Details

analyze1.7s (19.7%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample2.5s (28.2%)

Results

1.7s	8256×	body	128	valid
631.0ms	2347×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify105.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
480×	`neg-mul-1_binary64`
416×	`div-sub_binary64`
394×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	55	23
3	101	21
4	220	21
5	423	21
6	834	20
7	1845	19
8	3893	19
9	4281	19
10	4633	19
11	4956	19
12	4804	19

prune8.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series99.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

74.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
25.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

rewrite113.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
278×	`log1p-udef_binary64`
152×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Counts

2 → 84

Calls

2 calls:

108.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
108.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	289	29
2	4245	29
3	5032	29
0	0	0
1	0	0

simplify274.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1100×	`fma-def_binary64`
996×	`fma-neg_binary64`
177×	`sub-neg_binary64`
171×	`cancel-sign-sub-inv_binary64`
161×	`distribute-rgt-in_binary64`

Counts

156 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	1239
1	74	1197
2	167	1197
3	286	1134
4	468	1017
5	735	1017
6	1427	1017
7	1721	1017
8	1749	1017
9	1757	1017
10	1786	1017
11	1815	1017
12	2374	1017
13	2384	1017
14	2390	1017
15	2395	1017
16	2395	1017
17	2302	1017

prune196.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	98	5	103

Error

Counts

103 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	31.1b	(+.f64 (/.f64 x y) (-.f64 -2 (pow.f64 (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2)))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2))))

Compiler

Compiled 2612 to 1822 computations (30.2% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
✓	0.2b	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))

series91.0ms (1%)

Counts

2 → 72

Calls

2 calls:

67.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
24.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))

rewrite118.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

298×	`log1p-udef_binary64`
168×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
156×	`add-cbrt-cube_binary64`

Counts

2 → 90

Calls

2 calls:

114.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
113.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	328	29
2	4511	29
3	4921	29
0	0	0
1	0	0

simplify274.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1100×	`fma-def_binary64`
996×	`fma-neg_binary64`
177×	`sub-neg_binary64`
171×	`cancel-sign-sub-inv_binary64`
161×	`distribute-rgt-in_binary64`

Counts

162 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	1239
1	74	1197
2	167	1197
3	286	1134
4	468	1017
5	735	1017
6	1427	1017
7	1721	1017
8	1749	1017
9	1757	1017
10	1786	1017
11	1815	1017
12	2374	1017
13	2384	1017
14	2390	1017
15	2395	1017
16	2395	1017
17	2302	1017

prune184.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Error

Counts

112 → 5

Alt Table

Status	Error	Program
	14.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (.f64 (-.f64 4 (/.f64 4 (.f64 z z))) (/.f64 1 t)) (-.f64 -2 (/.f64 -2 z)))))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
▶	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2))))

Compiler

Compiled 2751 to 1905 computations (30.8% saved)

localize19.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series69.0ms (0.8%)

Counts

1 → 48

Calls

1 calls:

69.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

rewrite73.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

278×	`prod-diff_binary64`
266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`

Counts

1 → 25

Calls

1 calls:

72.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	291	19
2	3751	19
3	5069	19
0	0	0
1	0	0

simplify228.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

967×	`fma-neg_binary64`
737×	`fma-def_binary64`
183×	`sub-neg_binary64`
152×	`cancel-sign-sub-inv_binary64`
129×	`cancel-sign-sub_binary64`

Counts

73 → 36

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	909
1	59	909
2	111	909
3	150	909
4	212	792
5	365	792
6	622	792
7	1215	792
8	1792	792
9	2100	792
10	2103	792
11	2128	792
12	2107	792
13	2117	792
14	2386	792
15	2391	792
16	2391	792
17	2300	792

prune151.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	73	5	78

Error

Counts

78 → 5

Alt Table

Status	Error	Program
	14.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (.f64 (-.f64 4 (/.f64 4 (.f64 z z))) (/.f64 1 t)) (-.f64 -2 (/.f64 -2 z)))))
	9.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
✓	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2))))

Compiler

Compiled 1492 to 1069 computations (28.4% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2)
✓	0.6b	(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

series1.4s (16.4%)

Counts

3 → 72

Calls

3 calls:

821.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

550.0ms

(pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2)

59.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2))

rewrite68.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
171×	`pow3_binary64`
162×	`log-pow_binary64`

Counts

3 → 99

Calls

3 calls:

65.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2))

65.0ms

(pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2)

65.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	225	35
2	2662	35
3	4917	35
0	0	0
1	0	0

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
348×	`fma-neg_binary64`
304×	`times-frac_binary64`
266×	`cancel-sign-sub-inv_binary64`
237×	`associate-/l*_binary64`

Counts

171 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2162
1	441	2058
2	1425	1688
3	4589	1456
4	4997	1456
5	4952	1456

prune336.0ms (3.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	301	5	306

Error

Counts

306 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
✓	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	14.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (.f64 (-.f64 4 (/.f64 4 (.f64 z z))) (/.f64 1 t)) (-.f64 -2 (/.f64 -2 z)))))
	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) 2))))

Compiler

Compiled 9733 to 7245 computations (25.6% saved)

regimes464.0ms (5.3%)

Accuracy

Total 0.1b remaining (79%)

Threshold costs 0.1b (79%)

Counts

64 → 1

Compiler

Compiled 9338 to 7312 computations (21.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	18	22
2	27	22
3	39	22
4	44	22
5	46	22
6	45	22

end88.0ms (1%)

Compiler: Compiled 150 to 115 computations (23.3% saved)

Details

analyze1.7s (19.7%)

sample2.5s (28.2%)

simplify105.0ms (1.2%)

prune8.0ms (0.1%)

localize17.0ms (0.2%)

series99.0ms (1.1%)

rewrite113.0ms (1.3%)

simplify274.0ms (3.1%)

prune196.0ms (2.2%)

localize18.0ms (0.2%)

series91.0ms (1%)

rewrite118.0ms (1.3%)

simplify274.0ms (3.1%)

prune184.0ms (2.1%)

localize19.0ms (0.2%)

series69.0ms (0.8%)

rewrite73.0ms (0.8%)

simplify228.0ms (2.6%)

prune151.0ms (1.7%)

localize23.0ms (0.3%)

series1.4s (16.4%)

rewrite68.0ms (0.8%)

simplify99.0ms (1.1%)

prune336.0ms (3.8%)

regimes464.0ms (5.3%)

simplify3.0ms (0%)

end88.0ms (1%)

Profiling