Details

analyze119.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
0%	50%	50%	5
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	9.8%	72.7%	10
18.1%	8.8%	73.1%	11
19.6%	5.2%	75.2%	12
20%	4.5%	75.5%	13
20.7%	2.7%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.3s (30.6%)

Results

1.1s	8256×	body	128	valid
71.0ms	538×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
177×	`cancel-sign-sub-inv_binary64`
156×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	82	19
3	199	19
4	510	19
5	969	19
6	1470	19
7	2421	19
8	3626	19
9	4073	19
10	4231	19
11	4272	19
12	4275	19
13	4828	19
14	4828	19

Stop Event

1×

saturated

Counts

1 → 2

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 9 -3)
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.2b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series55.0ms (1.3%)

Counts

4 → 50

Calls

4 calls:

26.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
19.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
8.0ms	(sqrt.f64 (fma.f64 a 9 -3))
1.0ms	(fma.f64 a 9 -3)

rewrite68.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`prod-diff_binary64`
237×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	288	40
2	3706	40

Stop Event

1×	node limit

Counts

4 → 127

Calls

4 calls:

66.0ms	(fma.f64 a 9 -3)
66.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
66.0ms	(sqrt.f64 (fma.f64 a 9 -3))
66.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

374×	`fma-def_binary64`
353×	`associate-+l+_binary64`
283×	`associate-/l*_binary64`
276×	`times-frac_binary64`
230×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1065
1	321	1019
2	1140	867

Stop Event

1×	node limit

Counts

177 → 163

prune206.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	156	7	163
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	157	8	165

Error

0.0b

Counts

165 → 8

Alt Table

Status	Error	Program
	41.1b	(/.f64 (.f64 (fma.f64 a a -1/9) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))) (.f64 (+.f64 a 1/3) (+.f64 1 (-.f64 (/.f64 (*.f64 rand rand) (fma.f64 a 9 -3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))
▶	0.1b	(+.f64 (.f64 a (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
	11.3b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
	3.0b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2)))))
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 3)
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))))
	10.1b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (+.f64 a -1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3759 to 2941 computations (21.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
✓	0.1b	(pow.f64 (fma.f64 a 9 -3) -1/2)
✓	0.1b	(*.f64 a (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
✓	0.1b	(*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))

series194.0ms (4.7%)

Counts

4 → 84

Calls

4 calls:

66.0ms	(*.f64 a (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
65.0ms	(*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
58.0ms	(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
4.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite50.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log-prod_binary64`
306×	`pow2_binary64`
212×	`pow1/3_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	263	50
2	2808	50

Stop Event

1×	node limit

Counts

4 → 90

Calls

4 calls:

48.0ms	(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
48.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)
48.0ms	(*.f64 a (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
48.0ms	(*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

434×	`times-frac_binary64`
266×	`fma-def_binary64`
262×	`associate-/l*_binary64`
235×	`associate-/r*_binary64`
209×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	2870
1	716	2726
2	2315	2382

Stop Event

1×	node limit

Counts

174 → 200

prune394.0ms (9.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	296	2	298
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	299	7	306

Error

Counts

306 → 7

Alt Table

Status	Error	Program
	46.6b	(+.f64 (.f64 rand (.f64 a (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))) (*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
	11.3b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand a) a) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
	3.0b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2)))))
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 3)
▶	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))))
	10.1b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (+.f64 a -1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 10694 to 8565 computations (19.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3))
✓	0.2b	(/.f64 rand (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))
✓	0.6b	(cbrt.f64 (fma.f64 a 9 -3))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)

series113.0ms (2.7%)

Counts

4 → 44

Calls

4 calls:

77.0ms	(pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)
24.0ms	(/.f64 rand (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))
7.0ms	(cbrt.f64 (fma.f64 a 9 -3))
6.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3))

rewrite52.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

862×	`log1p-expm1-u_binary64`
862×	`expm1-log1p-u_binary64`
111×	`egg-rr`
95×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	225	29
2	2419	29

Stop Event

1×	node limit

Counts

4 → 111

Calls

4 calls:

50.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3))
50.0ms	(/.f64 rand (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))
50.0ms	(cbrt.f64 (fma.f64 a 9 -3))
50.0ms	(pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)

simplify38.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

369×	`fma-def_binary64`
324×	`times-frac_binary64`
310×	`associate-/l*_binary64`
277×	`associate-r_binary64`
217×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	1253
1	409	1202
2	1345	1027

Stop Event

1×	node limit

Counts

155 → 164

prune225.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	164	7	171

Error

Counts

171 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 (pow.f64 (cbrt.f64 rand) 2) 1) (/.f64 (cbrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
▶	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 (.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))))))
	11.3b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand a) a) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
	46.6b	(+.f64 (.f64 rand (.f64 a (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))) (*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))))
	10.1b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (+.f64 a -1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3951 to 3224 computations (18.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27)))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))))
✓	0.3b	(fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))
✓	1.0b	(cbrt.f64 -27)

series246.0ms (6%)

Counts

4 → 32

Calls

4 calls:

201.0ms	(/.f64 rand (sqrt.f64 (fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))))
31.0ms	(sqrt.f64 (fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27)))
13.0ms	(fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))
0.0ms	(cbrt.f64 -27)

rewrite48.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

814×	`log1p-expm1-u_binary64`
814×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
86×	`egg-rr`
85×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	197	29
2	2203	29

Stop Event

1×	node limit

Counts

4 → 86

Calls

4 calls:

46.0ms	(sqrt.f64 (fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27)))
46.0ms	(/.f64 rand (sqrt.f64 (fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))))
46.0ms	(fma.f64 (*.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))
46.0ms	(cbrt.f64 -27)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

437×	`distribute-rgt-neg-in_binary64`
357×	`cancel-sign-sub-inv_binary64`
344×	`*-commutative_binary64`
340×	`distribute-lft-neg-in_binary64`
258×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	667
1	148	667
2	428	579
3	1624	539
4	3783	534

Stop Event

1×	node limit

Counts

118 → 108

prune151.0ms (3.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	109	7	116

Error

Counts

116 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 (.f64 a -3) (cbrt.f64 -27) (cbrt.f64 -27))))))
	11.3b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand a) a) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))) 3)))
	46.6b	(+.f64 (.f64 rand (.f64 a (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))) (*.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))
	10.1b	(/.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (+.f64 a -1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 2311 to 1871 computations (19% saved)

regimes521.0ms (12.6%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Counts

119 → 1

Compiler

Compiled 9622 to 7822 computations (18.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	20	32

Stop Event

1×

saturated

end138.0ms (3.3%)

Compiler: Compiled 198 to 157 computations (20.7% saved)

Details

analyze119.0ms (2.9%)

sample1.3s (30.6%)

simplify69.0ms (1.7%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series55.0ms (1.3%)

rewrite68.0ms (1.7%)

simplify30.0ms (0.7%)

prune206.0ms (5%)

localize11.0ms (0.3%)

series194.0ms (4.7%)

rewrite50.0ms (1.2%)

simplify57.0ms (1.4%)

prune394.0ms (9.6%)

localize10.0ms (0.3%)

series113.0ms (2.7%)

rewrite52.0ms (1.3%)

simplify38.0ms (0.9%)

prune225.0ms (5.4%)

localize10.0ms (0.2%)

series246.0ms (6%)

rewrite48.0ms (1.2%)

simplify45.0ms (1.1%)

prune151.0ms (3.7%)

regimes521.0ms (12.6%)

simplify2.0ms (0%)

end138.0ms (3.3%)

Profiling