Details

analyze455.0ms (10.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.1s (23.7%)

Results

809.0ms	8256×	body	128	valid
62.0ms	664×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

4.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.6b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 44 to 31 computations (29.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 y) z)
✓	4.4b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

series15.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
5.0ms	(*.f64 (-.f64 1 y) z)

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`associate-l_binary64`
8×	`add-cube-cbrt_binary64`
6×	`associate-r_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
4.0ms	(*.f64 (-.f64 1 y) z)

simplify90.0ms (2%)

Algorithm

1×	egg-herbie

Rules

394×	`unsub-neg_binary64`
329×	`neg-mul-1_binary64`
328×	`sub-neg_binary64`
320×	`neg-sub0_binary64`
310×	`*-commutative_binary64`

Counts

105 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1393
1	253	1203
2	751	1133
3	2083	1115
4	3435	1115
5	4698	1115
6	4919	1115

prune97.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Error

0.0b

Counts

102 → 5

Alt Table

Status	Error	Program
	41.8b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 (-.f64 1 y) z))) (.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))) (.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))))
▶	2.1b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
	4.5b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x) (.f64 (fma.f64 (neg.f64 z) (-.f64 1 y) (.f64 z (-.f64 1 y))) x))
	17.7b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z)))) (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z))))
	31.5b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))))

Compiler

Compiled 1797 to 1158 computations (35.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
✓	3.2b	(.f64 (.f64 z x) (-.f64 y 1))

series22.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
9.0ms	(.f64 (.f64 z x) (-.f64 y 1))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`prod-diff_binary64`
36×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
26×	`associate-+r+_binary64`

Counts

2 → 94

Calls

2 calls:

6.0ms	(.f64 (.f64 z x) (-.f64 y 1))
4.0ms	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary64`
429×	`distribute-rgt-in_binary64`
423×	`fma-def_binary64`
394×	`distribute-lft-in_binary64`
347×	`*-commutative_binary64`

Counts

166 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	2074
1	331	1819
2	998	1809
3	3205	1807
4	4670	1807
5	4990	1807

prune140.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	148	5	153

Error

Counts

153 → 5

Alt Table

Status	Error	Program
▶	2.3b	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))
✓	2.1b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
	4.5b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x) (.f64 (fma.f64 (neg.f64 z) (-.f64 1 y) (.f64 z (-.f64 1 y))) x))
	29.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 z x) (-.f64 y 1))) (sqrt.f64 (.f64 (*.f64 z x) (-.f64 y 1)))))
	17.7b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z)))) (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z))))

Compiler

Compiled 3155 to 1841 computations (41.6% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))
✓	0.0b	(-.f64 (*.f64 y x) x)
✓	2.2b	(.f64 (-.f64 (.f64 y x) x) z)

series25.0ms (0.5%)

Counts

3 → 75

Calls

3 calls:

11.0ms	(.f64 (-.f64 (.f64 y x) x) z)
10.0ms	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))
4.0ms	(-.f64 (*.f64 y x) x)

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 60

Calls

3 calls:

5.0ms	(.f64 (-.f64 (.f64 y x) x) z)
3.0ms	(-.f64 (*.f64 y x) x)
2.0ms	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))

simplify147.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
737×	`fma-neg_binary64`
392×	`distribute-rgt-in_binary64`
372×	`distribute-lft-in_binary64`
199×	`cancel-sign-sub-inv_binary64`

Counts

135 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1637
1	323	1428
2	1234	1411
3	4308	1405
4	4980	1405

prune88.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	5	125

Error

Counts

125 → 5

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))
✓	2.1b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
▶	4.5b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x) (.f64 (fma.f64 (neg.f64 z) (-.f64 1 y) (.f64 z (-.f64 1 y))) x))
	29.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 z x) (-.f64 y 1))) (sqrt.f64 (.f64 (*.f64 z x) (-.f64 y 1)))))
	17.7b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z)))) (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z))))

Compiler

Compiled 1935 to 753 computations (61.1% saved)

localize21.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (-.f64 1 y))
✓	4.4b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x)
✓	28.6b	(fma.f64 (neg.f64 z) (-.f64 1 y) (*.f64 z (-.f64 1 y)))

series60.0ms (1.3%)

