Details

analyze1.3s (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	95%	5%	9
0%	68.9%	31.1%	10
0%	67.8%	32.2%	11
0.2%	51.5%	48.3%	12
0.3%	51.4%	48.3%	13
0.7%	50.3%	49%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample6.0s (27.8%)

Results

4.3s	23658×	body	128	invalid
1.6s	8256×	body	128	valid

Compiler

Compiled 50 to 36 computations (28% saved)

preprocess40.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

573×	`associate-/l*_binary64`
521×	`fma-def_binary64`
272×	`exp-sum_binary64`
215×	`associate-/r/_binary64`
205×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	416
1	315	416
2	833	384
3	2516	384
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l/_binary64`
548×	`associate-/r/_binary64`
488×	`associate-*l/_binary64`
274×	`unswap-sqr_binary64`
184×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	37	26
2	78	24
3	205	24
4	592	24
5	2082	24

Stop Event

1×	node limit

Counts

1 → 2

prune8.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	24.6b	(.f64 x (.f64 (/.f64 (pow.f64 z y) (exp.f64 b)) (/.f64 (pow.f64 a t) (*.f64 y a))))

Compiler

Compiled 132 to 87 computations (34.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 t 1) (log.f64 a))
✓	0.2b	(*.f64 y (log.f64 z))
✓	1.1b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	2.4b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series1.8s (8.5%)

Counts

4 → 176

Calls

45 calls:

202.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	0
152.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	inf
144.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	-inf
116.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	z	-inf
111.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	z	inf

rewrite43.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	61
1	383	57

Stop Event

1×	node limit

Counts

4 → 98

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
351×	`times-frac_binary64`
320×	`associate-/l*_binary64`
171×	`associate-r_binary64`
156×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	4857
1	569	4089
2	1929	3766

Stop Event

1×	node limit

Counts

274 → 172

prune230.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	165	7	172
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	167	7	174

Error

0.0b

Counts

174 → 7

Alt Table

Status	Error	Program
▶	3.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	26.9b	(pow.f64 (sqrt.f64 (.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) 2)
	23.6b	(.f64 (sqrt.f64 (.f64 x (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) (.f64 (sqrt.f64 (.f64 x (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) (/.f64 1 y)))
	24.3b	(.f64 x (+.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) (.f64 (log.f64 z) (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))))))
	20.1b	(/.f64 (.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y))) y)
	22.6b	(.f64 (/.f64 x (pow.f64 (cbrt.f64 y) 2)) (/.f64 (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)) (cbrt.f64 y)))
	23.1b	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))

Compiler

Compiled 4927 to 2074 computations (57.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (-.f64 t 1) (log.f64 a))
✓	0.2b	(*.f64 (log.f64 z) y)
✓	1.1b	(exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	2.4b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series1.8s (8.6%)

Counts

3 → 140

Calls

39 calls:

202.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	0
152.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	-inf
145.0ms	(exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 (-.f64 t 1) (log.f64 a))) b))	z	-inf
142.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)	x	inf
119.0ms	(exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (.f64 (-.f64 t 1) (log.f64 a))) b))	z	inf

rewrite39.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	383	48

Stop Event

1×	node limit

Counts

3 → 79

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
351×	`times-frac_binary64`
320×	`associate-/l*_binary64`
268×	`associate-/r*_binary64`
163×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	4589
1	549	3871
2	1851	3572

Stop Event

1×	node limit

Counts

219 → 146

prune169.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	171	8	179

Error

0.0b

Counts

179 → 8

Alt Table

Status	Error	Program
	26.9b	(pow.f64 (sqrt.f64 (.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) 2)
	25.9b	(/.f64 (*.f64 (/.f64 x a) (/.f64 (pow.f64 a t) (exp.f64 b))) y)
✓	3.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	23.6b	(.f64 (sqrt.f64 (.f64 x (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) (.f64 (sqrt.f64 (.f64 x (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) (/.f64 1 y)))
	24.3b	(.f64 x (+.f64 (/.f64 (pow.f64 a t) (.f64 y (.f64 a (exp.f64 b)))) (.f64 (log.f64 z) (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))))))
▶	20.1b	(/.f64 (.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y))) y)
	22.6b	(.f64 (/.f64 x (pow.f64 (cbrt.f64 y) 2)) (/.f64 (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)) (cbrt.f64 y)))
	23.1b	(.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))

Compiler

Compiled 4951 to 2036 computations (58.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y)))
✓	0.5b	(.f64 (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b))) (pow.f64 z y))
✓	0.5b	(/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b)))
✓	2.4b	(/.f64 (.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y))) y)

series3.5s (16.4%)

Counts

4 → 240

Calls

60 calls:

196.0ms	(/.f64 (.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y))) y)	x	0
133.0ms	(.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y)))	x	0
129.0ms	(.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y)))	x	-inf
113.0ms	(.f64 (/.f64 (pow.f64 a t) (.f64 a (exp.f64 b))) (pow.f64 z y))	a	inf
110.0ms	(.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y)))	x	inf

rewrite76.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
165×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`
152×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	75
1	319	75
2	4579	75

Stop Event

1×	node limit

Counts

4 → 133

simplify114.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

534×	`times-frac_binary64`
468×	`associate-/l*_binary64`
270×	`associate-/r*_binary64`
229×	`associate-r_binary64`
185×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	6144
1	989	6057
2	4071	6055

