Details

analyze2.5s (27.5%)

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%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample2.2s (24.8%)

Alt Table

Status	Error	Program
▶	21.0b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))

Symmetry

(sort x y)

(sort t a)

Results

1.4s	8256×	body	128	valid
749.0ms	4831×	body	128	invalid

Compiler

Compiled 132 to 92 computations (30.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x 9) y)
✓	0.2b	(-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (*.f64 z 4) t) a))
✓	5.4b	(.f64 (.f64 (*.f64 z 4) t) a)
✓	16.7b	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))

series115.0ms (1.3%)

Counts

4 → 204

Calls

4 calls:

78.0ms	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))
21.0ms	(-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (*.f64 z 4) t) a))
10.0ms	(.f64 (.f64 (*.f64 z 4) t) a)
6.0ms	(.f64 (.f64 x 9) y)

rewrite90.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

466×	`prod-diff_binary64`
210×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
198×	`add-log-exp_binary64`

Counts

4 → 128

Calls

4 calls:

86.0ms	(.f64 (.f64 x 9) y)
86.0ms	(-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (*.f64 z 4) t) a))
86.0ms	(.f64 (.f64 (*.f64 z 4) t) a)
86.0ms	(/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	421	64
2	4864	64
3	5682	64
0	0	0
1	0	0

prune308.0ms (3.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	319	13	332
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	320	13	333

Error

6.0b

Counts

333 → 13

Alt Table

Status	Error	Program
	21.2b	(.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (/.f64 1 (*.f64 z c)))
	31.9b	(/.f64 (-.f64 b (.f64 4 (.f64 a (.f64 t z)))) (.f64 c z))
	22.8b	(.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) z) (/.f64 1 c))
	18.2b	(/.f64 (+.f64 (+.f64 (fma.f64 x (.f64 9 y) (neg.f64 (.f64 (.f64 t a) (.f64 z 4)))) (fma.f64 (neg.f64 (.f64 t a)) (.f64 z 4) (.f64 (.f64 t a) (.f64 z 4)))) b) (.f64 z c))
▶	10.7b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (/.f64 (.f64 a t) c)))
	39.5b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))) 2)
	42.4b	(/.f64 b (*.f64 c z))
	43.1b	(.f64 (/.f64 (sqrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b)) 1) (/.f64 (sqrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b)) (.f64 z c)))
	40.0b	(.f64 -4 (/.f64 (.f64 a t) c))
	21.6b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b)) 2) (pow.f64 (cbrt.f64 (.f64 z c)) 2)) (cbrt.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (*.f64 z c))))
	19.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b)) 2) c) (/.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (*.f64 z 4) t) a)) b)) z))
	49.8b	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
	20.0b	(.f64 (/.f64 1 z) (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) c))

Compiler

Compiled 8816 to 4434 computations (49.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
✓	5.8b	(/.f64 (*.f64 a t) c)
✓	6.5b	(/.f64 b (*.f64 c z))
✓	8.3b	(/.f64 (.f64 y x) (.f64 c z))

series81.0ms (0.9%)

Counts

4 → 0

Calls

4 calls:

28.0ms	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
26.0ms	(/.f64 (.f64 y x) (.f64 c z))
15.0ms	(/.f64 b (*.f64 c z))
11.0ms	(/.f64 (*.f64 a t) c)

rewrite94.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

174×	`times-frac_binary64`
174×	`add-sqr-sqrt_binary64`
163×	`egg-rr`
162×	`add-log-exp_binary64`
162×	`log1p-expm1-u_binary64`

Counts

4 → 163

Calls

4 calls:

91.0ms	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
91.0ms	(/.f64 (*.f64 a t) c)
91.0ms	(/.f64 b (*.f64 c z))
91.0ms	(/.f64 (.f64 y x) (.f64 c z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	344	37
2	4919	37
3	5128	37
0	0	0
1	0	0

prune185.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	7	163
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	163	13	176

Error

0.5b

Counts

176 → 13

Alt Table

Status	Error	Program
	10.8b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (.f64 (/.f64 y (.f64 c z)) x))) (.f64 4 (/.f64 (.f64 a t) c)))
	22.8b	(.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) z) (/.f64 1 c))
▶	9.5b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (.f64 (/.f64 a c) t)))
	11.2b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (.f64 (/.f64 y z) (/.f64 x c)))) (.f64 4 (/.f64 (*.f64 a t) c)))
	10.8b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (.f64 (/.f64 a 1) (/.f64 t c))))
	21.2b	(.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (/.f64 1 (*.f64 z c)))
	39.5b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))) 2)
	42.4b	(/.f64 b (*.f64 c z))
	11.5b	(-.f64 (+.f64 (.f64 (/.f64 b c) (/.f64 1 z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (/.f64 (.f64 a t) c)))
	10.7b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (/.f64 1 (/.f64 (.f64 c z) (.f64 9 (.f64 y x))))) (.f64 4 (/.f64 (.f64 a t) c)))
	19.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b)) 2) c) (/.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (*.f64 z 4) t) a)) b)) z))
	10.7b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (pow.f64 (/.f64 c (.f64 a t)) -1)))
	20.0b	(.f64 (/.f64 1 z) (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) c))

Compiler

Compiled 5252 to 2038 computations (61.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
✓	4.0b	(*.f64 (/.f64 a c) t)
✓	6.5b	(/.f64 b (*.f64 c z))
✓	8.3b	(/.f64 (.f64 y x) (.f64 c z))

series81.0ms (0.9%)

Counts

4 → 36

Calls

4 calls:

29.0ms	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
25.0ms	(/.f64 (.f64 y x) (.f64 c z))
15.0ms	(/.f64 b (*.f64 c z))
11.0ms	(*.f64 (/.f64 a c) t)

rewrite89.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

174×	`add-sqr-sqrt_binary64`
162×	`add-log-exp_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-cube-cbrt_binary64`

