Details

analyze209.0ms (4.9%)

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
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
74.9%	25%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (33%)

Infinites

8.2% of outputs are infinite.

Results

732.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify112.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	1.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series51.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
19.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

11.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
7.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify124.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
905×	`times-frac_binary64`
465×	`fma-neg_binary64`
154×	`associate-/l*_binary64`
144×	`+-commutative_binary64`

Counts

190 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4749
1	800	4617
2	2672	4102
3	4971	4102
4	5241	4102

prune124.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	188	6	194

Error

0.0b

Counts

194 → 6

Alt Table

Status	Error	Program
▶	6.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	9.7b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	1.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	35.2b	(.f64 (.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y))) t)
	9.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	9.3b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

Compiler

Compiled 4566 to 1299 computations (71.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (-.f64 x y))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
✓	1.6b	(*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t)
✓	5.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))

series474.0ms (11.1%)

Counts

4 → 144

Calls

4 calls:

361.0ms	(*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t)
48.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))
36.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
28.0ms	(cbrt.f64 (-.f64 x y))

rewrite60.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64`
77×	`*-un-lft-identity_binary64`
68×	`add-exp-log_binary64`
61×	`associate-l_binary64`
59×	`cbrt-prod_binary64`

Counts

4 → 190

Calls

4 calls:

16.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))
13.0ms	(*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t)
8.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
2.0ms	(cbrt.f64 (-.f64 x y))

simplify218.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

387×	`fma-def_binary64`
380×	`times-frac_binary64`
365×	`associate-/l*_binary64`
250×	`associate-/r*_binary64`
240×	`*-commutative_binary64`

Counts

334 → 412

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	676	9800
1	1960	9015
2	4988	9015
3	5042	9015

prune341.0ms (8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	520	0	520
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	520	6	526

Error

0.0b

Counts

526 → 6

Alt Table

Status	Error	Program
✓	6.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	9.7b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	1.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	35.2b	(.f64 (.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y))) t)
▶	9.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	9.3b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

Compiler

Compiled 19910 to 7351 computations (63.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z y))
✓	9.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))

series49.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

32.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
17.0ms	(/.f64 t (-.f64 z y))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

2 → 87

Calls

2 calls:

9.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
4.0ms	(/.f64 t (-.f64 z y))

simplify110.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
695×	`fma-def_binary64`
344×	`fma-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`
204×	`sub-neg_binary64`

Counts

159 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3780
1	617	3669
2	2394	3214
3	4765	3214
4	4978	3214

prune106.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	159	6	165

Error

0.0b

Counts

165 → 6

Alt Table

Status	Error	Program
✓	6.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	9.7b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	1.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	35.2b	(.f64 (.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y))) t)
✓	9.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
▶	9.3b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

Compiler

Compiled 3449 to 971 computations (71.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z y)) t)
✓	9.2b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

series59.0ms (1.4%)

Counts

3 → 108

Calls

3 calls:

32.0ms	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
16.0ms	(*.f64 (/.f64 1 (-.f64 z y)) t)
11.0ms	(/.f64 1 (-.f64 z y))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
31×	`add-exp-log_binary64`
26×	`associate-l_binary64`

Counts

3 → 119

Calls

3 calls:

9.0ms	(*.f64 (/.f64 1 (-.f64 z y)) t)
9.0ms	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
4.0ms	(/.f64 1 (-.f64 z y))

simplify132.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
337×	`distribute-rgt-in_binary64`
289×	`cancel-sign-sub-inv_binary64`
283×	`fma-neg_binary64`
207×	`sub-neg_binary64`

Counts

227 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	4516
1	675	4300
2	2529	3660
3	4920	3660
4	5052	3660

prune124.0ms (2.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	221	6	227

Error

0.0b

Counts

227 → 6

Alt Table

Status	Error	Program
✓	6.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	9.7b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	1.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	35.2b	(.f64 (.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y))) t)
✓	9.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	9.3b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

Compiler

Compiled 4582 to 1799 computations (60.7% saved)

regimes374.0ms (8.8%)

Accuracy

Total 0.9b remaining (97.5%)

Threshold costs 0.9b (97.5%)

Counts

61 → 1

Compiler

Compiled 8074 to 4261 computations (47.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	20	49
2	26	49
3	28	49
4	29	49
5	29	49

end72.0ms (1.7%)

Compiler: Compiled 169 to 85 computations (49.7% saved)

Details

analyze209.0ms (4.9%)

sample1.4s (33%)

simplify112.0ms (2.6%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series51.0ms (1.2%)

rewrite28.0ms (0.6%)

simplify124.0ms (2.9%)

prune124.0ms (2.9%)

localize13.0ms (0.3%)

series474.0ms (11.1%)

rewrite60.0ms (1.4%)

simplify218.0ms (5.1%)

prune341.0ms (8%)

localize7.0ms (0.2%)

series49.0ms (1.1%)

rewrite20.0ms (0.5%)

simplify110.0ms (2.6%)

prune106.0ms (2.5%)

localize8.0ms (0.2%)

series59.0ms (1.4%)

rewrite31.0ms (0.7%)

simplify132.0ms (3.1%)

prune124.0ms (2.9%)

regimes374.0ms (8.8%)

simplify4.0ms (0.1%)

end72.0ms (1.7%)

Profiling