Details

analyze12.5s (17.5%)

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%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
6.2%	93.5%	0.2%	11
6.2%	93.5%	0.2%	12
7.8%	92%	0.2%	13
8.6%	91.2%	0.2%	14

Compiler

Compiled 115 to 84 computations (27% saved)

sample47.5s (66.8%)

Results

12.3s	1481×	body	4096	valid
9.1s	1778×	body	2048	valid
7.2s	852×	body	4096	invalid
5.8s	1116×	body	2048	invalid
3.2s	924×	body	1024	valid
2.8s	3454×	body	128	valid
2.3s	675×	body	1024	invalid
1.4s	80×	body	8192	valid
882.0ms	392×	body	512	valid
765.0ms	44×	body	8192	invalid
725.0ms	1017×	body	128	invalid
652.0ms	293×	body	512	invalid
194.0ms	147×	body	256	valid
136.0ms	97×	body	256	invalid

Compiler

Compiled 230 to 168 computations (27% saved)

preprocess55.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

432×	`fma-def_binary64`
225×	`distribute-neg-frac_binary64`
202×	`distribute-lft-in_binary64`
202×	`distribute-rgt-in_binary64`
193×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	249	1925
1	735	1903
2	2737	1903
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 114 to 83 computations (27.2% saved)

simplify21.0ms (0%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-/l/_binary64`
526×	`associate-/r/_binary64`
263×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`
157×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	175
1	104	173
2	339	173
3	1688	170

Stop Event

1×	node limit

Counts

1 → 2

prune12.0ms (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

41.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	46.3b	(fma.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale)) (.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 x-scale x-scale)) -4) (.f64 (/.f64 (/.f64 (.f64 4 (.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) (.f64 y-scale (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale)))
▶	41.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

Status

Error

Program

46.3b

(fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (/.f64 (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale)))

▶

41.3b

(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

Compiler

Compiled 670 to 462 computations (31% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.6b	(/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)
✓	27.2b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	27.5b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	30.9b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

series2.2s (3.1%)

Counts

4 → 144

Calls

36 calls:

207.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))	angle	inf
205.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))	angle	-inf
184.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))	y-scale	inf
166.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))	y-scale	-inf
163.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))	x-scale	0

rewrite61.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

457×	`pow1_binary64`
429×	`add-log-exp_binary64`
429×	`log1p-expm1-u_binary64`
429×	`expm1-log1p-u_binary64`
423×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	196
1	924	196

Stop Event

1×	node limit

Counts

4 → 43

simplify154.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

424×	`times-frac_binary64`
388×	`associate-/l*_binary64`
341×	`associate-r_binary64`
253×	`associate-/r*_binary64`
223×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	296	14367
1	1250	13161

Stop Event

1×	node limit

Counts

187 → 110

prune776.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	235	6	241
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	237	6	243

Error

22.7b

Counts

243 → 6

Alt Table

Status	Error	Program
▶	31.8b	(.f64 -4 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 (/.f64 b x-scale) (/.f64 b x-scale)))))
	38.6b	(/.f64 (neg.f64 (fma.f64 4 (.f64 (/.f64 (/.f64 (.f64 a a) x-scale) x-scale) (.f64 b (.f64 b (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)))) (fma.f64 4 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) x-scale) (/.f64 (.f64 (.f64 b a) (.f64 b a)) x-scale)) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) 8) (/.f64 (.f64 (/.f64 x-scale (.f64 b b)) (/.f64 x-scale (.f64 a a))) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)))))) (*.f64 y-scale y-scale))
	40.3b	(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 y-scale (.f64 b b)) (/.f64 y-scale (.f64 a a)))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 b (.f64 b (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 a a)) (/.f64 (.f64 y-scale y-scale) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))))))) (.f64 x-scale x-scale))
	40.9b	(.f64 -1 (/.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 y-scale 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (pow.f64 y-scale 2))) (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 a 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))) 2)))) (pow.f64 y-scale 2))))) (pow.f64 x-scale 2)))
	41.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (.f64 (/.f64 (.f64 2 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64))))) (/.f64 x-scale (cos.f64 (.f64 (.f64 angle 1/180) (PI.f64))))) (/.f64 1 y-scale))) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	32.1b	0

Compiler

Compiled 29823 to 20243 computations (32.1% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 (/.f64 b x-scale) (/.f64 b x-scale)))))
✓	0.3b	(*.f64 (/.f64 b x-scale) (/.f64 b x-scale))
✓	17.8b	(/.f64 (.f64 y-scale y-scale) (.f64 (/.f64 b x-scale) (/.f64 b x-scale)))
✓	19.1b	(/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (*.f64 (/.f64 b x-scale) (/.f64 b x-scale))))

series410.0ms (0.6%)

