Details

analyze401.0ms (8.7%)

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)

sample1.2s (26.6%)

Results

965.0ms	8256×	body	128	valid
72.0ms	730×	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

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

3.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
▶	3.8b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 66 to 45 computations (31.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 y) z)
✓	3.6b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

series26.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(*.f64 (-.f64 1 y) z)
9.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

rewrite12.0ms (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 (-.f64 1 y) z)
5.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

simplify96.0ms (2.1%)

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

prune89.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	5	103

Error

0.0b

Counts

103 → 5

Alt Table

Status	Error	Program
	14.8b	(.f64 x (-.f64 1 (.f64 (sqrt.f64 (-.f64 1 y)) (*.f64 (sqrt.f64 (-.f64 1 y)) z))))
▶	2.0b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
	3.8b	(+.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))
	12.5b	(.f64 x (-.f64 1 (/.f64 (.f64 z (-.f64 1 (*.f64 y y))) (+.f64 1 y))))
	31.8b	(.f64 x (-.f64 1 (.f64 (+.f64 1 (sqrt.f64 y)) (*.f64 (-.f64 1 (sqrt.f64 y)) z))))

Compiler

Compiled 1747 to 1120 computations (35.9% 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))

series20.0ms (0.4%)

Counts

2 → 72

Calls

2 calls:

10.0ms	(.f64 (.f64 z x) (-.f64 y 1))
10.0ms	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))

rewrite19.0ms (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))
5.0ms	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))

simplify101.0ms (2.2%)

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

prune129.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	150	3	153

Error

Counts

153 → 3

Alt Table

Status	Error	Program
✓	2.0b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
	3.8b	(+.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))
▶	1.8b	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))

Compiler

Compiled 3067 to 1779 computations (42% 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)
✓	1.7b	(.f64 (-.f64 (.f64 y x) x) z)

series24.0ms (0.5%)

Counts

3 → 75

Calls

3 calls:

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

rewrite13.0ms (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 x (.f64 (-.f64 (.f64 y x) x) z))
3.0ms	(-.f64 (*.f64 y x) x)

simplify72.0ms (1.6%)

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

prune77.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Error

Counts

123 → 3

Alt Table

Status	Error	Program
✓	2.0b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
▶	3.8b	(+.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))
✓	1.8b	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))

Compiler

Compiled 1847 to 691 computations (62.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (-.f64 1 y))
✓	3.6b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x)
✓	26.2b	(fma.f64 (neg.f64 z) (-.f64 1 y) (*.f64 z (-.f64 1 y)))

series23.0ms (0.5%)

Counts

3 → 84

Calls

3 calls:

10.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z (-.f64 1 y)))) x)
9.0ms	(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))
2.0ms	(.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)))

simplify84.0ms (1.8%)

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

prune181.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	204	3	207

Error

Counts

207 → 3

Alt Table

Status	Error	Program
✓	2.0b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
✓	3.8b	(+.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))
✓	1.8b	(+.f64 x (.f64 (-.f64 (.f64 y x) x) z))

Compiler

Compiled 6735 to 3888 computations (42.3% saved)

regimes1.8s (39.9%)

Accuracy

Total 0.3b remaining (95.4%)

Threshold costs 0.3b (95.4%)

Counts

148 → 3

Compiler

Compiled 20210 to 13769 computations (31.9% saved)

bsearch22.0ms (0.5%)

Steps

Iters	Range		Point
6	2.1403540062738518e-97	7.731303432436667e-89	5.61320657470593e-89
3	-7.524550666313537e+38	-5.84567037087261e+25	-2.426846197592874e+27

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	69
1	45	69
2	54	69
3	59	69
4	61	69
5	60	69

end59.0ms (1.3%)

Compiler: Compiled 152 to 89 computations (41.4% saved)

Details

analyze401.0ms (8.7%)

sample1.2s (26.6%)

simplify42.0ms (0.9%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series26.0ms (0.6%)

rewrite12.0ms (0.3%)

simplify96.0ms (2.1%)

prune89.0ms (1.9%)

localize5.0ms (0.1%)

series20.0ms (0.4%)

rewrite19.0ms (0.4%)

simplify101.0ms (2.2%)

prune129.0ms (2.8%)

localize5.0ms (0.1%)

series24.0ms (0.5%)

rewrite13.0ms (0.3%)

simplify72.0ms (1.6%)

prune77.0ms (1.7%)

localize11.0ms (0.2%)

series23.0ms (0.5%)

rewrite12.0ms (0.3%)

simplify84.0ms (1.8%)

prune181.0ms (3.9%)

regimes1.8s (39.9%)

bsearch22.0ms (0.5%)

simplify4.0ms (0.1%)

end59.0ms (1.3%)

Profiling