Details

analyze492.0ms (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample70.0ms (1.2%)

Algorithm

1×

intervals

Results

36.0ms	135×	body	8192	exit
10.0ms	201×	body	128	valid
3.0ms	22×	body	512	valid
3.0ms	32×	body	256	valid
0.0ms	1×	body	1024	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

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

15.2b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	15.2b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	15.7b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 78 to 43 computations (44.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
5.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite160.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

14.6b

Rules

38×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`
12×	`div-sub_binary64`
12×	`add-exp-log_binary64`
12×	`pow1_binary64`

Counts

3 → 146

Calls

3 calls:

17.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
14.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
13.0ms	(/.f64 x (exp.f64 wj))

Compiler

Compiled 2846 to 1225 computations (57% saved)

series88.0ms (1.5%)

Error

0.1b

Counts

3 → 45

Calls

3 calls:

27.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
25.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
12.0ms	(/.f64 x (exp.f64 wj))

Compiler

Compiled 1395 to 881 computations (36.8% saved)

simplify139.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-neg_binary64`
551×	`cancel-sign-sub-inv_binary64`
195×	`associate-r_binary64`
190×	`sub-neg_binary64`
172×	`fma-def_binary64`

Counts

191 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	3301
1	695	3162
2	2948	3126
3	4873	3125
4	5076	3125

prune50.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	87	4	91

Error

0.1b

Counts

91 → 4

Alt Table

Status	Error	Program
	43.9b	(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
	43.5b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))
▶	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))
	15.7b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 1589 to 719 computations (54.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3)))
0.1b	(fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))
4.3b	(*.f64 x (pow.f64 wj 3))
9.0b	(.f64 x (.f64 wj wj))

rewrite163.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

22×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
16×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 136

Calls

4 calls:

14.0ms	(*.f64 x (pow.f64 wj 3))
14.0ms	(.f64 x (.f64 wj wj))
12.0ms	(fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))
9.0ms	(fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3)))

Compiler

Compiled 3676 to 1872 computations (49.1% saved)

series110.0ms (1.9%)

Error

0.1b

Counts

4 → 33

Calls

4 calls:

38.0ms	(fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3)))
27.0ms	(fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))
16.0ms	(*.f64 x (pow.f64 wj 3))
15.0ms	(.f64 x (.f64 wj wj))

Compiler

Compiled 1881 to 1155 computations (38.6% saved)

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

673×	`unswap-sqr_binary64`
617×	`fma-neg_binary64`
470×	`fma-def_binary64`
212×	`log-prod_binary64`
209×	`cancel-sign-sub-inv_binary64`

Counts

169 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	2091
1	345	1794
2	1306	1752
3	4328	1752
4	4974	1752

prune64.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	98	4	102

Error

0.1b

Counts

102 → 4

Alt Table

Status	Error	Program
	43.9b	(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (fma.f64 wj wj (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
	43.5b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))
✓	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))
▶	15.7b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 2156 to 1099 computations (49% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 wj (exp.f64 wj))
0.0b	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))
0.5b	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
5.5b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

rewrite160.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

43×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
16×	`add-log-exp_binary64`

Counts

4 → 181

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
15.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
14.0ms	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))
14.0ms	(*.f64 wj (exp.f64 wj))

Compiler

Compiled 5627 to 672 computations (88.1% saved)

series100.0ms (1.8%)

Error

0.1b

Counts

4 → 50

Calls

4 calls:

34.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
29.0ms	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
8.0ms	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))
6.0ms	(*.f64 wj (exp.f64 wj))

Compiler

Compiled 1741 to 917 computations (47.3% saved)

simplify210.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-neg_binary64`
239×	`associate-r_binary64`
236×	`associate-l_binary64`
192×	`fma-def_binary64`
117×	`+-commutative_binary64`

Counts

231 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	4900
1	746	4555
2	3516	4353
3	4978	4351
4	4943	4351
5	5178	4351

prune67.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	148	4	152

Error

0.1b

Counts

152 → 4

Alt Table

Status	Error	Program
	43.5b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))
▶	17.6b	(.f64 (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))) (.f64 (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))) (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj))))))))
✓	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))
✓	15.7b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 2974 to 711 computations (76.1% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))))
5.5b	(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))
5.5b	(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))
5.5b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

rewrite155.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

55×	`add-cube-cbrt_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`flip3--_binary64`
20×	`add-log-exp_binary64`
14×	`pow1_binary64`

Counts

4 → 179

Calls

4 calls:

