Details

analyze396.0ms (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.3s (71.7%)

Results

1.5s	2562×	body	1024	valid
731.0ms	1224×	body	2048	valid
518.0ms	1285×	body	512	valid
286.0ms	2499×	body	128	valid
155.0ms	638×	body	256	valid
35.0ms	48×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

43.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.6b	(+.f64 x (hypot.f64 1 x))
✓	2.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series10.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 44

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
2.0ms	(+.f64 x (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
376×	`fma-def_binary64`
361×	`sub-neg_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1089
1	394	1025
2	959	1013
3	2675	1013
4	4999	1013
5	5338	1013

prune59.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	4	114

Error

Counts

114 → 4

Alt Table

Status	Error	Program
▶	33.4b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
✓	43.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	61.0b	(log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))
	47.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 1591 to 1198 computations (24.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	20.5b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
3.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite1.0ms (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 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
0.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-l_binary64`
578×	`associate-r_binary64`
480×	`distribute-lft-in_binary64`
480×	`distribute-rgt-in_binary64`
291×	`fma-def_binary64`

Counts

44 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	584
1	65	520
2	153	518
3	599	518
4	3541	518
5	4941	518

prune21.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	31	4	35

Error

Counts

35 → 4

Alt Table

Status	Error	Program
✓	33.4b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
✓	43.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	61.0b	(log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))
▶	47.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 516 to 393 computations (23.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
✓	0.1b	(/.f64 1/8 (pow.f64 x 3))
✓	10.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

series13.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(/.f64 1/8 (pow.f64 x 3))
4.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
3.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))

rewrite58.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
63×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`
40×	`fma-def_binary64`

Counts

3 → 142

Calls

3 calls:

25.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
21.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify84.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

409×	`fma-def_binary64`
378×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
334×	`associate-*l/_binary64`
284×	`associate-/l/_binary64`

Counts

166 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	2065
1	402	1967
2	1395	1913
3	4765	1912
4	5079	1912

prune96.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
✓	33.4b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
✓	43.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	61.0b	(log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))
✓	47.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 3343 to 2655 computations (20.6% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (+.f64 x (hypot.f64 1 x)))
✓	0.4b	(log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x))))
	0.6b	(+.f64 x (hypot.f64 1 x))
✓	2.9b	(log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))
3.0ms	(log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x))))
2.0ms	(exp.f64 (+.f64 x (hypot.f64 1 x)))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
12×	`exp-prod_binary64`
12×	`log-prod_binary64`
11×	`log-pow_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

3 → 54

Calls

3 calls:

3.0ms	(log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))
3.0ms	(log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x))))
3.0ms	(exp.f64 (+.f64 x (hypot.f64 1 x)))

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-neg_binary64`
454×	`associate-/r*_binary64`
390×	`cancel-sign-sub-inv_binary64`
359×	`fma-def_binary64`
295×	`sub-neg_binary64`

Counts

90 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	1233
1	373	1132
2	954	1124
3	2665	1123
4	4897	1123
5	5089	1123

prune73.0ms (1.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	173	4	177

Error

Counts

177 → 4

Alt Table

Status	Error	Program
✓	33.4b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
✓	43.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	61.0b	(log.f64 (log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x)))))
✓	47.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 2429 to 1895 computations (22% saved)

regimes84.0ms (1.8%)

Accuracy

Total 0.3b remaining (92.2%)

Threshold costs 0.3b (92.2%)

Counts

19 → 3

Compiler

Compiled 549 to 427 computations (22.2% saved)

bsearch40.0ms (0.9%)

Steps

Iters	Range		Point
11	7.402877636321493e-6	3829999244233452.5	1.3153391522167552
9	-1039788.0836829162	-0.7837819865369465	-1.1457422521714031

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	52
1	37	52
2	45	52
3	49	52
4	52	52
5	53	52
6	52	52

end77.0ms (1.7%)

Compiler: Compiled 111 to 84 computations (24.3% saved)

Details

analyze396.0ms (8.6%)

sample3.3s (71.7%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series10.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify80.0ms (1.8%)

prune59.0ms (1.3%)

localize9.0ms (0.2%)

series7.0ms (0.2%)

rewrite1.0ms (0%)

simplify55.0ms (1.2%)

prune21.0ms (0.5%)

localize6.0ms (0.1%)

series13.0ms (0.3%)

rewrite58.0ms (1.3%)

simplify84.0ms (1.8%)

prune96.0ms (2.1%)

localize6.0ms (0.1%)

series9.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify78.0ms (1.7%)

prune73.0ms (1.6%)

regimes84.0ms (1.8%)

bsearch40.0ms (0.9%)

simplify3.0ms (0.1%)

end77.0ms (1.7%)

Profiling