Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.7s (30.5%)

Results

700.0ms	2102×	body	1024	valid
426.0ms	4362×	body	128	valid
260.0ms	1082×	body	512	valid
94.0ms	499×	body	256	valid
82.0ms	211×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

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

29.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	3.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

rewrite218.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

1304×	`*-un-lft-identity_binary64`
1000×	`times-frac_binary64`
859×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
523×	`add-cube-cbrt_binary64`

Counts

2 → 748

Calls

2 calls:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify730.0ms (13.3%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-neg_binary64`
418×	`distribute-rgt-in_binary64`
361×	`unsub-neg_binary64`
255×	`fma-udef_binary64`
202×	`associate-+r-_binary64`

Counts

772 → 551

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	521	54026
1	1234	30580
2	2848	22272
3	4495	22270
4	4718	22270

prune656.0ms (12%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	547	4	551
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	547	5	552

Error

0.0b

Counts

552 → 5

Alt Table

Status	Error	Program
✓	29.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
▶	31.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	31.4b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
	47.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)))))
	32.7b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 29220 to 21602 computations (26.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 x x))
✓	0.3b	(/.f64 1 (pow.f64 x 4))
✓	6.5b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
✓	9.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

series11.0ms (0.2%)

Counts

4 → 36

Calls

4 calls:

3.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
3.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
2.0ms	(/.f64 1 (pow.f64 x 4))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite171.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

512×	`*-un-lft-identity_binary64`
377×	`add-sqr-sqrt_binary64`
332×	`times-frac_binary64`
278×	`prod-diff_binary64`
232×	`add-cube-cbrt_binary64`

Counts

4 → 467

Calls

4 calls:

48.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
18.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
3.0ms	(/.f64 1 (*.f64 x x))
3.0ms	(/.f64 1 (pow.f64 x 4))

simplify462.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-neg_binary64`
199×	`associate-l_binary64`
191×	`associate-r_binary64`
183×	`sub-neg_binary64`
172×	`exp-prod_binary64`

Counts

503 → 470

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	331	19401
1	843	15538
2	2858	13558
3	4318	13558
4	4976	13558
5	4835	13558

prune591.0ms (10.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	468	2	470
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	469	6	475

Error

Counts

475 → 6

Alt Table

Status	Error	Program
▶	31.4b	(+.f64 (fma.f64 -3 (/.f64 1 x) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))
✓	29.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	31.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	47.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)))))
	32.7b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	54.6b	(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 (/.f64 -3 x) 3) (pow.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 3)) (pow.f64 x 4)) (.f64 (+.f64 (.f64 (/.f64 -3 x) (/.f64 -3 x)) (+.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))))) 1)) (.f64 (+.f64 (.f64 (/.f64 -3 x) (/.f64 -3 x)) (+.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))))) (pow.f64 x 4)))

Compiler

Compiled 25339 to 18771 computations (25.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (*.f64 x x))
✓	0.3b	(/.f64 -1 (pow.f64 x 4))
	6.5b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
✓	9.8b	(+.f64 (fma.f64 -3 (/.f64 1 x) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))

series6.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(+.f64 (fma.f64 -3 (/.f64 1 x) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))
3.0ms	(/.f64 -1 (pow.f64 x 4))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`

Counts

2 → 65

Calls

2 calls:

9.0ms	(+.f64 (fma.f64 -3 (/.f64 1 x) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))
3.0ms	(/.f64 -1 (pow.f64 x 4))

simplify106.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

530×	`fma-neg_binary64`
504×	`unsub-neg_binary64`
398×	`div-sub_binary64`
252×	`distribute-rgt-in_binary64`
215×	`distribute-lft-in_binary64`

Counts

77 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1688
1	282	1524
2	717	1448
3	2880	1448
4	4899	1448
5	4985	1448
6	4940	1448

prune157.0ms (2.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	172	6	178

Error

Counts

178 → 6

Alt Table

Status	Error	Program
✓	31.4b	(+.f64 (fma.f64 -3 (/.f64 1 x) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))
✓	29.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	31.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	47.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)))))
▶	32.7b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	54.6b	(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 (/.f64 -3 x) 3) (pow.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 3)) (pow.f64 x 4)) (.f64 (+.f64 (.f64 (/.f64 -3 x) (/.f64 -3 x)) (+.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))))) 1)) (.f64 (+.f64 (.f64 (/.f64 -3 x) (/.f64 -3 x)) (+.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))))) (pow.f64 x 4)))

Compiler

Compiled 5969 to 4546 computations (23.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 x 3))
✓	7.6b	(fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x))

series6.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

3.0ms	(fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x))
2.0ms	(+.f64 x (pow.f64 x 3))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 29

Calls

2 calls:

7.0ms	(+.f64 x (pow.f64 x 3))
0.0ms	(fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x))

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Rules

513×	`fma-neg_binary64`
392×	`*-commutative_binary64`
361×	`associate-+r+_binary64`
342×	`associate-+l+_binary64`
289×	`distribute-rgt-out_binary64`

Counts

47 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	551
1	116	497
2	361	497
3	1504	495
4	3527	494
5	4794	494

prune49.0ms (0.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	52	6	58

Error

Counts

58 → 6

Alt Table

Status	Error	Program
✓	31.4b	(+.f64 (fma.f64 -3 (/.f64 1 x) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))
✓	29.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	31.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	47.1b	(+.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)))))
✓	32.7b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	54.6b	(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 (/.f64 -3 x) 3) (pow.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 3)) (pow.f64 x 4)) (.f64 (+.f64 (.f64 (/.f64 -3 x) (/.f64 -3 x)) (+.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))))) 1)) (.f64 (+.f64 (.f64 (/.f64 -3 x) (/.f64 -3 x)) (+.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3)))))) (pow.f64 x 4)))

Compiler

Compiled 1119 to 739 computations (34% saved)

regimes194.0ms (3.5%)

Accuracy

Total 0.0b remaining (41.1%)

Threshold costs 0.0b (41.1%)

Counts

59 → 3

Compiler

Compiled 4074 to 3070 computations (24.6% saved)

bsearch39.0ms (0.7%)

Steps

Iters	Range		Point
10	85.12132175397775	7907210314430.959	2074.932321600268
9	-13138.89396616099	-0.0506589835992668	-2956.959262914682

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	87
1	41	87
2	58	87
3	77	87
4	89	87
5	94	87
6	95	87
7	92	87

end186.0ms (3.4%)

Compiler: Compiled 389 to 288 computations (26% saved)

Details

analyze6.0ms (0.1%)

sample1.7s (30.5%)

simplify87.0ms (1.6%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series6.0ms (0.1%)

rewrite218.0ms (4%)

simplify730.0ms (13.3%)

prune656.0ms (12%)

localize14.0ms (0.2%)

series11.0ms (0.2%)

rewrite171.0ms (3.1%)

simplify462.0ms (8.4%)

prune591.0ms (10.8%)

localize17.0ms (0.3%)

series6.0ms (0.1%)

rewrite15.0ms (0.3%)

simplify106.0ms (1.9%)

prune157.0ms (2.9%)

localize7.0ms (0.1%)

series6.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify55.0ms (1%)

prune49.0ms (0.9%)

regimes194.0ms (3.5%)

bsearch39.0ms (0.7%)

simplify4.0ms (0.1%)

end186.0ms (3.4%)

Profiling