Details

analyze13.0ms (0.5%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample155.0ms (6%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 45 to 27 computations (40% saved)

simplify103.0ms (4%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.6b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 y 4)))
✓	2.7b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	30.1b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series38.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
10.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))
8.0ms	(fma.f64 x x (.f64 y (.f64 y 4)))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
2.0ms	(fma.f64 x x (.f64 y (.f64 y 4)))
0.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

simplify92.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
500×	`div-sub_binary64`
426×	`fma-neg_binary64`
356×	`cancel-sign-sub-inv_binary64`
223×	`distribute-rgt-in_binary64`

Counts

121 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	2496
1	221	2296
2	581	2284
3	2083	2266
4	4490	2230
5	5508	2230

prune73.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	4	112

Error

0.4b

Counts

112 → 4

Alt Table

Status	Error	Program
	30.6b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.8b	-1
▶	30.0b	1
	30.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))) (.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 y 4)))) (cbrt.f64 (fma.f64 x x (.f64 y (.f64 y 4)))))) (/.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 x x (.f64 y (*.f64 y 4))))))

Compiler

Compiled 3018 to 1456 computations (51.8% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

0.4b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	30.6b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.8b	-1
✓	30.0b	1
	30.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))) (.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 y 4)))) (cbrt.f64 (fma.f64 x x (.f64 y (.f64 y 4)))))) (/.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 x x (.f64 y (*.f64 y 4))))))

Compiler

Compiled 173 to 101 computations (41.6% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
✓	0.0b	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	2.7b	(fma.f64 -4 (.f64 y y) (.f64 x x))
	30.1b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series49.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
19.0ms	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`exp-prod_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 50

Calls

2 calls:

8.0ms	(exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
3.0ms	(log.f64 (exp.f64 (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))

simplify109.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-neg_binary64`
384×	`times-frac_binary64`
352×	`distribute-rgt-neg-in_binary64`
280×	`distribute-neg-frac_binary64`
255×	`associate-/r*_binary64`

Counts

98 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	2849
1	308	2692
2	829	2650
3	3328	2638
4	4967	2638
5	4975	2638

prune145.0ms (5.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	211	3	214

Error

0.4b

Counts

214 → 3

Alt Table

Status	Error	Program
▶	30.6b	(log.f64 (pow.f64 (E.f64) (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.8b	-1
✓	30.0b	1

Compiler

Compiled 6420 to 3355 computations (47.7% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (pow.f64 (E.f64) (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
✓	0.0b	(pow.f64 (E.f64) (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4)))))
	2.7b	(fma.f64 -4 (.f64 y y) (.f64 x x))
	30.1b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series97.0ms (3.8%)

Counts

2 → 48

Calls

2 calls:

49.0ms

(log.f64 (pow.f64 (E.f64) (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (fma.f64 x x (*.f64 y (*.f64 y 4))))))

48.0ms

(pow.f64 (E.f64) (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (fma.f64 x x (*.f64 y (*.f64 y 4)))))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow-unpow_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`

Counts

2 → 51

Calls

2 calls:

3.0ms

(pow.f64 (E.f64) (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (fma.f64 x x (*.f64 y (*.f64 y 4)))))

2.0ms

(log.f64 (pow.f64 (E.f64) (/.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)) (fma.f64 x x (*.f64 y (*.f64 y 4))))))

simplify89.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-neg_binary64`
474×	`times-frac_binary64`
313×	`associate-r_binary64`
289×	`associate-/r*_binary64`
288×	`associate-/l*_binary64`

Counts

99 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	3006
1	372	2870
2	1092	2795
3	4469	2783
4	4971	2783

prune134.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	203	3	206

Error

0.4b

Counts

206 → 3

Alt Table

Status	Error	Program
✓	30.6b	(log.f64 (pow.f64 (E.f64) (/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))))
	33.8b	-1
✓	30.0b	1

Compiler

Compiled 6191 to 3146 computations (49.2% saved)

regimes292.0ms (11.4%)

Accuracy

Total 12.7b remaining (97.2%)

Threshold costs 0b (0%)

Counts

25 → 4

Compiler

Compiled 3418 to 1987 computations (41.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	69
1	32	69
2	31	69

end1.0ms (0%)

Compiler: Compiled 49 to 35 computations (28.6% saved)

sample1.1s (42.6%)

Algorithm

1×

intervals

Results

810.0ms

8000×

body

128

valid

Compiler

Compiled 101 to 70 computations (30.7% saved)

Details

analyze13.0ms (0.5%)

sample155.0ms (6%)

simplify103.0ms (4%)

prune3.0ms (0.1%)

localize11.0ms (0.4%)

series38.0ms (1.5%)

rewrite7.0ms (0.3%)

simplify92.0ms (3.6%)

prune73.0ms (2.9%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize13.0ms (0.5%)

series49.0ms (1.9%)

rewrite15.0ms (0.6%)

simplify109.0ms (4.3%)

prune145.0ms (5.7%)

localize14.0ms (0.5%)

series97.0ms (3.8%)

rewrite8.0ms (0.3%)

simplify89.0ms (3.5%)

prune134.0ms (5.2%)

regimes292.0ms (11.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample1.1s (42.6%)

Profiling