Counts

4 → 156

Calls

39 calls:

19.0ms	(/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (*.f64 (/.f64 b x-scale) (/.f64 b x-scale))))	b	inf
17.0ms	(.f64 -4 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 (/.f64 b x-scale) (/.f64 b x-scale)))))	b	-inf
16.0ms	(/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (*.f64 (/.f64 b x-scale) (/.f64 b x-scale))))	a	0
16.0ms	(.f64 -4 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 (/.f64 b x-scale) (/.f64 b x-scale)))))	a	-inf
16.0ms	(.f64 -4 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 (/.f64 b x-scale) (/.f64 b x-scale)))))	b	0

rewrite70.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`log1p-udef_binary64`
147×	`add-sqr-sqrt_binary64`
144×	`*-un-lft-identity_binary64`
144×	`pow1_binary64`
136×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	290	46
2	4328	46

Stop Event

1×	node limit

Counts

4 → 149

simplify64.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

812×	`associate-*l/_binary64`
734×	`associate-l_binary64`
587×	`associate-/l/_binary64`
466×	`associate-/r/_binary64`
286×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	3072
1	54	3072
2	196	3072
3	1624	3072

Stop Event

1×	node limit

Counts

305 → 160

prune213.0ms (0.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	148	12	160
Fresh	5	0	5
Picked	0	1	1
Done	0	0	0
Total	153	13	166

Error

1.8b

Counts

166 → 13

Alt Table

Status	Error	Program
	20.2b	(.f64 -4 (/.f64 (.f64 a a) (*.f64 (/.f64 x-scale (/.f64 b y-scale)) (/.f64 x-scale (/.f64 b y-scale)))))
	14.3b	(.f64 -4 (.f64 a (/.f64 1 (/.f64 (pow.f64 (*.f64 y-scale (/.f64 x-scale b)) 2) a))))
	29.0b	(.f64 (.f64 a a) (.f64 (.f64 (/.f64 b y-scale) (/.f64 b y-scale)) (/.f64 (/.f64 -4 x-scale) x-scale)))
	22.1b	(.f64 -4 (.f64 (pow.f64 (/.f64 b x-scale) 2) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale))))
✓	31.8b	(.f64 -4 (/.f64 (.f64 a a) (/.f64 (.f64 y-scale y-scale) (.f64 (/.f64 b x-scale) (/.f64 b x-scale)))))
▶	6.8b	(.f64 -4 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2))
	14.3b	(/.f64 (.f64 a -4) (/.f64 (pow.f64 (.f64 y-scale (/.f64 x-scale b)) 2) a))
	18.4b	(/.f64 (/.f64 (.f64 (.f64 a a) -4) (.f64 y-scale (/.f64 x-scale b))) (.f64 y-scale (/.f64 x-scale b)))
	28.3b	(.f64 -4 (.f64 a (.f64 a (/.f64 (pow.f64 (/.f64 b x-scale) 2) (.f64 y-scale y-scale)))))
	17.5b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (/.f64 b x-scale)) (/.f64 b x-scale)))
	26.5b	(.f64 -4 (.f64 (/.f64 (*.f64 a a) y-scale) (/.f64 (pow.f64 (/.f64 b x-scale) 2) y-scale)))
	21.8b	(.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2) 3)))
	16.2b	(.f64 -4 (.f64 b (.f64 b (.f64 (/.f64 a (.f64 y-scale x-scale)) (/.f64 a (.f64 y-scale x-scale))))))

Compiler

Compiled 3248 to 1577 computations (51.4% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2))
✓	0.3b	(pow.f64 (/.f64 a (*.f64 y-scale (/.f64 x-scale b))) 2)
✓	5.0b	(/.f64 a (*.f64 y-scale (/.f64 x-scale b)))
✓	6.0b	(*.f64 y-scale (/.f64 x-scale b))

series290.0ms (0.4%)

Counts

4 → 180

Calls

45 calls:

36.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2))	y-scale	-inf
30.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2))	x-scale	0
17.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2))	b	-inf
16.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2))	b	0
16.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 y-scale (/.f64 x-scale b))) 2))	a	inf

rewrite64.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

658×	`log-prod_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
189×	`log-pow_binary64`
143×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	257	46
2	3307	46

