Details

analyze5.0ms (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 (17.5%)

Results

678.0ms	2096×	body	1024	valid
448.0ms	4343×	body	128	valid
286.0ms	1108×	body	512	valid
90.0ms	515×	body	256	valid
79.0ms	194×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify86.0ms (0.9%)

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

31.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.4b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite222.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

1322×	`*-un-lft-identity_binary64`
1012×	`times-frac_binary64`
869×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
533×	`add-cube-cbrt_binary64`

Counts

3 → 783

Calls

3 calls:

42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
7.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
4.0ms	(/.f64 x (+.f64 x 1))

simplify970.0ms (10%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
367×	`unsub-neg_binary64`
299×	`fma-udef_binary64`
213×	`sub-neg_binary64`
202×	`associate-+r-_binary64`

Counts

819 → 619

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	545	54602
1	1290	31108
2	3043	22839
3	4323	22837
4	4983	22837
5	4991	22837
6	4742	22837

prune737.0ms (7.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	615	4	619
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	615	5	620

Error

0.0b

Counts

620 → 5

Alt Table

Status	Error	Program
▶	29.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	30.0b	(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))))))
	34.1b	(+.f64 1 (*.f64 x (+.f64 3 x)))
	31.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	31.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 30496 to 22477 computations (26.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (pow.f64 x 4))
✓	0.6b	(/.f64 1 (*.f64 x x))
✓	7.5b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
✓	10.2b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

series13.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
4.0ms	(-.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 1 (pow.f64 x 4))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite163.0ms (1.7%)

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)))
20.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
4.0ms	(/.f64 1 (pow.f64 x 4))
3.0ms	(/.f64 1 (*.f64 x x))

simplify449.0ms (4.6%)

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

prune625.0ms (6.5%)

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

0.0b

Counts

475 → 6

Alt Table

Status	Error	Program
✓	29.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	57.8b	(/.f64 (-.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 -3 (fma.f64 (/.f64 3 (pow.f64 x 3)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 -1 (.f64 x x))) (/.f64 1 (pow.f64 x 4)))) (+.f64 (/.f64 x (pow.f64 x 6)) (/.f64 (.f64 27 x) (pow.f64 x 9))))) (.f64 x (fma.f64 (/.f64 3 (pow.f64 x 3)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 -1 (.f64 x x))) (/.f64 1 (pow.f64 x 4))))) (.f64 (pow.f64 x 5) (fma.f64 (/.f64 3 (pow.f64 x 3)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 -1 (.f64 x x))) (/.f64 1 (pow.f64 x 4)))))
	34.1b	(+.f64 1 (*.f64 x (+.f64 3 x)))
	31.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
▶	30.5b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 -3) (cbrt.f64 -3)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (cbrt.f64 -3) (cbrt.f64 x)) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))
✓	31.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 25245 to 18711 computations (25.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 x)
	0.6b	(/.f64 1 (*.f64 x x))
	7.5b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
✓	10.2b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 -3) (cbrt.f64 -3)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (cbrt.f64 -3) (cbrt.f64 x)) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))

series72.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

36.0ms

(cbrt.f64 x)

36.0ms

(+.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 -3) (cbrt.f64 -3)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (cbrt.f64 -3) (cbrt.f64 x)) (neg.f64 (*.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`cbrt-prod_binary64`

Counts

2 → 31

Calls

2 calls:

8.0ms

(+.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 -3) (cbrt.f64 -3)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (cbrt.f64 -3) (cbrt.f64 x)) (neg.f64 (*.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))

1.0ms

(cbrt.f64 x)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-neg_binary64`
294×	`div-sub_binary64`
246×	`unsub-neg_binary64`
228×	`associate-/r*_binary64`
192×	`associate-l_binary64`