18.0ms	(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))
18.0ms	(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))
16.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
12.0ms	(cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))))

Compiler

Compiled 12832 to 746 computations (94.2% saved)

series263.0ms (4.6%)

Error

0.1b

Counts

4 → 56

Calls

4 calls:

80.0ms	(cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))))
58.0ms	(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))
58.0ms	(-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))
39.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 7288 to 3000 computations (58.8% saved)

simplify256.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

876×	`fma-def_binary64`
820×	`times-frac_binary64`
404×	`fma-neg_binary64`
169×	`sub-neg_binary64`
155×	`associate-r_binary64`

Counts

235 → 165

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	297	7831
1	750	6770
2	2227	5955
3	4843	5946
4	5000	5942
5	4847	5942

prune69.0ms (1.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	164	5	169

Error

0.1b

Counts

169 → 5

Alt Table

Status	Error	Program
	37.5b	(.f64 (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))) (.f64 (cbrt.f64 (/.f64 (+.f64 0 (pow.f64 (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))) 6)) (+.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj))))) 0))) (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj))))))))
	43.5b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))
	17.6b	(.f64 (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))) (.f64 (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj)))))) (cbrt.f64 (-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (exp.f64 (+.f64 wj (log1p.f64 wj))))))))
	2.3b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))
	15.7b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 8340 to 956 computations (88.5% saved)

regimes725.0ms (12.7%)

Accuracy

Total 0.4b remaining (78.9%)

Threshold costs 0.4b (78.9%)

Compiler

Compiled 12826 to 6964 computations (45.7% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 18 to 8 computations (55.6% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

83×	`distribute-rgt-neg-in_binary64`
65×	`cancel-sign-sub-inv_binary64`
54×	`neg-sub0_binary64`
54×	`neg-mul-1_binary64`
53×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	101
1	58	101
2	81	101
3	100	101
4	126	101
5	145	101
6	168	101
7	213	101
8	259	101
9	313	101
10	353	101
11	383	101
12	419	101
13	446	101
14	457	101
15	462	101
16	464	101
17	458	101

end1.0ms (0%)

Compiler: Compiled 70 to 41 computations (41.4% saved)

sample2.1s (37%)

Algorithm

1×

intervals

Results

998.0ms	3834×	body	8192	exit
334.0ms	6478×	body	128	valid
111.0ms	745×	body	512	valid
78.0ms	751×	body	256	valid
5.0ms	26×	body	1024	valid
4.0ms	79×	body	128	invalid
1.0ms	13×	body	128	overflowed

Compiler

Compiled 279 to 132 computations (52.7% saved)

Iter	Nodes	Cost
0	36	101
1	58	101
2	81	101
3	100	101
4	126	101
5	145	101
6	168	101
7	213	101
8	259	101
9	313	101
10	353	101
11	383	101
12	419	101
13	446	101
14	457	101
15	462	101
16	464	101
17	458	101

Iter	Nodes	Cost
0	36	101
1	58	101
2	81	101
3	100	101
4	126	101
5	145	101
6	168	101
7	213	101
8	259	101
9	313	101
10	353	101
11	383	101
12	419	101
13	446	101
14	457	101
15	462	101
16	464	101
17	458	101

Details

analyze492.0ms (8.6%)

sample70.0ms (1.2%)

simplify85.0ms (1.5%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

rewrite160.0ms (2.8%)

series88.0ms (1.5%)

simplify139.0ms (2.4%)

prune50.0ms (0.9%)

localize15.0ms (0.3%)

rewrite163.0ms (2.8%)

series110.0ms (1.9%)

simplify93.0ms (1.6%)

prune64.0ms (1.1%)

localize8.0ms (0.1%)

rewrite160.0ms (2.8%)

series100.0ms (1.8%)

simplify210.0ms (3.7%)

prune67.0ms (1.2%)

localize21.0ms (0.4%)

rewrite155.0ms (2.7%)

series263.0ms (4.6%)

simplify256.0ms (4.5%)

prune69.0ms (1.2%)

regimes725.0ms (12.7%)

bsearch7.0ms (0.1%)

simplify21.0ms (0.4%)

end1.0ms (0%)

sample2.1s (37%)

Profiling

Iter	Nodes	Cost
0	36	101
1	58	101
2	81	101
3	100	101
4	126	101
5	145	101
6	168	101
7	213	101
8	259	101
9	313	101
10	353	101
11	383	101
12	419	101
13	446	101
14	457	101
15	462	101
16	464	101
17	458	101