Details

analyze1.2s (12.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample92.0ms (0.9%)

Algorithm

1×

intervals

Results

58.0ms	131×	body	2048	valid
16.0ms	64×	body	1024	valid
5.0ms	27×	body	512	valid
3.0ms	22×	body	256	valid
1.0ms	12×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

686×	`div-sub_binary64`
546×	`sub-neg_binary64`
397×	`neg-mul-1_binary64`
344×	`neg-sub0_binary64`
311×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	72	17
3	203	17
4	532	17
5	1340	17
6	2710	17
7	3748	17
8	4643	17
9	4981	17

prune3.0ms (0%)

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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.4b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
0.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series9.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
2.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

667×	`times-frac_binary64`
628×	`fma-def_binary64`
405×	`fma-neg_binary64`
337×	`associate-/l*_binary64`
292×	`associate-/r*_binary64`

Counts

63 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1379
1	209	1264
2	549	1261
3	1434	1259
4	4502	1259
5	5039	1259

prune48.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Error

0.4b

Counts

94 → 3

Alt Table

Status	Error	Program
	1.9b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
▶	0.4b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.4b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Compiler

Compiled 1283 to 928 computations (27.7% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.0b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.4b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

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 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

series637.0ms (6.5%)

Counts

1 → 12

Calls

1 calls:

636.0ms

(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
518×	`div-exp_binary64`
383×	`sub-neg_binary64`
308×	`times-frac_binary64`
284×	`neg-sub0_binary64`

Counts

23 → 43

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	452
1	35	417
2	75	417
3	233	417
4	895	417
5	2288	417
6	4154	417
7	4698	417
8	5375	417

prune112.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Error

0.4b

Counts

139 → 4

Alt Table

Status	Error	Program
	1.9b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	1.9b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	1.3b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
▶	0.4b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Compiler

Compiled 1949 to 1450 computations (25.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

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

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series1.0ms (0%)

Counts

1 → 0

Calls

1 calls:

1.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

simplify153.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1816×	`fma-def_binary64`
578×	`sqr-pow_binary64`
513×	`associate-l_binary64`
493×	`*-commutative_binary64`
354×	`unswap-sqr_binary64`

Counts

10 → 11

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	211
1	29	182
2	45	182
3	77	182
4	161	182
5	401	182
6	1153	182
7	2143	182
8	2224	182
9	2406	182
10	2629	182
11	2908	182
12	3210	182
13	4308	182
14	4749	182
15	4748	182

prune19.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	9	2	11
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	11	4	15

Error

0.4b

Counts

15 → 4

Alt Table

Status	Error	Program
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	1.3b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
▶	0.4b	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	1.9b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))

Compiler

Compiled 477 to 357 computations (25.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
✓	0.0b	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	0.4b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite4.0ms (0%)

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 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
1.0ms	(log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))

series1.0s (10.5%)

Counts

2 → 0

Calls

2 calls:

550.0ms	(log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
482.0ms	(exp.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))

simplify158.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-def_binary64`
558×	`associate-l_binary64`
452×	`unswap-sqr_binary64`
421×	`associate-*l/_binary64`
419×	`*-commutative_binary64`

Counts

31 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	688
1	55	589
2	80	589
3	124	581
4	239	581
5	541	581
6	1438	581
7	2701	581
8	3325	581
9	4796	581
10	4983	581
11	4802	581

prune108.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	56	6	62

Error

0.4b

Counts

62 → 6

Alt Table

Status	Error	Program
	1.3b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	1.4b	(exp.f64 (+.f64 (*.f64 (log.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) 2) (log.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))
	2.4b	(exp.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))) (log.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))
	2.0b	(*.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 2) (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	0.4b	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))) (sqrt.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))
	3.2b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (cbrt.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))) (cbrt.f64 (log.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))

Compiler

Compiled 1210 to 934 computations (22.8% saved)

regimes561.0ms (5.7%)

Accuracy

Total 0.0b remaining (1.6%)

Threshold costs 0.0b (1.6%)

Compiler

Compiled 6103 to 4681 computations (23.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	61
1	19	61
2	18	61

end2.0ms (0%)

Compiler: Compiled 42 to 30 computations (28.6% saved)

sample5.3s (54.4%)

Algorithm

1×

intervals

Results

2.8s	3977×	body	2048	valid
1.1s	1994×	body	1024	valid
439.0ms	1005×	body	512	valid
115.0ms	515×	body	256	valid
64.0ms	508×	body	128	valid
1.0ms	1×	body	4096	valid
1.0ms	9×	body	128	nan

Compiler

Compiled 266 to 201 computations (24.4% saved)

Details

analyze1.2s (12.4%)

sample92.0ms (0.9%)

simplify79.0ms (0.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite5.0ms (0%)

series9.0ms (0.1%)

simplify92.0ms (0.9%)

prune48.0ms (0.5%)

localize11.0ms (0.1%)

rewrite1.0ms (0%)

series637.0ms (6.5%)

simplify95.0ms (1%)

prune112.0ms (1.1%)

localize8.0ms (0.1%)

rewrite1.0ms (0%)

series1.0ms (0%)

simplify153.0ms (1.6%)

prune19.0ms (0.2%)

localize10.0ms (0.1%)

rewrite4.0ms (0%)

series1.0s (10.5%)

simplify158.0ms (1.6%)

prune108.0ms (1.1%)

regimes561.0ms (5.7%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample5.3s (54.4%)

Profiling