Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample5.0s (74.9%)

Results

3.5s	4262×	body	2048	valid
901.0ms	2148×	body	1024	valid
381.0ms	984×	body	512	valid
106.0ms	494×	body	256	valid
64.0ms	368×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

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

31.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
2.0ms	(-.f64 (exp.f64 x) 2)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`

Counts

2 → 69

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(-.f64 (exp.f64 x) 2)

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
326×	`fma-def_binary64`
296×	`distribute-rgt-in_binary64`
282×	`distribute-lft-in_binary64`
268×	`distribute-rgt-out_binary64`

Counts

85 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1174
1	295	959
2	717	942
3	2801	932
4	4435	932
5	4838	932

prune63.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	2	115

Error

0.0b

Counts

115 → 2

Alt Table

Status	Error	Program
✓	31.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	0.2b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

Compiler

Compiled 2063 to 1172 computations (43.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))

series14.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

6.0ms	(*.f64 1/20160 (pow.f64 x 8))
4.0ms	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
4.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(*.f64 1/20160 (pow.f64 x 8))
0.0ms	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
0.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
628×	`unswap-sqr_binary64`
530×	`*-commutative_binary64`
354×	`log-prod_binary64`
302×	`associate-+r+_binary64`

Counts

71 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	92	1093
1	162	1007
2	375	989
3	1442	989
4	3258	983
5	4893	983
6	5054	983

prune63.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	67	4	71

Error

Counts

71 → 4

Alt Table

Status	Error	Program
✓	31.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.2b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
▶	1.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 (.f64 (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	3.3b	(exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

Compiler

Compiled 1684 to 1263 computations (25% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	28.4b	(cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

series76.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

37.0ms

(cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

33.0ms

(*.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

5.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

12.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

1.0ms

(cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

simplify115.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-l_binary64`
390×	`unswap-sqr_binary64`
345×	`associate-r_binary64`
329×	`fma-def_binary64`
306×	`fma-neg_binary64`

Counts

129 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3616
1	471	3274
2	1163	2714
3	3750	2504
4	5163	2504

prune532.0ms (8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	342	4	346

Error

Counts

346 → 4

Alt Table

Status	Error	Program
✓	31.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.2b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	1.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 (.f64 (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
▶	3.3b	(exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

Compiler

Compiled 16260 to 12260 computations (24.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	3.1b	(exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
✓	28.5b	(log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

series12.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

7.0ms

(log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

4.0ms

(exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms

(exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

1.0ms

(log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-+l+_binary64`
429×	`associate-+r+_binary64`
258×	`times-frac_binary64`
238×	`fma-def_binary64`
226×	`exp-prod_binary64`

Counts

55 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1604
1	220	1416
2	527	1402
3	1741	1394
4	4618	1394
5	5070	1394

prune217.0ms (3.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	143	4	147

Error

Counts

147 → 4

Alt Table

Status	Error	Program
✓	31.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.2b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	1.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 (.f64 (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8)))) (cbrt.f64 (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (cbrt.f64 (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
✓	3.3b	(exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

Compiler

Compiled 3688 to 2839 computations (23% saved)

regimes70.0ms (1.1%)

Accuracy

Total 0.5b remaining (96.9%)

Threshold costs 0.5b (96.9%)

Counts

38 → 1

Compiler

Compiled 1420 to 1072 computations (24.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	16	25
2	16	25

end111.0ms (1.7%)

Compiler: Compiled 127 to 94 computations (26% saved)

Details

analyze4.0ms (0.1%)

sample5.0s (74.9%)

simplify65.0ms (1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite16.0ms (0.2%)

simplify77.0ms (1.1%)

prune63.0ms (0.9%)

localize10.0ms (0.2%)

series14.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify84.0ms (1.3%)

prune63.0ms (0.9%)

localize13.0ms (0.2%)

series76.0ms (1.1%)

rewrite24.0ms (0.4%)

simplify115.0ms (1.7%)

prune532.0ms (8%)

localize14.0ms (0.2%)

series12.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify76.0ms (1.1%)

prune217.0ms (3.2%)

regimes70.0ms (1.1%)

simplify2.0ms (0%)

end111.0ms (1.7%)

Profiling