Counts

3 → 84

Calls

3 calls:

48.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x)
8.0ms	(fma.f64 (neg.f64 z) (-.f64 1 y) (*.f64 z (-.f64 1 y)))
4.0ms	(*.f64 z (-.f64 1 y))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 81

Calls

3 calls:

5.0ms	(*.f64 z (-.f64 1 y))
3.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x)
0.0ms	(fma.f64 (neg.f64 z) (-.f64 1 y) (*.f64 z (-.f64 1 y)))

simplify97.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

641×	`unsub-neg_binary64`
346×	`*-commutative_binary64`
319×	`fma-def_binary64`
315×	`exp-prod_binary64`
308×	`associate-+r+_binary64`

Counts

165 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1703
1	280	1423
2	887	1296
3	2087	1296
4	3647	1296
5	4901	1296

prune214.0ms (4.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	204	5	209

Error

Counts

209 → 5

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))
✓	2.1b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
✓	4.5b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x) (.f64 (fma.f64 (neg.f64 z) (-.f64 1 y) (.f64 z (-.f64 1 y))) x))
	29.3b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 z x) (-.f64 y 1))) (sqrt.f64 (.f64 (*.f64 z x) (-.f64 y 1)))))
	17.7b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z)))) (sqrt.f64 (-.f64 1 (.f64 (-.f64 1 y) z))))

Compiler

Compiled 6779 to 3919 computations (42.2% saved)

regimes1.6s (35.8%)

Accuracy

Total 0.9b remaining (98.4%)

Threshold costs 0.9b (98.4%)

Counts

137 → 3

Compiler

Compiled 18701 to 13097 computations (30% saved)

bsearch34.0ms (0.7%)

Steps

Iters	Range		Point
5	2.8789439620644936e-123	2.2654446249076073e-122	7.834655119261467e-123
8	-2.219803332419874e+130	-2.0792485518620442e+126	-2.114852865568445e+126

Compiler

Compiled 4 to 3 computations (25% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

72×	`distribute-rgt-neg-in_binary64`
61×	`cancel-sign-sub-inv_binary64`
45×	`distribute-lft-neg-in_binary64`
44×	`distribute-lft-neg-out_binary64`
42×	`neg-sub0_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	75
1	52	75
2	68	73
3	82	73
4	94	73
5	105	73
6	121	73
7	137	73
8	163	73
9	199	73
10	258	73
11	312	73
12	350	73
13	360	73
14	356	73

end89.0ms (2%)

Compiler: Compiled 202 to 136 computations (32.7% saved)

Iter	Nodes	Cost
0	28	75
1	52	75
2	68	73
3	82	73
4	94	73
5	105	73
6	121	73
7	137	73
8	163	73
9	199	73
10	258	73
11	312	73
12	350	73
13	360	73
14	356	73

Iter	Nodes	Cost
0	28	75
1	52	75
2	68	73
3	82	73
4	94	73
5	105	73
6	121	73
7	137	73
8	163	73
9	199	73
10	258	73
11	312	73
12	350	73
13	360	73
14	356	73

Details

analyze455.0ms (10.1%)

sample1.1s (23.7%)

simplify42.0ms (0.9%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series15.0ms (0.3%)

rewrite11.0ms (0.3%)

simplify90.0ms (2%)

prune97.0ms (2.2%)

localize5.0ms (0.1%)

series22.0ms (0.5%)

rewrite17.0ms (0.4%)

simplify101.0ms (2.3%)

prune140.0ms (3.1%)

localize5.0ms (0.1%)

series25.0ms (0.5%)

rewrite11.0ms (0.3%)

simplify147.0ms (3.3%)

prune88.0ms (1.9%)

localize21.0ms (0.5%)

series60.0ms (1.3%)

rewrite12.0ms (0.3%)

simplify97.0ms (2.2%)

prune214.0ms (4.7%)

regimes1.6s (35.8%)

bsearch34.0ms (0.7%)

simplify12.0ms (0.3%)

end89.0ms (2%)

Profiling

Iter	Nodes	Cost
0	28	75
1	52	75
2	68	73
3	82	73
4	94	73
5	105	73
6	121	73
7	137	73
8	163	73
9	199	73
10	258	73
11	312	73
12	350	73
13	360	73
14	356	73