Details

analyze1.2s (20.1%)

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)

sample97.0ms (1.6%)

Algorithm

1×

intervals

Results

42.0ms	119×	body	2048	valid
21.0ms	15×	body	256	valid
19.0ms	80×	body	1024	valid
5.0ms	27×	body	512	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify72.0ms (1.2%)

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 (0.1%)

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize7.0ms (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))
✓	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.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)))

rewrite4.0ms (0.1%)

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)))

simplify74.0ms (1.2%)

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 → 60

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

prune57.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	5	61

Error

0.5b

Counts

61 → 5

Alt Table

Status	Error	Program
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.0b	(.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)))))
	1.5b	(cbrt.f64 (.f64 (.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.5b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
▶	0.5b	(acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 1439 to 1038 computations (27.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.0b	(exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.5b	(acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

series10.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms

(exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

3.0ms

(log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

2.0ms

(acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`exp-prod_binary64`
18×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`

Counts

3 → 60

Calls

3 calls:

3.0ms

(log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

2.0ms

(exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

1.0ms

(acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

592×	`fma-neg_binary64`
562×	`associate-l_binary64`
342×	`fma-def_binary64`
333×	`associate-/r*_binary64`
290×	`times-frac_binary64`

Counts

96 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	1974
1	288	1827
2	692	1796
3	1767	1793
4	4468	1793
5	4988	1793
6	4972	1793

prune152.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	170	4	174

Error

0.5b

Counts

174 → 4

Alt Table

Status	Error	Program
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	1.5b	(cbrt.f64 (.f64 (.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
▶	0.5b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 3990 to 2976 computations (25.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.0b	(log1p.f64 (acos.f64 (/.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)))))
	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series572.0ms (9.5%)

Counts

2 → 24

Calls

2 calls:

570.0ms	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
2.0ms	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
0.0ms	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

simplify134.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
724×	`unswap-sqr_binary64`
466×	`times-frac_binary64`
417×	`unsub-neg_binary64`
335×	`fma-def_binary64`

Counts

46 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	950
1	40	873
2	50	873
3	66	873
4	91	873
5	133	873
6	225	873
7	462	873
8	1063	873
9	2763	873
10	3925	873
11	4716	873
12	4964	873

prune95.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	92	5	97

Error

0.5b

Counts

97 → 5

Alt Table

Status	Error	Program
▶	0.5b	(expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	3.2b	(expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	2.0b	(expm1.f64 (cbrt.f64 (.f64 (.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))

Compiler

Compiled 2338 to 1737 computations (25.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))
	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
✓	1.0b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))
✓	1.0b	(pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)

series20.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

15.0ms

(pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)

2.0ms

(expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))

2.0ms

(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 59

Calls

3 calls:

2.0ms

(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))

2.0ms

(pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)

0.0ms

(expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))

simplify148.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

573×	`fma-def_binary64`
494×	`log-prod_binary64`
433×	`exp-prod_binary64`
425×	`*-commutative_binary64`
389×	`pow-sqr_binary64`

Counts

95 → 68

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	74	2232
1	94	2021
2	258	2005
3	1132	2005
4	2166	2002
5	4059	2002
6	4483	2002
7	4917	2002
8	4873	2002

prune81.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	80	6	86

Error

0.5b

Counts

86 → 6

Alt Table

Status	Error	Program
	0.5b	(-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3)))) 1)
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (acos.f64 (log.f64 (exp.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	3.2b	(expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	2.0b	(expm1.f64 (cbrt.f64 (.f64 (.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	2.0b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 3))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 3)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))))

Compiler

Compiled 2401 to 1837 computations (23.5% saved)

regimes455.0ms (7.5%)

Accuracy

Total 0.0b remaining (4.5%)

Threshold costs 0.0b (4.5%)

Counts

114 → 1

Compiler

Compiled 9366 to 7082 computations (24.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	18	21
2	16	21

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample2.7s (44.1%)

Algorithm

1×

intervals

Results

1.5s	4035×	body	2048	valid
487.0ms	1963×	body	1024	valid
181.0ms	1019×	body	512	valid
62.0ms	480×	body	256	valid
33.0ms	502×	body	128	valid
1.0ms	1×	body	4096	valid
0.0ms	7×	body	128	nan

Compiler

Compiled 275 to 206 computations (25.1% saved)

Details

analyze1.2s (20.1%)

sample97.0ms (1.6%)

simplify72.0ms (1.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series5.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify74.0ms (1.2%)

prune57.0ms (1%)

localize11.0ms (0.2%)

series10.0ms (0.2%)

rewrite10.0ms (0.2%)

simplify114.0ms (1.9%)

prune152.0ms (2.5%)

localize11.0ms (0.2%)

series572.0ms (9.5%)

rewrite2.0ms (0%)

simplify134.0ms (2.2%)

prune95.0ms (1.6%)

localize13.0ms (0.2%)

series20.0ms (0.3%)

rewrite6.0ms (0.1%)

simplify148.0ms (2.5%)

prune81.0ms (1.3%)

regimes455.0ms (7.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.7s (44.1%)

Profiling