Stop Event

1×	node limit

Counts

4 → 141

simplify100.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

815×	`associate-l_binary64`
588×	`associate-/l/_binary64`
450×	`associate-/r/_binary64`
258×	`times-frac_binary64`
220×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	2988
1	74	2988
2	226	2988
3	1521	2988
4	4829	2988
5	4982	2988

Stop Event

1×	node limit

Counts

321 → 152

prune226.0ms (0.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	144	8	152
Fresh	5	6	11
Picked	1	0	1
Done	1	0	1
Total	151	14	165

Error

0.0b

Counts

165 → 14

Alt Table

Status	Error	Program
	29.0b	(.f64 (.f64 a a) (.f64 (.f64 (/.f64 b y-scale) (/.f64 b y-scale)) (/.f64 (/.f64 -4 x-scale) x-scale)))
	22.1b	(.f64 -4 (.f64 (pow.f64 (/.f64 b x-scale) 2) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale))))
	18.4b	(/.f64 (/.f64 (.f64 (.f64 a a) -4) (.f64 y-scale (/.f64 x-scale b))) (.f64 y-scale (/.f64 x-scale b)))
	6.3b	(.f64 -4 (pow.f64 (.f64 (/.f64 (/.f64 a y-scale) x-scale) b) 2))
	26.5b	(.f64 -4 (.f64 (/.f64 (*.f64 a a) y-scale) (/.f64 (pow.f64 (/.f64 b x-scale) 2) y-scale)))
	11.7b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) a) (/.f64 (/.f64 b x-scale) y-scale)))
	16.2b	(.f64 -4 (.f64 b (.f64 b (.f64 (/.f64 a (.f64 y-scale x-scale)) (/.f64 a (.f64 y-scale x-scale))))))
▶	6.2b	(.f64 -4 (pow.f64 (/.f64 a (.f64 x-scale (/.f64 y-scale b))) 2))
	6.3b	(.f64 -4 (pow.f64 (/.f64 (.f64 a b) (*.f64 y-scale x-scale)) 2))
	17.1b	(.f64 -4 (.f64 (.f64 a (/.f64 b y-scale)) (/.f64 (.f64 b a) (.f64 x-scale (.f64 y-scale x-scale)))))
	14.3b	(/.f64 (.f64 a -4) (/.f64 (pow.f64 (.f64 y-scale (/.f64 x-scale b)) 2) a))
	7.0b	(.f64 -4 (/.f64 1 (.f64 (/.f64 (/.f64 x-scale b) (/.f64 a y-scale)) (/.f64 (/.f64 x-scale b) (/.f64 a y-scale)))))
	6.7b	(.f64 -4 (/.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) (/.f64 (/.f64 x-scale b) (/.f64 a y-scale))))
	6.7b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) (cbrt.f64 (pow.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) 2))) (cbrt.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)))))

Compiler

Compiled 3108 to 1453 computations (53.2% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (pow.f64 (/.f64 a (.f64 x-scale (/.f64 y-scale b))) 2))
✓	0.3b	(pow.f64 (/.f64 a (*.f64 x-scale (/.f64 y-scale b))) 2)
✓	4.4b	(*.f64 x-scale (/.f64 y-scale b))
✓	5.0b	(/.f64 a (*.f64 x-scale (/.f64 y-scale b)))

series254.0ms (0.4%)

Counts

4 → 180

Calls

45 calls:

17.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 x-scale (/.f64 y-scale b))) 2))	a	-inf
16.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 x-scale (/.f64 y-scale b))) 2))	b	inf
16.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 x-scale (/.f64 y-scale b))) 2))	a	inf
16.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 x-scale (/.f64 y-scale b))) 2))	b	0
16.0ms	(.f64 -4 (pow.f64 (/.f64 a (.f64 x-scale (/.f64 y-scale b))) 2))	b	-inf

rewrite64.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

658×	`log-prod_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
189×	`log-pow_binary64`
143×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	257	46
2	3307	46

Stop Event

1×	node limit

Counts

4 → 141

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-l_binary64`
582×	`associate-/l/_binary64`
445×	`associate-/r/_binary64`
258×	`times-frac_binary64`
216×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	2988
1	74	2988
2	226	2988
3	1521	2988
4	4799	2988
5	4952	2988

