Details

analyze1.0s (26%)

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
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.1s (28.4%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

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

3.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.3b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	3.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	3.7b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	6.5b	(/.f64 (.f64 y t) (.f64 2 z))

series113.0ms (2.9%)

Counts

4 → 156

Calls

4 calls:

45.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
31.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
22.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
15.0ms	(/.f64 (.f64 y t) (.f64 2 z))

rewrite122.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`
164×	`egg-rr`
146×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`

Counts

4 → 164

Calls

4 calls:

118.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
118.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
118.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
118.0ms	(/.f64 (.f64 y t) (.f64 2 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	279	58
2	4155	58
3	4989	58
4	4939	58
0	0	0
1	0	0

simplify119.0ms (3%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
529×	`times-frac_binary64`
349×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
248×	`associate-r_binary64`

Counts

320 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	2999
1	276	2989
2	906	2895
3	4287	2885
4	4959	2885
5	4950	2885

prune146.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	206	3	209

Error

0.0b

Counts

209 → 3

Alt Table

Status	Error	Program
▶	0.9b	(-.f64 x (/.f64 y (-.f64 z (*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z)))))))
	27.2b	(fma.f64 2 (/.f64 z t) x)
✓	3.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 4652 to 2512 computations (46% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 2 (/.f64 t z))
✓	0.8b	(/.f64 1 (/.f64 2 (/.f64 t z)))
✓	3.1b	(*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z))))
✓	3.7b	(/.f64 y (-.f64 z (*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z))))))

series65.0ms (1.7%)

Counts

4 → 120

Calls

4 calls:

38.0ms	(/.f64 y (-.f64 z (*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z))))))
14.0ms	(*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z))))
7.0ms	(/.f64 1 (/.f64 2 (/.f64 t z)))
6.0ms	(/.f64 2 (/.f64 t z))

rewrite78.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

784×	`prod-diff_binary64`
139×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`
130×	`add-log-exp_binary64`

Counts

4 → 117

Calls

4 calls:

76.0ms	(/.f64 2 (/.f64 t z))
76.0ms	(/.f64 1 (/.f64 2 (/.f64 t z)))
76.0ms	(*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z))))
76.0ms	(/.f64 y (-.f64 z (*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	278	40
2	3677	40
3	5238	40
0	0	0
1	0	0

simplify91.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

529×	`times-frac_binary64`
517×	`unswap-sqr_binary64`
456×	`fma-neg_binary64`
341×	`associate-/l*_binary64`
299×	`associate-/r*_binary64`

Counts

237 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	1883
1	196	1875
2	693	1855
3	3584	1845
4	4918	1845
5	4948	1845

prune106.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
✓	0.9b	(-.f64 x (/.f64 y (-.f64 z (*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z)))))))
	27.2b	(fma.f64 2 (/.f64 z t) x)
▶	1.2b	(-.f64 x (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (*.f64 y (/.f64 (/.f64 t z) 2)))))))
✓	3.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 2646 to 1514 computations (42.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 y)
✓	0.8b	(.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (.f64 y (/.f64 (/.f64 t z) 2)))))
✓	2.8b	(.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (*.f64 y (/.f64 (/.f64 t z) 2))))))
✓	3.1b	(*.f64 y (/.f64 (/.f64 t z) 2))

series156.0ms (4%)

Counts

4 → 120

Calls

4 calls:

73.0ms	(.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (.f64 y (/.f64 (/.f64 t z) 2)))))
35.0ms	(cbrt.f64 y)
33.0ms	(.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (*.f64 y (/.f64 (/.f64 t z) 2))))))
15.0ms	(*.f64 y (/.f64 (/.f64 t z) 2))

rewrite97.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

678×	`prod-diff_binary64`
162×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Counts

4 → 90

Calls

4 calls:

96.0ms	(cbrt.f64 y)
96.0ms	(.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (.f64 y (/.f64 (/.f64 t z) 2)))))
96.0ms	(.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (*.f64 y (/.f64 (/.f64 t z) 2))))))
96.0ms	(*.f64 y (/.f64 (/.f64 t z) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	333	47
2	4154	47
3	5410	47
0	0	0
1	0	0

simplify106.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

952×	`times-frac_binary64`
577×	`fma-def_binary64`
223×	`fma-neg_binary64`
117×	`distribute-rgt-neg-in_binary64`
114×	`unswap-sqr_binary64`

Counts

210 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	3383
1	501	3327
2	1865	3287
3	4900	3287
4	4984	3287

prune136.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
✓	0.9b	(-.f64 x (/.f64 y (-.f64 z (*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z)))))))
▶	27.2b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (*.f64 y (/.f64 (/.f64 t z) 2)))))))
✓	3.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 4308 to 2632 computations (38.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 2 (/.f64 z t) x)

rewrite73.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

678×	`log1p-expm1-u_binary64`
678×	`expm1-log1p-u_binary64`
152×	`prod-diff_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`

Counts

1 → 26

Calls

1 calls:

72.0ms

(fma.f64 2 (/.f64 z t) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	145	8
2	1745	8
3	4988	8
4	5136	8
0	0	0
1	0	0

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`

Counts

62 → 29

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	249
1	13	249
2	17	249
3	21	249
4	23	249
5	24	249
6	24	249

prune17.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	29	4	33

Error

Counts

33 → 4

Alt Table

Status	Error	Program
✓	0.9b	(-.f64 x (/.f64 y (-.f64 z (*.f64 y (/.f64 1 (/.f64 2 (/.f64 t z)))))))
✓	27.2b	(fma.f64 2 (/.f64 z t) x)
✓	1.2b	(-.f64 x (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (-.f64 z (*.f64 y (/.f64 (/.f64 t z) 2)))))))
✓	3.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 382 to 214 computations (44% saved)

regimes170.0ms (4.3%)

Accuracy

Total 0.9b remaining (99.3%)

Threshold costs 0.9b (99.3%)

Counts

29 → 1

Compiler

Compiled 2938 to 1954 computations (33.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	16	19
2	28	19
3	37	19
4	43	19
5	45	19
6	45	19

end70.0ms (1.8%)

Compiler: Compiled 105 to 70 computations (33.3% saved)

Details

analyze1.0s (26%)

sample1.1s (28.4%)

simplify57.0ms (1.4%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series113.0ms (2.9%)

rewrite122.0ms (3.1%)

simplify119.0ms (3%)

prune146.0ms (3.7%)

localize9.0ms (0.2%)

series65.0ms (1.7%)

rewrite78.0ms (2%)

simplify91.0ms (2.3%)

prune106.0ms (2.7%)

localize13.0ms (0.3%)

series156.0ms (4%)

rewrite97.0ms (2.5%)

simplify106.0ms (2.7%)

prune136.0ms (3.5%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite73.0ms (1.9%)

simplify13.0ms (0.3%)

prune17.0ms (0.4%)

regimes170.0ms (4.3%)

simplify3.0ms (0.1%)

end70.0ms (1.8%)

Profiling