Details

analyze130.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample69.0ms (1.5%)

Algorithm

1×

intervals

Results

31.0ms	69×	body	1024	valid
10.0ms	138×	body	128	valid
7.0ms	27×	body	512	valid
5.0ms	8×	body	2048	valid
2.0ms	14×	body	256	valid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

978×	`times-frac_binary64`
434×	`unswap-sqr_binary64`
378×	`associate-*l/_binary64`
368×	`fma-neg_binary64`
358×	`fma-def_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	19	15
2	25	15
3	34	15
4	59	15
5	113	15
6	235	15
7	600	15
8	1504	15
9	2557	15
10	4582	15
11	4956	15
12	4701	15

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

29.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 36 to 33 computations (8.3% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	3.4b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series34.0ms (0.7%)

Counts

2 → 16

Calls

2 calls:

18.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
16.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
62×	`add-cube-cbrt_binary64`
54×	`prod-diff_binary64`

Counts

2 → 132

Calls

2 calls:

18.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
7.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

simplify193.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

401×	`fma-neg_binary64`
396×	`associate-/l*_binary64`
334×	`associate-*l/_binary64`
305×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`

Counts

148 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	2989
1	302	2912
2	706	2515
3	1914	2437
4	4803	2437
5	4954	2437

prune267.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	3	188

Error

Counts

188 → 3

Alt Table

Status	Error	Program
	31.5b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	29.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
▶	29.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1)) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1))) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))

Compiler

Compiled 4588 to 4206 computations (8.3% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	0.0b	(.f64 (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1)) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))
✓	0.0b	(cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1))
	3.4b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series834.0ms (18.2%)

Counts

2 → 24

Calls

2 calls:

465.0ms	(cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1))
369.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1)) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
66×	`cbrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
24×	`difference-of-squares_binary64`
19×	`swap-sqr_binary64`

Counts

2 → 99

Calls

2 calls:

25.0ms	(.f64 (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1)) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))
9.0ms	(cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1))

simplify190.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
625×	`log-prod_binary64`
500×	`unswap-sqr_binary64`
427×	`associate-l_binary64`
342×	`associate-r_binary64`

Counts

123 → 149

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	4717
1	313	4357
2	839	4203
3	2076	4091
4	4455	4037
5	4871	4037
6	5189	4037

prune1.2s (25.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	794	0	794
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	794	3	797

Error

Counts

797 → 3

Alt Table

Status	Error	Program
▶	31.5b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	29.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
✓	29.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1)) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1))) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))

Compiler

Compiled 38394 to 35184 computations (8.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/3 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

435×	`neg-mul-1_binary64`
394×	`associate-l_binary64`
372×	`associate-r_binary64`
317×	`distribute-rgt-out_binary64`
261×	`exp-prod_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	232
1	35	197
2	87	197
3	323	197
4	1660	197
5	4537	197
6	5209	197

prune8.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	16	3	19

Error

Counts

19 → 3

Alt Table

Status	Error	Program
✓	31.5b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	29.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
✓	29.8b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1)) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1))) (cbrt.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))

Compiler

Compiled 206 to 161 computations (21.8% saved)

regimes190.0ms (4.2%)

Accuracy

Total 0.2b remaining (90.4%)

Threshold costs 0.2b (90.4%)

Counts

8 → 3

Compiler

Compiled 1924 to 1745 computations (9.3% saved)

bsearch0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	33	80
2	34	80
3	31	80

end2.0ms (0%)

Compiler: Compiled 55 to 48 computations (12.7% saved)

sample1.2s (26.7%)

Algorithm

1×

intervals

Results

486.0ms	2086×	body	1024	valid
177.0ms	4200×	body	128	valid
138.0ms	966×	body	512	valid
60.0ms	217×	body	2048	valid
50.0ms	531×	body	256	valid

Compiler

Compiled 127 to 113 computations (11% saved)

Details

analyze130.0ms (2.9%)

sample69.0ms (1.5%)

simplify70.0ms (1.5%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

series34.0ms (0.7%)

rewrite46.0ms (1%)

simplify193.0ms (4.2%)

prune267.0ms (5.8%)

localize18.0ms (0.4%)

series834.0ms (18.2%)

rewrite46.0ms (1%)

simplify190.0ms (4.2%)

prune1.2s (25.5%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify59.0ms (1.3%)

prune8.0ms (0.2%)

regimes190.0ms (4.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end2.0ms (0%)

sample1.2s (26.7%)

Profiling