Counts

4 → 147

Calls

4 calls:

86.0ms	(.f64 9 (/.f64 (.f64 y x) (*.f64 c z)))
86.0ms	(*.f64 (/.f64 a c) t)
86.0ms	(/.f64 b (*.f64 c z))
86.0ms	(/.f64 (.f64 y x) (.f64 c z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	344	37
2	4833	37
3	5015	37
0	0	0
1	0	0

prune161.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	186	10	196

Error

0.0b

Counts

196 → 10

Alt Table

Status	Error	Program
	11.5b	(-.f64 (+.f64 (.f64 (/.f64 b c) (/.f64 1 z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (/.f64 (.f64 a t) c)))
	10.8b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (.f64 (/.f64 y c) (/.f64 x z)))) (.f64 4 (*.f64 (/.f64 a c) t)))
	22.8b	(.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) z) (/.f64 1 c))
	10.8b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (.f64 (/.f64 a 1) (/.f64 t c))))
	21.2b	(.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (/.f64 1 (*.f64 z c)))
	39.5b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))) 2)
▶	9.5b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (.f64 (/.f64 y z) (/.f64 x c)))) (.f64 4 (*.f64 (/.f64 a c) t)))
	19.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b)) 2) c) (/.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (*.f64 z 4) t) a)) b)) z))
	10.7b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (pow.f64 (/.f64 c (.f64 a t)) -1)))
	20.0b	(.f64 (/.f64 1 z) (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) c))

Compiler

Compiled 5434 to 1998 computations (63.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 9 (.f64 (/.f64 y z) (/.f64 x c)))
✓	4.0b	(*.f64 (/.f64 a c) t)
✓	6.5b	(/.f64 b (*.f64 c z))
✓	9.5b	(*.f64 (/.f64 y z) (/.f64 x c))

series86.0ms (1%)

Counts

4 → 132

Calls

4 calls:

34.0ms	(.f64 9 (.f64 (/.f64 y z) (/.f64 x c)))
26.0ms	(*.f64 (/.f64 y z) (/.f64 x c))
15.0ms	(/.f64 b (*.f64 c z))
11.0ms	(*.f64 (/.f64 a c) t)

rewrite46.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

187×	`add-sqr-sqrt_binary64`
174×	`add-log-exp_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
173×	`add-cube-cbrt_binary64`

Counts

4 → 151

Calls

4 calls:

42.0ms	(.f64 9 (.f64 (/.f64 y z) (/.f64 x c)))
42.0ms	(*.f64 (/.f64 a c) t)
42.0ms	(/.f64 b (*.f64 c z))
42.0ms	(*.f64 (/.f64 y z) (/.f64 x c))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	369	37
2	5093	37
0	0	0
1	0	0

prune273.0ms (3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	283	10	293

Error

0.0b

Counts

293 → 10

Alt Table

Status	Error	Program
	11.5b	(-.f64 (+.f64 (.f64 (/.f64 b c) (/.f64 1 z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (/.f64 (.f64 a t) c)))
	10.8b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (.f64 (/.f64 y c) (/.f64 x z)))) (.f64 4 (*.f64 (/.f64 a c) t)))
	22.8b	(.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) z) (/.f64 1 c))
	10.8b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (.f64 (/.f64 a 1) (/.f64 t c))))
	21.2b	(.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (/.f64 1 (*.f64 z c)))
	39.5b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) (.f64 z c))) 2)
✓	9.5b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (.f64 (/.f64 y z) (/.f64 x c)))) (.f64 4 (*.f64 (/.f64 a c) t)))
	19.7b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b)) 2) c) (/.f64 (cbrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (*.f64 z 4) t) a)) b)) z))
	10.7b	(-.f64 (+.f64 (/.f64 b (.f64 c z)) (.f64 9 (/.f64 (.f64 y x) (.f64 c z)))) (.f64 4 (pow.f64 (/.f64 c (.f64 a t)) -1)))
	20.0b	(.f64 (/.f64 1 z) (/.f64 (+.f64 (-.f64 (.f64 (.f64 x 9) y) (.f64 (.f64 (.f64 z 4) t) a)) b) c))

Compiler

Compiled 7285 to 2365 computations (67.5% saved)

regimes2.1s (23.2%)

Accuracy

Total 4.8b remaining (95.6%)

Threshold costs 0b (0%)

Counts

78 → 5

Compiler

Compiled 27692 to 18620 computations (32.8% saved)

bsearch4.0ms (0%)

Compiler: Compiled 26 to 18 computations (30.8% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative_binary64`
22×	`+-commutative_binary64`
18×	`sub-neg_binary64`
15×	`distribute-lft-neg-in_binary64`
15×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	293
1	112	291
2	149	291
3	184	291
4	206	291
5	215	291
6	217	291
7	215	291

end516.0ms (5.7%)

Compiler: Compiled 1533 to 889 computations (42% saved)

Details

analyze2.5s (27.5%)

sample2.2s (24.8%)

localize13.0ms (0.1%)

series115.0ms (1.3%)

rewrite90.0ms (1%)

prune308.0ms (3.4%)

localize15.0ms (0.2%)

series81.0ms (0.9%)

rewrite94.0ms (1%)

prune185.0ms (2.1%)

localize15.0ms (0.2%)

series81.0ms (0.9%)

rewrite89.0ms (1%)

prune161.0ms (1.8%)

localize16.0ms (0.2%)

series86.0ms (1%)

rewrite46.0ms (0.5%)

prune273.0ms (3%)

regimes2.1s (23.2%)

bsearch4.0ms (0%)

simplify13.0ms (0.1%)

end516.0ms (5.7%)

Profiling