Details

analyze114.0ms (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample26.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

409×	`fma-def_binary64`
352×	`fma-neg_binary64`
228×	`div-sub_binary64`
166×	`associate-/l/_binary64`
143×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	33	10
4	46	10
5	74	10
6	122	10
7	209	10
8	354	10
9	556	10
10	694	10
11	793	10
12	804	10
13	804	10
14	808	10
15	820	10
16	830	10
17	754	10

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

8.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.4b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 x0 (-.f64 1 x1))
✓	7.5b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`add-sqr-sqrt_binary64`
128×	`*-un-lft-identity_binary64`
91×	`times-frac_binary64`
78×	`add-cube-cbrt_binary64`
72×	`prod-diff_binary64`

Counts

2 → 158

Calls

2 calls:

17.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
5.0ms	(/.f64 x0 (-.f64 1 x1))

series46.0ms (1%)

Counts

2 → 36

Calls

2 calls:

25.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
21.0ms	(/.f64 x0 (-.f64 1 x1))

simplify154.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

505×	`associate-*l/_binary64`
466×	`fma-neg_binary64`
269×	`associate-/r*_binary64`
237×	`associate-/r/_binary64`
236×	`associate-/l/_binary64`

Counts

194 → 328

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3668
1	420	3244
2	1658	2590
3	4745	2590
4	5039	2590

prune81.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	326	2	328
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	327	2	329

Error

2.9b

Counts

329 → 2

Alt Table

Status	Error	Program
▶	3.7b	(+.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))
	16.9b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))

Status

Error

Program

▶

3.7b

(+.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

16.9b

(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))

Compiler

Compiled 4126 to 1898 computations (54% saved)

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	7.4b	(fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))
✓	61.9b	(fma.f64 (neg.f64 (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))

New

Error

Program

✓

7.4b

(fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

✓

61.9b

(fma.f64 (neg.f64 (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms

(fma.f64 (neg.f64 (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))

0.0ms

(fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

series222.0ms (4.9%)

Counts

2 → 36

Calls

2 calls:

132.0ms

(fma.f64 (neg.f64 (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))

89.0ms

(fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

558×	`fma-neg_binary64`
442×	`fma-def_binary64`
340×	`associate-l_binary64`
319×	`distribute-rgt-neg-out_binary64`
297×	`div-sub_binary64`

Counts

56 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	607
1	157	487
2	510	455
3	2476	455
4	4588	455
5	4941	455

prune31.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	98	2	100

Error

2.7b

Counts

100 → 2

Alt Table

Status	Error	Program
	16.9b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))
▶	3.5b	(+.f64 (exp.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0))))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

Status

Error

Program

16.9b

(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))

▶

3.5b

(+.f64 (exp.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

Compiler

Compiled 2052 to 545 computations (73.4% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.0b	(exp.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))))
	7.4b	(fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))
	61.9b	(fma.f64 (neg.f64 (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`exp-prod_binary64`
3×	`exp-sum_binary64`
3×	`log-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 17

Calls

1 calls:

2.0ms

(exp.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))))

series1.0s (22.9%)

Counts

1 → 24

Calls

1 calls:

1.0s	(exp.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))))

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

669×	`times-frac_binary64`
381×	`cancel-sign-sub-inv_binary64`
338×	`fma-neg_binary64`
237×	`fma-def_binary64`
212×	`div-sub_binary64`

Counts

41 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	810
1	179	621
2	484	516
3	1931	505
4	4277	505
5	4993	505
6	4980	505
7	4957	505

prune52.0ms (1.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	2	179

Error

1.9b

Counts

179 → 2

Alt Table

Status	Error	Program
	16.9b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))
▶	2.6b	(+.f64 (pow.f64 E.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0))))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

Status

Error

Program

16.9b

(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))

▶

2.6b

(+.f64 (pow.f64 E.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

Compiler

Compiled 3904 to 1125 computations (71.2% saved)

localize18.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.3b	(pow.f64 E.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))))
	7.4b	(fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))
	61.9b	(fma.f64 (neg.f64 (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow-unpow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

1 → 24

Calls

1 calls:

2.0ms

(pow.f64 E.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))))

series1.3s (29.4%)

Counts

1 → 24

Calls

1 calls:

1.3s	(pow.f64 E.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))))

simplify120.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

669×	`times-frac_binary64`
381×	`cancel-sign-sub-inv_binary64`
338×	`fma-neg_binary64`
232×	`fma-def_binary64`
192×	`unswap-sqr_binary64`

Counts

48 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	100	1098
1	226	915
2	587	774
3	2102	774
4	4469	696
5	4824	696
6	4951	696

prune58.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	290	0	290
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	290	2	292

Error

1.9b

Counts

292 → 2

Alt Table

Status	Error	Program
	16.9b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))
✓	2.6b	(+.f64 (pow.f64 E.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (.f64 (cbrt.f64 x0) (.f64 (cbrt.f64 x0) (cbrt.f64 x0))))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

Status

Error

Program

16.9b

(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))

✓

2.6b

(+.f64 (pow.f64 E.f64 (log.f64 (fma.f64 x0 (/.f64 1 (-.f64 1 x1)) (neg.f64 (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0))))))) (fma.f64 (neg.f64 (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)) (*.f64 (cbrt.f64 x0) (*.f64 (cbrt.f64 x0) (cbrt.f64 x0)))))

Compiler

Compiled 4479 to 1267 computations (71.7% saved)

regimes51.0ms (1.1%)

Accuracy

Total 0.7b remaining (26.1%)

Threshold costs 0.7b (26.1%)

Compiler

Compiled 1680 to 876 computations (47.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
1	32	61
2	45	61
3	51	61
4	53	61
5	52	61

end1.0ms (0%)

Compiler: Compiled 39 to 17 computations (56.4% saved)

sample851.0ms (18.7%)

Algorithm

1×

intervals

Results

254.0ms	8000×	body	128	valid
237.0ms	8000×	pre	128	true

Compiler

Compiled 120 to 63 computations (47.5% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	33	10
4	46	10
5	74	10
6	122	10
7	209	10
8	354	10
9	556	10
10	694	10
11	793	10
12	804	10
13	804	10
14	808	10
15	820	10
16	830	10
17	754	10

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	33	10
4	46	10
5	74	10
6	122	10
7	209	10
8	354	10
9	556	10
10	694	10
11	793	10
12	804	10
13	804	10
14	808	10
15	820	10
16	830	10
17	754	10

Details

analyze114.0ms (2.5%)

sample26.0ms (0.6%)

simplify56.0ms (1.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite37.0ms (0.8%)

series46.0ms (1%)

simplify154.0ms (3.4%)

prune81.0ms (1.8%)

localize13.0ms (0.3%)

rewrite2.0ms (0%)

series222.0ms (4.9%)

simplify78.0ms (1.7%)

prune31.0ms (0.7%)

localize16.0ms (0.4%)

rewrite3.0ms (0.1%)

series1.0s (22.9%)

simplify121.0ms (2.7%)

prune52.0ms (1.1%)

localize18.0ms (0.4%)

rewrite5.0ms (0.1%)

series1.3s (29.4%)

simplify120.0ms (2.6%)

prune58.0ms (1.3%)

regimes51.0ms (1.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample851.0ms (18.7%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	20	10
3	33	10
4	46	10
5	74	10
6	122	10
7	209	10
8	354	10
9	556	10
10	694	10
11	793	10
12	804	10
13	804	10
14	808	10
15	820	10
16	830	10
17	754	10