Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	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)

sample1.9s (6.2%)

Results

765.0ms	2093×	body	1024	valid
525.0ms	4422×	body	128	valid
286.0ms	1041×	body	512	valid
95.0ms	214×	body	2048	valid
92.0ms	486×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify112.0ms (0.4%)

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

prune3.0ms (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

26.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize13.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	1.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series13.0ms (0%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite462.0ms (1.5%)

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:

80.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
11.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify1.4s (4.5%)

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

prune966.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	545	6	551
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	546	6	552

Error

0.0b

Counts

552 → 6

Alt Table

Status	Error	Program
▶	26.1b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))))
	26.8b	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	35.2b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	35.3b	(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))))))
	45.0b	(+.f64 (fma.f64 (/.f64 x (-.f64 (.f64 x x) (.f64 1 1))) (-.f64 x 1) (neg.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (cbrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (+.f64 (sqrt.f64 x) 1)))))
	28.5b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 29428 to 21756 computations (26.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))))
✓	0.0b	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
✓	0.1b	(pow.f64 (/.f64 x (+.f64 x 1)) 3)
✓	1.5b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))

series19.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))))
5.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
3.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)
3.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)

rewrite2.4s (7.9%)

Algorithm

1×	rewrite-expression-head

Rules

6608×	`*-un-lft-identity_binary64`
4959×	`times-frac_binary64`
4306×	`add-sqr-sqrt_binary64`
3164×	`cube-prod_binary64`
3164×	`unpow-prod-down_binary64`

Counts

4 → 3824

Calls

4 calls:

275.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))))
198.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
9.0ms	(pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)
6.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

simplify8.8s (28.9%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
537×	`fma-def_binary64`
440×	`fma-udef_binary64`
249×	`unsub-neg_binary64`
180×	`sub-neg_binary64`

Counts

3872 → 1311

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1209	379737
1	2688	347590
2	4746	347590
3	5241	347590

prune8.3s (27.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1309	2	1311
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	1311	6	1317

Error

0.0b

Counts

1317 → 6

Alt Table

Status	Error	Program
	27.8b	(/.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (/.f64 x (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)) (neg.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 x -1)) 3) (pow.f64 (+.f64 1 x) 3)))) (fma.f64 (neg.f64 (pow.f64 (/.f64 1 (+.f64 x -1)) 3)) (pow.f64 (+.f64 1 x) 3) (.f64 (pow.f64 (/.f64 1 (+.f64 x -1)) 3) (pow.f64 (+.f64 1 x) 3)))) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))))
▶	26.8b	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	35.2b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	35.3b	(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))))))
	45.2b	(/.f64 (+.f64 (fma.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) 3) (pow.f64 (/.f64 x (cbrt.f64 (+.f64 x 1))) 3) (neg.f64 (.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) 3) (pow.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) 3)))) (fma.f64 (neg.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) 3)) (pow.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) 3) (.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) 3) (pow.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) 3)))) (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))))
	28.5b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 141565 to 106762 computations (24.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	1.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series26.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

20.0ms

(sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

6.0ms

(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite427.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

863×	`*-un-lft-identity_binary64`
324×	`times-frac_binary64`
235×	`distribute-lft-out--_binary64`
202×	`sqrt-prod_binary64`
152×	`distribute-lft-out_binary64`

Counts

2 → 196

Calls

2 calls:

139.0ms

(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

111.0ms

(sqrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

simplify436.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

543×	`distribute-rgt-in_binary64`
532×	`fma-neg_binary64`
297×	`associate-l_binary64`
273×	`associate-r_binary64`
246×	`fma-def_binary64`

Counts

212 → 173

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	177	6292
1	351	5987
2	990	5837
3	2758	5696
4	4973	5688
5	5174	5688

prune3.6s (11.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1317	2	1319
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	1322	3	1325

Error

Counts

1325 → 3

Alt Table

Status	Error	Program
	35.2b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))
▶	24.0b	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
	28.5b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 84539 to 62680 computations (25.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 x) (-.f64 x 1))
✓	0.0b	(-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x)
✓	1.2b	(+.f64 (-.f64 x 1) (-.f64 -1 x))
✓	13.3b	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))

series19.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
6.0ms	(-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x)
5.0ms	(*.f64 (+.f64 1 x) (-.f64 x 1))
2.0ms	(+.f64 (-.f64 x 1) (-.f64 -1 x))

rewrite90.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
45×	`prod-diff_binary64`
45×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`

Counts

4 → 187

Calls

4 calls:

21.0ms	(+.f64 (-.f64 x 1) (-.f64 -1 x))
20.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
15.0ms	(*.f64 (+.f64 1 x) (-.f64 x 1))
9.0ms	(-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x)

simplify222.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-neg_binary64`
299×	`distribute-rgt-in_binary64`
280×	`cancel-sign-sub-inv_binary64`
277×	`distribute-lft-in_binary64`
184×	`associate-l_binary64`

Counts

235 → 297

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	290	3681
1	701	2973
2	3052	2946
3	4665	2943
4	4967	2943

prune512.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	297	3	300

Error

Counts

300 → 3

Alt Table

Status	Error	Program
	35.2b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))
✓	24.0b	(/.f64 (-.f64 (fma.f64 x (+.f64 (-.f64 x 1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (-.f64 x 1)))
	28.5b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 9194 to 6348 computations (31% saved)

regimes432.0ms (1.4%)

Accuracy

Total 0.0b remaining (56.4%)

Threshold costs 0.0b (56.4%)

Counts

71 → 3

Compiler

Compiled 4867 to 3663 computations (24.7% saved)

bsearch11.0ms (0%)

Steps

Iters	Range		Point
1	11899428.512545833	14830770.002124036	13365099.257334935
1	-3.882171361997238e+30	-1029732765015344400.0	-2.005334843764889e+24

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
7×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	50	62
2	68	62
3	77	62
4	82	62
5	83	62
6	80	62

end176.0ms (0.6%)

Compiler: Compiled 141 to 106 computations (24.8% saved)

Details

analyze4.0ms (0%)

sample1.9s (6.2%)

simplify112.0ms (0.4%)

prune3.0ms (0%)

localize13.0ms (0%)

series13.0ms (0%)

rewrite462.0ms (1.5%)

simplify1.4s (4.5%)

prune966.0ms (3.2%)

localize20.0ms (0.1%)

series19.0ms (0.1%)

rewrite2.4s (7.9%)

simplify8.8s (28.9%)

prune8.3s (27.4%)

localize15.0ms (0.1%)

series26.0ms (0.1%)

rewrite427.0ms (1.4%)

simplify436.0ms (1.4%)

prune3.6s (11.7%)

localize22.0ms (0.1%)

series19.0ms (0.1%)

rewrite90.0ms (0.3%)

simplify222.0ms (0.7%)

prune512.0ms (1.7%)

regimes432.0ms (1.4%)

bsearch11.0ms (0%)

simplify8.0ms (0%)

end176.0ms (0.6%)

Profiling