Details

analyze1.5s (20.5%)

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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.1%	87.7%	0.2%	13
21.4%	78.3%	0.4%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.6s (22.4%)

Results

922.0ms	6894×	body	128	valid
163.0ms	1270×	body	128	invalid
150.0ms	505×	body	512	valid
149.0ms	390×	body	1024	valid
99.0ms	400×	body	256	valid
30.0ms	67×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify89.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

836×	`unsub-neg_binary64`
769×	`fma-def_binary64`
696×	`div-sub_binary64`
646×	`sub-neg_binary64`
478×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	21	19
2	52	17
3	144	17
4	421	17
5	1092	17
6	2657	17
7	3901	17
8	4408	17
9	4807	17
10	4881	17

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

11.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	24.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 100 to 55 computations (45% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series93.0ms (1.3%)

Counts

2 → 108

Calls

2 calls:

63.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
29.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite71.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

514×	`fma-def_binary64`
264×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

2 → 74

Calls

2 calls:

70.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
70.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3776	27
3	5340	27
0	0	0
1	0	0

simplify111.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

512×	`cancel-sign-sub-inv_binary64`
445×	`sub-neg_binary64`
351×	`associate-+r+_binary64`
288×	`distribute-neg-in_binary64`
271×	`+-commutative_binary64`

Counts

182 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	5085
1	820	5085
2	3265	5049
3	4994	5049

prune122.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	133	9	142
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	133	11	144

Error

0.6b

Counts

144 → 11

Alt Table

Status	Error	Program
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
▶	15.7b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
	24.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	43.6b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	40.4b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	42.4b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	31.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	44.9b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x) 3))
	42.8b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) 2)

Compiler

Compiled 5022 to 1652 computations (67.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	3.2b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
✓	5.8b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series159.0ms (2.2%)

Counts

2 → 120

Calls

2 calls:

92.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
66.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite80.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

284×	`expm1-udef_binary64`
284×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

2 → 77

Calls

2 calls:

78.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
78.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	287	33
2	4401	33
3	5270	33
0	0	0
1	0	0

simplify139.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

612×	`cancel-sign-sub-inv_binary64`
570×	`sub-neg_binary64`
563×	`associate-+r+_binary64`
422×	`associate-+l+_binary64`
362×	`+-commutative_binary64`

Counts

197 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	7336
1	1017	7336
2	3902	6730
3	5411	6730

prune203.0ms (2.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	238	10	248

Error

0.6b

Counts

248 → 10

Alt Table

Status	Error	Program
	42.4b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	40.4b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	39.7b	(fma.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
▶	15.8b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	43.6b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	31.9b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	42.2b	(+.f64 x (/.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (sqrt.f64 (-.f64 a z))) (sqrt.f64 (-.f64 a z))))

Compiler

Compiled 8702 to 2769 computations (68.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
✓	4.1b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
✓	6.1b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series185.0ms (2.6%)

Counts

3 → 168

Calls

3 calls:

92.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
66.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))
27.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

rewrite146.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
149×	`add-log-exp_binary64`

Counts

3 → 122

Calls

3 calls:

140.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
140.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
140.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	296	43
2	4767	43
3	5265	43
0	0	0
1	0	0

simplify183.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-+r+_binary64`
461×	`associate-+l+_binary64`
408×	`+-commutative_binary64`
333×	`fma-neg_binary64`
293×	`associate--l+_binary64`

Counts

290 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	8872
1	1200	8755
2	4639	8149
3	4987	8149

prune182.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	232	10	242

Error

0.6b

Counts

242 → 10

Alt Table

Status	Error	Program
	42.4b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	40.4b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	39.7b	(fma.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
✓	15.8b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	43.6b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
▶	12.0b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	16.1b	(+.f64 x (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 y z)) 2) (-.f64 a z)) (/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 1 (-.f64 t x)))))

Compiler

Compiled 8477 to 2688 computations (68.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
✓	3.5b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

series80.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

60.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
20.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

rewrite74.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

516×	`fma-def_binary64`
264×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

2 → 74

Calls

2 calls:

72.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
72.0ms	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3780	27
3	5347	27
0	0	0
1	0	0

simplify98.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

574×	`cancel-sign-sub-inv_binary64`
500×	`sub-neg_binary64`
341×	`associate-+r+_binary64`
297×	`+-commutative_binary64`
288×	`distribute-neg-in_binary64`

Counts

170 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	4642
1	835	4633
2	3385	4573
3	5205	4573

prune172.0ms (2.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	158	10	168

Error

0.6b

Counts

168 → 10

Alt Table

Status	Error	Program
	42.4b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	40.4b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	21.0b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))
	12.0b	(fma.f64 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 a z))) (-.f64 t x) x)
	39.7b	(fma.f64 (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (sqrt.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) x)
✓	15.8b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))
	35.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	15.5b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	43.6b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
✓	12.0b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)

Compiler

Compiled 5218 to 1687 computations (67.7% saved)

regimes1.7s (23.2%)

Accuracy

Total 4.1b remaining (82.4%)

Threshold costs 0b (0%)

Counts

128 → 5

Compiler

Compiled 17244 to 10158 computations (41.1% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

153×	`cancel-sign-sub-inv_binary64`
141×	`distribute-rgt-neg-in_binary64`
93×	`distribute-lft-neg-in_binary64`
93×	`neg-sub0_binary64`
93×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	293
1	78	293
2	107	293
3	147	293
4	205	293
5	252	293
6	306	293
7	366	293
8	431	293
9	510	293
10	615	293
11	702	293
12	758	293
13	793	293
14	814	293
15	823	293
16	825	293
17	821	293

end156.0ms (2.2%)

Compiler: Compiled 676 to 250 computations (63% saved)

Iter	Nodes	Cost
0	52	293
1	78	293
2	107	293
3	147	293
4	205	293
5	252	293
6	306	293
7	366	293
8	431	293
9	510	293
10	615	293
11	702	293
12	758	293
13	793	293
14	814	293
15	823	293
16	825	293
17	821	293

Iter	Nodes	Cost
0	52	293
1	78	293
2	107	293
3	147	293
4	205	293
5	252	293
6	306	293
7	366	293
8	431	293
9	510	293
10	615	293
11	702	293
12	758	293
13	793	293
14	814	293
15	823	293
16	825	293
17	821	293

Details

analyze1.5s (20.5%)

sample1.6s (22.4%)

simplify89.0ms (1.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series93.0ms (1.3%)

rewrite71.0ms (1%)

simplify111.0ms (1.6%)

prune122.0ms (1.7%)

localize8.0ms (0.1%)

series159.0ms (2.2%)

rewrite80.0ms (1.1%)

simplify139.0ms (1.9%)

prune203.0ms (2.8%)

localize8.0ms (0.1%)

series185.0ms (2.6%)

rewrite146.0ms (2%)

simplify183.0ms (2.6%)

prune182.0ms (2.6%)

localize8.0ms (0.1%)

series80.0ms (1.1%)

rewrite74.0ms (1%)

simplify98.0ms (1.4%)

prune172.0ms (2.4%)

regimes1.7s (23.2%)

bsearch6.0ms (0.1%)

simplify38.0ms (0.5%)

end156.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	52	293
1	78	293
2	107	293
3	147	293
4	205	293
5	252	293
6	306	293
7	366	293
8	431	293
9	510	293
10	615	293
11	702	293
12	758	293
13	793	293
14	814	293
15	823	293
16	825	293
17	821	293