.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	42.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (.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 2) (/.f64 D d)) 2)) h) l)))
	39.9b	(.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))))))
	52.6b	(fma.f64 (.f64 M M) (.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (.f64 1/8 (.f64 (/.f64 D d) D))) (.f64 d (neg.f64 (sqrt.f64 (/.f64 1 (.f64 h l))))))
	46.1b	(.f64 (sqrt.f64 (/.f64 1 (.f64 h l))) (neg.f64 d))
	23.7b	(.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 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
	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 2) (/.f64 D d)) 2)) h) l)))

Compiler

Compiled 5749 to 3593 computations (37.5% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (.f64 (pow.f64 (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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 2) (/.f64 D d)) 2)) h) l)))
	8.0b	(pow.f64 (/.f64 d h) (/.f64 1 2))
	8.0b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) h) l)
	11.4b	(cbrt.f64 (/.f64 d l))

series227.0ms (1.8%)

Counts

1 → 36

Calls

1 calls:

227.0ms

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

rewrite27.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`log1p-expm1-u_binary64`
276×	`expm1-log1p-u_binary64`
271×	`add-cbrt-cube_binary64`
269×	`add-cube-cbrt_binary64`
263×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	42
1	652	40

Stop Event

1×	node limit

Counts

1 → 12

Calls

1 calls:

26.0ms

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

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-r_binary64`
447×	`cancel-sign-sub-inv_binary64`
425×	`associate-l_binary64`
264×	`unswap-sqr_binary64`
242×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	1292
1	75	1244
2	190	1244
3	669	1244
4	3515	1244

Stop Event

1×	node limit

Counts

48 → 22

prune97.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	86	17	103

Error

10.6b

Counts

103 → 17

Alt Table

Status	Error	Program
	23.6b	(.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))))
	34.8b	(pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (/.f64 (.f64 1/2 (pow.f64 (.f64 (*.f64 M 1/2) (/.f64 D d)) 2)) (/.f64 l h)))) 1)
	46.1b	(.f64 (sqrt.f64 (/.f64 1 (.f64 h l))) (neg.f64 d))
	42.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (neg.f64 d)) (sqrt.f64 (neg.f64 h))) (.f64 (pow.f64 (pow.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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 2) (/.f64 D d)) 2)) h) l)))
	42.5b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (/.f64 d h) (/.f64 d l))) (-.f64 1 (.f64 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))) 3))
	43.7b	(.f64 (sqrt.f64 (/.f64 1 (.f64 l h))) d)
	23.1b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 d h)) (cbrt.f64 (sqrt.f64 (/.f64 d h)))) (.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 2) (/.f64 D d)) 2)) h) l)))
	39.8b	(.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))))
	41.9b	(.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 2) (/.f64 D d)) 2)) h) l)))
	40.5b	(.f64 (.f64 (/.f64 (sqrt.f64 d) (sqrt.f64 h)) (.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 2) (/.f64 D d)) 2)) h) l)))
	23.8b	(.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))))
	40.4b	(.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 2) (/.f64 D d)) 2)) h) l)))
	39.9b	(.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))))))
	39.9b	(.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))))
	52.6b	(fma.f64 (.f64 M M) (.f64 (sqrt.f64 (/.f64 h (pow.f64 l 3))) (.f64 1/8 (.f64 (/.f64 D d) D))) (.f64 d (neg.f64 (sqrt.f64 (/.f64 1 (.f64 h l))))))
	23.7b	(.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 1/2 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))) 2)))
	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 2) (/.f64 D d)) 2)) h) l)))

Compiler

Compiled 3999 to 2410 computations (39.7% saved)

regimes1.4s (10.8%)

Accuracy

Total 7.5b remaining (42.5%)

Threshold costs 0b (0%)

Counts

98 → 3

Compiler

Compiled 27343 to 20491 computations (25.1% saved)

bsearch458.0ms (3.6%)

Steps

Iters	Range		Point
5	2.736328770159259e-69	8.121305587837426e-69	4.820219395017622e-69
7	-3.4930118362846327e-129	-6.855183360026509e-131	-2.3875216497193884e-129

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	171
1	88	171
2	114	171
3	134	171
4	150	171
5	157	171
6	160	171
7	161	171

Stop Event

1×

saturated

end578.0ms (4.6%)

Compiler: Compiled 1093 to 788 computations (27.9% saved)

Details

analyze2.2s (17.4%)

sample5.9s (46.6%)

simplify17.0ms (0.1%)

prune5.0ms (0%)

localize24.0ms (0.2%)

series371.0ms (2.9%)

rewrite42.0ms (0.3%)

simplify73.0ms (0.6%)

prune115.0ms (0.9%)

localize22.0ms (0.2%)

series352.0ms (2.8%)

rewrite31.0ms (0.2%)

simplify73.0ms (0.6%)

prune116.0ms (0.9%)

localize29.0ms (0.2%)

series235.0ms (1.9%)

rewrite29.0ms (0.2%)

simplify44.0ms (0.4%)

prune144.0ms (1.1%)

localize31.0ms (0.2%)

series227.0ms (1.8%)

rewrite27.0ms (0.2%)

simplify44.0ms (0.3%)

prune97.0ms (0.8%)

regimes1.4s (10.8%)

bsearch458.0ms (3.6%)

simplify8.0ms (0.1%)

end578.0ms (4.6%)

Profiling