Details

analyze7.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample2.4s (30.1%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

914×	`times-frac_binary32`
551×	`associate-/l*_binary32`
460×	`associate-/l/_binary32`
360×	`associate-*l/_binary32`
311×	`associate-/r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	54	34
2	173	32
3	800	32

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Status

Error

Program

0.5b

(*.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (*.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))

▶

0.4b

(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 154 to 106 computations (31.2% saved)

localize89.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.3b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.8b	(sinh.f32 (/.f32 1 v))

series55.0ms (0.7%)

Counts

4 → 24

Calls

4 calls:

28.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
15.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
7.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
5.0ms	(sinh.f32 (/.f32 1 v))

rewrite65.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary32`
163×	`add-sqr-sqrt_binary32`
152×	`log1p-expm1-u_binary32`
152×	`expm1-log1p-u_binary32`
150×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	332	32
2	4356	32

Stop Event

1×	node limit

Counts

4 → 131

Calls

4 calls:

62.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
62.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
62.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
62.0ms	(sinh.f32 (/.f32 1 v))

simplify28.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

509×	`unswap-sqr_binary32`
478×	`times-frac_binary32`
374×	`fma-def_binary32`
322×	`associate-*l/_binary32`
302×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	408
1	125	392
2	279	392
3	636	392
4	1902	392

Stop Event

1×	node limit

Counts

155 → 149

prune241.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	138	11	149
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	139	12	151

Error

0.1b

Counts

151 → 12

Alt Table

Status	Error	Program
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (sqrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 2))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)) 3) 1/3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) v))
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (-.f32 (exp.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))) 1))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 4742 to 2365 computations (50.1% saved)

localize88.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.3b	(*.f32 cosTheta_i (/.f32 1 v))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	0.8b	(sinh.f32 (/.f32 1 v))

series5.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f32 cosTheta_i (/.f32 1 v))

rewrite29.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`log1p-expm1-u_binary32`
495×	`expm1-log1p-u_binary32`
405×	`unpow-prod-down_binary32`
272×	`log-prod_binary32`
142×	`pow2_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	120	4
2	1434	4

Stop Event

1×	node limit

Counts

1 → 30

Calls

1 calls:

29.0ms

(*.f32 cosTheta_i (/.f32 1 v))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96

Stop Event

1×

saturated

Counts

54 → 30

prune297.0ms (3.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	128	5	133
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	131	14	145

Error

0.0b

Counts

145 → 14

Alt Table

Status	Error	Program
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (sqrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 2))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)) 3) 1/3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (-.f32 (exp.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2)))) 1))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 3))

Compiler

Compiled 4628 to 2770 computations (40.1% saved)

localize68.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 cosTheta_i (/.f32 1 v))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.6b	(exp.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))))
	0.8b	(sinh.f32 (/.f32 1 v))

series2.1s (25.7%)

Counts

1 → 12

Calls

1 calls:

2.1s	(exp.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))))

rewrite44.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`expm1-log1p-u_binary32`
809×	`log1p-expm1-u_binary32`
314×	`prod-diff_binary32`
95×	`add-sqr-sqrt_binary32`
88×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	198	15
2	2290	15

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

43.0ms

(exp.f32 (log1p.f32 (*.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))))

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary32`
463×	`associate-l_binary32`
419×	`associate-/r/_binary32`
338×	`associate-/l/_binary32`
294×	`associate-r_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	186
1	69	180
2	145	180
3	323	180
4	935	180
5	3800	180

Stop Event

1×	node limit

Counts

35 → 33

prune325.0ms (4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	141	14	155

Error

0.0b

Counts

155 → 14

Alt Table

Status	Error	Program
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (sqrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 2))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (-.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) 2)) (cbrt.f32 (log1p.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) 1))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)) 3) 1/3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (-.f32 (exp.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2)))) 1))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (-.f32 (pow.f32 (E.f32) (log1p.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) 1))

Compiler

Compiled 5448 to 3484 computations (36% saved)

localize59.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.3b	(/.f32 1 (/.f32 v cosTheta_O))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	0.8b	(sinh.f32 (/.f32 1 v))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(/.f32 1 (/.f32 v cosTheta_O))

rewrite36.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`log1p-expm1-u_binary32`
571×	`expm1-log1p-u_binary32`
302×	`log-prod_binary32`
108×	`pow1/3_binary32`
107×	`expm1-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	4
2	1620	4

Stop Event

1×	node limit

Counts

1 → 43

Calls

1 calls:

35.0ms

(/.f32 1 (/.f32 v cosTheta_O))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96

Stop Event

1×

saturated

Counts

67 → 44

prune339.0ms (4.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	147	14	161

Error

0.0b

Counts

161 → 14

Alt Table

Status	Error	Program
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (-.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) 2)) (cbrt.f32 (log1p.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) 1))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)) 3) 1/3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (-.f32 (exp.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2)))) 1))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)))) (pow.f32 (sqrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2))) 2))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 (/.f32 (pow.f32 (cbrt.f32 cosTheta_O) 2) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (cbrt.f32 cosTheta_O) (cbrt.f32 v))))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (-.f32 (pow.f32 (E.f32) (log1p.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) 1))

Compiler

Compiled 4641 to 2562 computations (44.8% saved)

regimes1.4s (17.8%)

Accuracy

Total 0.3b remaining (76.1%)

Threshold costs 0.3b (76.1%)

Counts

143 → 1

Compiler

Compiled 40866 to 29650 computations (27.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
4×	`+-commutative_binary32`
4×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	37
1	35	37
2	46	37
3	53	37
4	57	37
5	58	37

Stop Event

1×

saturated

end277.0ms (3.4%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 636 to 467 computations (26.6% saved)

Details

analyze7.0ms (0.1%)

sample2.4s (30.1%)

simplify15.0ms (0.2%)

prune4.0ms (0.1%)

localize89.0ms (1.1%)

series55.0ms (0.7%)

rewrite65.0ms (0.8%)

simplify28.0ms (0.3%)

prune241.0ms (3%)

localize88.0ms (1.1%)

series5.0ms (0.1%)

rewrite29.0ms (0.4%)

simplify7.0ms (0.1%)

prune297.0ms (3.7%)

localize68.0ms (0.8%)

series2.1s (25.7%)

rewrite44.0ms (0.5%)

simplify32.0ms (0.4%)

prune325.0ms (4%)

localize59.0ms (0.7%)

series7.0ms (0.1%)

rewrite36.0ms (0.4%)

simplify7.0ms (0.1%)

prune339.0ms (4.2%)

regimes1.4s (17.8%)

simplify3.0ms (0%)

end277.0ms (3.4%)

Profiling