Details

analyze393.0ms (6.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample2.4s (38.4%)

Results

1.1s	4024×	body	256	valid
611.0ms	1502×	body	512	valid
440.0ms	2730×	body	128	valid
124.0ms	841×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify353.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-neg_binary64`
1363×	`fma-def_binary64`
898×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	64	22
3	135	22
4	201	22
5	335	22
6	554	22
7	929	22
8	1477	22
9	2115	22
10	2599	22
11	2554	22
12	2602	22
13	2671	22
14	3117	22
15	2327	22
16	2375	22
17	2383	22
18	2389	22
19	2395	22
20	2397	22
21	2397	22
22	2585	22
23	2685	22
24	2619	22
25	2631	22
26	2661	22
27	2677	22
28	2707	22
29	2707	22
30	2751	22
31	2851	22
32	2827	22
33	2827	22
34	2638	22

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

53.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	53.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	53.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	0.3b	(.f64 (.f64 3 a) c)
✓	24.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series108.0ms (1.7%)

Counts

4 → 100

Calls

4 calls:

58.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
36.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite114.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`fma-def_binary64`
366×	`fma-neg_binary64`
285×	`egg-rr`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`

Counts

4 → 285

Calls

4 calls:

107.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
107.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
107.0ms	(.f64 (.f64 3 a) c)
107.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	297	56
2	3769	56
3	5480	56

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
459×	`associate-/l*_binary64`
396×	`associate-/r*_binary64`
333×	`fma-def_binary64`
308×	`fma-neg_binary64`

Counts

385 → 338

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1940
1	368	1868
2	1240	1839
3	4908	1833
4	5068	1833

prune213.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	334	4	338
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	335	5	340

Error

0.1b

Counts

340 → 5

Alt Table

Status	Error	Program
	53.4b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
✓	53.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	1.3b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
	1.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	2.1b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))

Compiler

Compiled 10144 to 5547 computations (45.3% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 a a) (pow.f64 c 3))
✓	0.3b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
✓	0.3b	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
✓	0.4b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

series176.0ms (2.8%)

Counts

4 → 120

Calls

4 calls:

83.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
59.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
17.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
17.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite82.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

188×	`add-sqr-sqrt_binary64`
185×	`log1p-expm1-u_binary64`
185×	`expm1-log1p-u_binary64`
179×	`add-cbrt-cube_binary64`
178×	`add-log-exp_binary64`

Counts

4 → 128

Calls

4 calls:

80.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
80.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
80.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
80.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	49
1	413	49
2	4883	49
3	4920	49

simplify102.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

940×	`times-frac_binary64`
670×	`associate-l_binary64`
666×	`associate-/l*_binary64`
354×	`associate-/r*_binary64`
257×	`unswap-sqr_binary64`

Counts

248 → 135

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	1524
1	56	1524
2	173	1524
3	727	1524
4	4832	1524
5	4918	1524
6	4997	1524
7	4983	1524

prune216.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	135	5	140

Error

0.1b

Counts

140 → 5

Alt Table

Status	Error	Program
	53.4b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
✓	53.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	1.3b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
▶	1.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	2.1b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))

Compiler

Compiled 6470 to 3974 computations (38.6% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
✓	0.4b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))

series136.0ms (2.2%)

Counts

4 → 24

Calls

4 calls:

87.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
19.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
18.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
12.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite69.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`
161×	`add-sqr-sqrt_binary64`

Counts

4 → 92

Calls

4 calls:

67.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
67.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
67.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
67.0ms	(.f64 (.f64 c a) (*.f64 c a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	371	34
2	3890	34
3	4815	34

simplify170.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1022×	`sqr-pow_binary64`
785×	`associate-l_binary64`
636×	`*-commutative_binary64`
598×	`fabs-mul_binary64`
578×	`cube-prod_binary64`

Counts

116 → 94

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	240
1	16	240
2	35	240
3	88	240
4	295	240
5	1349	240
6	1413	240
7	1542	240
8	1721	240
9	1930	240
10	2180	240
11	2322	240
12	2724	240
13	3047	240
14	3626	240
15	3983	240
16	4262	240
17	4371	240
18	4402	240
19	4414	240
20	4876	240

prune153.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	94	5	99

Error

0.1b

Counts

99 → 5

Alt Table

Status	Error	Program
	53.4b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
✓	53.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	1.3b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
✓	1.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
▶	2.1b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))

Compiler

Compiled 5201 to 3190 computations (38.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))
	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
	0.4b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
	0.5b	(.f64 (.f64 c a) (*.f64 c a))

series102.0ms (1.6%)

Counts

1 → 36

Calls

1 calls:

102.0ms

(/.f64 (fma.f64 -3/2 (/.f64 (*.f64 c a) b) (fma.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (*.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))

rewrite62.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`add-sqr-sqrt_binary64`
243×	`log1p-expm1-u_binary64`
243×	`expm1-log1p-u_binary64`
239×	`add-cbrt-cube_binary64`
235×	`add-cube-cbrt_binary64`

Counts

1 → 18

Calls

1 calls:

62.0ms

(/.f64 (fma.f64 -3/2 (/.f64 (*.f64 c a) b) (fma.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16 (*.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8))) (*.f64 3 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	48
1	534	48
2	4960	48
3	5124	48

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

716×	`associate-/r*_binary64`
439×	`fma-def_binary64`
435×	`associate-/r/_binary64`
434×	`fma-neg_binary64`
421×	`cancel-sign-sub-inv_binary64`

Counts

54 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	1200
1	98	1200
2	311	1146
3	1518	1123
4	5266	1123

prune140.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	103	6	109

Error

0.1b

Counts

109 → 6

Alt Table

Status	Error	Program
	53.4b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
✓	53.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	2.3b	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) -9/8))) 3) (pow.f64 (*.f64 a 3) 3)))
	2.1b	(pow.f64 (/.f64 (.f64 a 3) (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) -27/16 (.f64 (/.f64 (pow.f64 (*.f64 c a) 2) (pow.f64 b 3)) -9/8)))) -1)
✓	1.3b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
✓	1.7b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))

Compiler

Compiled 4095 to 2354 computations (42.5% saved)

regimes853.0ms (13.6%)

Accuracy

Total 1.3b remaining (86.6%)

Threshold costs 0b (0%)

Counts

124 → 1

Compiler

Compiled 23328 to 15698 computations (32.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	61
1	36	61
2	36	61

end193.0ms (3.1%)

Compiler: Compiled 319 to 218 computations (31.7% saved)

Details

analyze393.0ms (6.3%)

sample2.4s (38.4%)

simplify353.0ms (5.6%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series108.0ms (1.7%)

rewrite114.0ms (1.8%)

simplify86.0ms (1.4%)

prune213.0ms (3.4%)

localize27.0ms (0.4%)

series176.0ms (2.8%)

rewrite82.0ms (1.3%)

simplify102.0ms (1.6%)

prune216.0ms (3.4%)

localize27.0ms (0.4%)

series136.0ms (2.2%)

rewrite69.0ms (1.1%)

simplify170.0ms (2.7%)

prune153.0ms (2.4%)

localize19.0ms (0.3%)

series102.0ms (1.6%)

rewrite62.0ms (1%)

simplify46.0ms (0.7%)

prune140.0ms (2.2%)

regimes853.0ms (13.6%)

simplify3.0ms (0%)

end193.0ms (3.1%)

Profiling