Stop Event

1×	node limit

Counts

373 → 242

prune299.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	238	4	242
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	242	8	250

Error

Counts

250 → 8

Alt Table

Status	Error	Program
	22.6b	(.f64 (/.f64 x (pow.f64 (cbrt.f64 y) 2)) (/.f64 (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)) (cbrt.f64 y)))
▶	19.8b	(.f64 x (/.f64 1 (.f64 (/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))))
✓	3.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	26.9b	(pow.f64 (sqrt.f64 (.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) 2)
	20.1b	(/.f64 (/.f64 (.f64 (.f64 (pow.f64 a t) (pow.f64 z y)) x) (*.f64 a (exp.f64 b))) y)
	24.0b	(/.f64 (.f64 (exp.f64 (.f64 (log.f64 z) y)) (.f64 (exp.f64 (.f64 (log.f64 a) t)) x)) (.f64 (exp.f64 b) (.f64 y a)))
✓	20.1b	(/.f64 (.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y))) y)
	19.8b	(.f64 x (.f64 (/.f64 (pow.f64 z y) (/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t))) (/.f64 1 y)))

Compiler

Compiled 7099 to 1855 computations (73.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (.f64 (/.f64 (.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y))))
✓	0.4b	(/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t))
✓	0.4b	(.f64 (/.f64 (.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))
✓	1.9b	(.f64 x (/.f64 1 (.f64 (/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))))

series3.3s (15.5%)

Counts

4 → 228

Calls

57 calls:

138.0ms	(.f64 x (/.f64 1 (.f64 (/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))))	x	0
114.0ms	(.f64 x (/.f64 1 (.f64 (/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))))	x	-inf
114.0ms	(.f64 (/.f64 (.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))	a	-inf
106.0ms	(.f64 (/.f64 (.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))	b	-inf
106.0ms	(.f64 x (/.f64 1 (.f64 (/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))))	b	inf

rewrite43.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

185×	`add-sqr-sqrt_binary64`
175×	`egg-rr`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`
170×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	81
1	364	78

Stop Event

1×	node limit

Counts

4 → 175

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

601×	`times-frac_binary64`
519×	`associate-/l*_binary64`
432×	`associate-r_binary64`
342×	`associate-/r*_binary64`
299×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	331	6684
1	1259	6488

Stop Event

1×	node limit

Counts

403 → 302

prune302.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	299	3	302
Fresh	4	1	5
Picked	0	1	1
Done	0	2	2
Total	303	7	310

Error

Counts

310 → 7

Alt Table

Status	Error	Program
	23.1b	(/.f64 (/.f64 x (/.f64 y (pow.f64 z y))) (*.f64 (/.f64 a (pow.f64 a t)) (exp.f64 b)))
✓	19.8b	(.f64 x (/.f64 1 (.f64 (/.f64 (*.f64 a (exp.f64 b)) (pow.f64 a t)) (/.f64 y (pow.f64 z y)))))
✓	3.1b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 z) y) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	9.7b	(.f64 (exp.f64 (-.f64 (-.f64 (.f64 (log.f64 z) y) (.f64 t (neg.f64 (log.f64 a)))) b)) (/.f64 x (.f64 y a)))
	26.9b	(pow.f64 (sqrt.f64 (.f64 (/.f64 x y) (/.f64 (.f64 (pow.f64 a (+.f64 t -1)) (pow.f64 z y)) (exp.f64 b)))) 2)
	19.8b	(.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (/.f64 (pow.f64 z y) y)))
✓	20.1b	(/.f64 (.f64 x (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y))) y)

Compiler

Compiled 8377 to 2324 computations (72.3% saved)

regimes1.9s (8.7%)

Accuracy

Total 1.4b remaining (99%)

Threshold costs 0b (0%)

Counts

126 → 2

Compiler

Compiled 32583 to 21982 computations (32.5% saved)

bsearch5.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(log.f64 a)

Steps

Iters	Point		Range
-54.988702570892116	∈ [	-54.988702570892116	,	-35.420513213998404	]

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`cancel-sign-sub-inv_binary64`
13×	`distribute-rgt-neg-in_binary64`
12×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	68
1	52	66
2	78	66
3	113	66
4	138	66
5	145	66

Stop Event

1×

saturated

end121.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 260 to 158 computations (39.2% saved)

Details

analyze1.3s (6.1%)

sample6.0s (27.8%)

preprocess40.0ms (0.2%)

simplify19.0ms (0.1%)

prune8.0ms (0%)

localize15.0ms (0.1%)

series1.8s (8.5%)

rewrite43.0ms (0.2%)

simplify82.0ms (0.4%)

prune230.0ms (1.1%)

localize14.0ms (0.1%)

series1.8s (8.6%)

rewrite39.0ms (0.2%)

simplify83.0ms (0.4%)

prune169.0ms (0.8%)

localize12.0ms (0.1%)

series3.5s (16.4%)

rewrite76.0ms (0.4%)

simplify114.0ms (0.5%)

prune299.0ms (1.4%)

localize13.0ms (0.1%)

series3.3s (15.5%)

rewrite43.0ms (0.2%)

simplify86.0ms (0.4%)

prune302.0ms (1.4%)

regimes1.9s (8.7%)

bsearch5.0ms (0%)

simplify4.0ms (0%)

end121.0ms (0.6%)

Profiling