Details

analyze117.0ms (2.8%)

Algorithm

1×

Search

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

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample44.0ms (1.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
13.0ms	256×	pre	128	true

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify64.0ms (1.5%)

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

prune3.0ms (0.1%)

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

8.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.0b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 x0 (-.f64 1 x1))
✓	7.1b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

series44.0ms (1%)

Counts

2 → 36

Calls

2 calls:

23.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
21.0ms	(/.f64 x0 (-.f64 1 x1))

rewrite70.0ms (1.7%)

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:

27.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
8.0ms	(/.f64 x0 (-.f64 1 x1))

simplify229.0ms (5.4%)

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 → 193

Iterations

Useful iterations: 2 (0.0ms)

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

prune145.0ms (3.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	2	194

Error

2.8b

Counts

194 → 2

Alt Table

Status	Error	Program
▶	3.5b	(+.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)))))
	18.6b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))

Status

Error

Program

▶

3.5b

(+.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)))))

18.6b

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

Compiler

Compiled 4133 to 1902 computations (54% saved)

localize26.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	7.1b	(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

✓

7.1b

(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))))

series133.0ms (3.2%)

Counts

2 → 36

Calls

2 calls:

87.0ms

(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))))

45.0ms

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

rewrite3.0ms (0.1%)

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:

1.0ms

(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))))

1.0ms

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

simplify95.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

669×	`times-frac_binary64`
408×	`fma-neg_binary64`
382×	`fma-def_binary64`
326×	`cancel-sign-sub-inv_binary64`
264×	`associate-l_binary64`

Counts

56 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	607
1	154	487
2	516	455
3	2205	455
4	4381	455
5	4976	455

prune52.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	57	2	59

Error

2.6b

Counts

59 → 2

Alt Table

Status	Error	Program
	18.6b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))
▶	3.2b	(+.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

18.6b

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

▶

3.2b

(+.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 1985 to 527 computations (73.5% saved)

localize33.0ms (0.8%)

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)))))))
	7.1b	(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))))

series45.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

45.0ms

(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)))))))

rewrite6.0ms (0.2%)

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:

4.0ms

(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)))))))

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

512×	`times-frac_binary64`
381×	`fma-neg_binary64`
334×	`distribute-rgt-out_binary64`
331×	`fma-def_binary64`
271×	`cancel-sign-sub-inv_binary64`

Counts

41 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	657
1	154	604
2	492	514
3	1947	493
4	4277	493
5	5052	493

prune92.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	2	104

Error

1.7b

Counts

104 → 2

Alt Table

Status	Error	Program
	18.6b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))
▶	2.3b	(+.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

18.6b

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

▶

2.3b

(+.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 3790 to 1105 computations (70.8% saved)

localize45.0ms (1.1%)

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)))))))
	7.1b	(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))))

series1.0s (24.4%)

Counts

1 → 24

Calls

1 calls:

1.0s	(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)))))))

rewrite10.0ms (0.2%)

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:

6.0ms

(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)))))))

simplify141.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
381×	`fma-neg_binary64`
280×	`cancel-sign-sub-inv_binary64`
251×	`distribute-rgt-out_binary64`
230×	`fma-def_binary64`

Counts

48 → 58

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	96	1086
1	227	915
2	578	798
3	1888	708
4	4286	704
5	4939	704
6	4930	704

prune116.0ms (2.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	115	2	117

Error

1.7b

Counts

117 → 2

Alt Table

Status	Error	Program
	18.6b	(*.f64 x0 (+.f64 (+.f64 (fma.f64 x1 x1 x1) (pow.f64 x1 3)) (pow.f64 x1 4)))
✓	2.3b	(+.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

18.6b

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

✓

2.3b

(+.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 4425 to 1260 computations (71.5% saved)

regimes88.0ms (2.1%)

Accuracy

Total 0.7b remaining (26.1%)

Threshold costs 0.7b (26.1%)

Counts

14 → 1

Compiler

Compiled 1672 to 868 computations (48.1% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
6×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	51
1	33	51
2	50	51
3	63	49
4	79	49
5	84	49
6	80	49

end1.0ms (0%)

Compiler: Compiled 32 to 18 computations (43.8% saved)

sample1.5s (35%)

Algorithm

1×

intervals

Results

451.0ms	8000×	body	128	valid
446.0ms	8000×	pre	128	true

Compiler

Compiled 113 to 64 computations (43.4% 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

analyze117.0ms (2.8%)

sample44.0ms (1.1%)

simplify64.0ms (1.5%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series44.0ms (1%)

rewrite70.0ms (1.7%)

simplify229.0ms (5.4%)

prune145.0ms (3.5%)

localize26.0ms (0.6%)

series133.0ms (3.2%)

rewrite3.0ms (0.1%)

simplify95.0ms (2.2%)

prune52.0ms (1.2%)

localize33.0ms (0.8%)

series45.0ms (1.1%)

rewrite6.0ms (0.2%)

simplify86.0ms (2.1%)

prune92.0ms (2.2%)

localize45.0ms (1.1%)

series1.0s (24.4%)

rewrite10.0ms (0.2%)

simplify141.0ms (3.4%)

prune116.0ms (2.8%)

regimes88.0ms (2.1%)

simplify8.0ms (0.2%)

end1.0ms (0%)

sample1.5s (35%)

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