Counts

55 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1565
1	213	1315
2	642	1080
3	3049	961
4	4658	961
5	4964	961

prune165.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	167	6	173

Error

0.0b

Counts

173 → 6

Alt Table

Status	Error	Program
✓	29.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	57.8b	(/.f64 (-.f64 (.f64 (pow.f64 x 4) (-.f64 (.f64 -3 (fma.f64 (/.f64 3 (pow.f64 x 3)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 -1 (.f64 x x))) (/.f64 1 (pow.f64 x 4)))) (+.f64 (/.f64 x (pow.f64 x 6)) (/.f64 (.f64 27 x) (pow.f64 x 9))))) (.f64 x (fma.f64 (/.f64 3 (pow.f64 x 3)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 -1 (.f64 x x))) (/.f64 1 (pow.f64 x 4))))) (.f64 (pow.f64 x 5) (fma.f64 (/.f64 3 (pow.f64 x 3)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 -1 (.f64 x x))) (/.f64 1 (pow.f64 x 4)))))
	34.1b	(+.f64 1 (*.f64 x (+.f64 3 x)))
▶	31.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	30.5b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 -3) (cbrt.f64 -3)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (cbrt.f64 -3) (cbrt.f64 x)) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))
✓	31.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 7395 to 5120 computations (30.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	0.0b	(*.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	0.1b	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series16.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms

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

6.0ms

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

4.0ms

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

rewrite309.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

912×	`*-un-lft-identity_binary64`
344×	`times-frac_binary64`
248×	`distribute-lft-out--_binary64`
217×	`cbrt-prod_binary64`
171×	`cbrt-div_binary64`

Counts

3 → 297

Calls

3 calls:

96.0ms

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

72.0ms

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

27.0ms

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

simplify530.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
348×	`fma-neg_binary64`
336×	`*-commutative_binary64`
250×	`associate-l_binary64`
215×	`times-frac_binary64`

Counts

333 → 349

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	368	20281
1	737	19756
2	1902	16994
3	4571	16791
4	4784	16750
5	4746	16750
6	4959	16750

prune3.1s (32.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1854	2	1856
Fresh	2	0	2
Picked	1	0	1
Done	1	2	3
Total	1858	4	1862

Error

Counts

1862 → 4

Alt Table

Status	Error	Program
✓	29.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	29.3b	(/.f64 (-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (+.f64 x -1)))
	34.1b	(fma.f64 x (+.f64 x 3) 1)
✓	30.5b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 -3) (cbrt.f64 -3)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (cbrt.f64 -3) (cbrt.f64 x)) (neg.f64 (.f64 (+.f64 (/.f64 1 (.f64 x x)) (/.f64 3 (pow.f64 x 3))) 1))) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 154645 to 114576 computations (25.9% saved)

regimes190.0ms (2%)

Accuracy

Total 0.0b remaining (56.1%)

Threshold costs 0.0b (56.1%)

Counts

57 → 3

Compiler

Compiled 3795 to 2879 computations (24.1% saved)

bsearch15.0ms (0.2%)

Steps

Iters	Range		Point
3	7428.514536328033	105992.72939524964	39024.27154499961
3	-1890131552972676000.0	-75287546.85287057	-586015145795.7788

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-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	36	103
1	51	103
2	67	103
3	87	103
4	96	103
5	100	103
6	101	103
7	98	103

end111.0ms (1.1%)

Compiler: Compiled 230 to 170 computations (26.1% saved)

Details

analyze5.0ms (0.1%)

sample1.7s (17.5%)

simplify86.0ms (0.9%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series8.0ms (0.1%)

rewrite222.0ms (2.3%)

simplify970.0ms (10%)

prune737.0ms (7.6%)

localize13.0ms (0.1%)

series13.0ms (0.1%)

rewrite163.0ms (1.7%)

simplify449.0ms (4.6%)

prune625.0ms (6.5%)

localize22.0ms (0.2%)

series72.0ms (0.7%)

rewrite11.0ms (0.1%)

simplify83.0ms (0.9%)

prune165.0ms (1.7%)

localize9.0ms (0.1%)

series16.0ms (0.2%)

rewrite309.0ms (3.2%)

simplify530.0ms (5.5%)

prune3.1s (32.5%)

regimes190.0ms (2%)

bsearch15.0ms (0.2%)

simplify5.0ms (0.1%)

end111.0ms (1.1%)

Profiling