Stop Event

1×	node limit

Counts

321 → 152

prune209.0ms (0.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	151	15	166

Error

0.0b

Counts

166 → 15

Alt Table

Status	Error	Program
	5.9b	(.f64 -4 (/.f64 1 (.f64 (/.f64 x-scale (/.f64 a (/.f64 y-scale b))) (/.f64 x-scale (/.f64 a (/.f64 y-scale b))))))
	18.3b	(.f64 -4 (.f64 (.f64 (/.f64 a x-scale) (/.f64 a x-scale)) (.f64 (/.f64 b y-scale) (/.f64 b y-scale))))
	8.6b	(.f64 -4 (/.f64 (.f64 (/.f64 a x-scale) (*.f64 (/.f64 b y-scale) (/.f64 a x-scale))) (/.f64 y-scale b)))
	22.1b	(.f64 -4 (.f64 (pow.f64 (/.f64 b x-scale) 2) (*.f64 (/.f64 a y-scale) (/.f64 a y-scale))))
	6.4b	(.f64 -4 (pow.f64 (.f64 (/.f64 a (*.f64 x-scale y-scale)) b) 2))
	18.4b	(/.f64 (/.f64 (.f64 (.f64 a a) -4) (.f64 y-scale (/.f64 x-scale b))) (.f64 y-scale (/.f64 x-scale b)))
	10.2b	(.f64 -4 (.f64 a (.f64 (/.f64 (/.f64 b y-scale) x-scale) (.f64 (/.f64 b y-scale) (/.f64 a x-scale)))))
	17.1b	(.f64 -4 (.f64 (.f64 a (/.f64 b y-scale)) (/.f64 (.f64 b a) (.f64 x-scale (.f64 y-scale x-scale)))))
	7.6b	(.f64 -4 (/.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) (/.f64 x-scale (/.f64 a (/.f64 y-scale b)))))
	14.3b	(/.f64 (.f64 a -4) (/.f64 (pow.f64 (.f64 y-scale (/.f64 x-scale b)) 2) a))
	7.0b	(.f64 -4 (/.f64 1 (.f64 (/.f64 (/.f64 x-scale b) (/.f64 a y-scale)) (/.f64 (/.f64 x-scale b) (/.f64 a y-scale)))))
	6.7b	(.f64 -4 (/.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) (/.f64 (/.f64 x-scale b) (/.f64 a y-scale))))
	6.7b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) (cbrt.f64 (pow.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) 2))) (cbrt.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)))))
	11.7b	(.f64 -4 (.f64 (.f64 (.f64 (/.f64 b x-scale) (/.f64 a y-scale)) a) (/.f64 (/.f64 b x-scale) y-scale)))
	16.2b	(.f64 -4 (.f64 b (.f64 b (.f64 (/.f64 a (.f64 y-scale x-scale)) (/.f64 a (.f64 y-scale x-scale))))))

Compiler

Compiled 2850 to 1280 computations (55.1% saved)

regimes3.7s (5.2%)

Accuracy

Total 5.6b remaining (99.5%)

Threshold costs 0b (0%)

Counts

196 → 4

Compiler

Compiled 48920 to 35007 computations (28.4% saved)

bsearch1.9s (2.7%)

Algorithm

3×	binary-search

Calls

3 calls:

675.0ms	b
645.0ms	b
571.0ms	b

Steps

Iters

Point

Range

4.219578132211491e-111

∈ [

3.6472207478991976e-112

1.1066045667362352e-107

]

4.846779570882606e-306

∈ [

-1.693396014411953e-300

1.4181788932772905e-303

]

-2.6997996404559677e+28

∈ [

-4.4428866070924923e+30

-1.1104286431624609e+26

]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	82
1	43	82

Stop Event

1×

saturated

end177.0ms (0.2%)

Stop Event

1×

fuel

Compiler

Compiled 456 to 272 computations (40.4% saved)

Details

analyze12.5s (17.5%)

sample47.5s (66.8%)

preprocess55.0ms (0.1%)

simplify21.0ms (0%)

prune12.0ms (0%)

localize38.0ms (0.1%)

series2.2s (3.1%)

rewrite61.0ms (0.1%)

simplify154.0ms (0.2%)

prune776.0ms (1.1%)

localize39.0ms (0.1%)

series410.0ms (0.6%)

rewrite70.0ms (0.1%)

simplify64.0ms (0.1%)

prune213.0ms (0.3%)

localize8.0ms (0%)

series290.0ms (0.4%)

rewrite64.0ms (0.1%)

simplify100.0ms (0.1%)

prune226.0ms (0.3%)

localize8.0ms (0%)

series254.0ms (0.4%)

rewrite64.0ms (0.1%)

simplify98.0ms (0.1%)

prune209.0ms (0.3%)

regimes3.7s (5.2%)

bsearch1.9s (2.7%)

simplify3.0ms (0%)

end177.0ms (0.2%)

Profiling