Details

analyze1.2s (11.4%)

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)

sample3.9s (38.4%)

Results

2.4s	4142×	body	2048	valid
920.0ms	2028×	body	1024	valid
311.0ms	1015×	body	512	valid
119.0ms	518×	body	256	valid
75.0ms	553×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify71.0ms (0.7%)

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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(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 1 expressions with local error:

New	Error	Program
✓	0.8b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(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 → 10

Calls

1 calls:

0.0ms

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

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
548×	`times-frac_binary64`
398×	`unsub-neg_binary64`
363×	`distribute-neg-in_binary64`
362×	`unswap-sqr_binary64`

Counts

22 → 13

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	454
1	31	419
2	40	419
3	53	419
4	76	419
5	112	419
6	187	419
7	376	419
8	808	419
9	2217	419
10	3234	419
11	4326	419
12	4857	419

prune14.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	10	4	14

Error

0.8b

Counts

14 → 4

Alt Table

Status	Error	Program
	1.7b	(.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)))))
	2.3b	(.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)))))
	1.7b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))
▶	0.8b	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 449 to 321 computations (28.5% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.0b	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.8b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series432.0ms (4.2%)

Counts

2 → 24

Calls

2 calls:

430.0ms	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
2.0ms	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -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 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
1.0ms	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

simplify125.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

620×	`unswap-sqr_binary64`
480×	`fma-neg_binary64`
451×	`fma-def_binary64`
352×	`associate-/l*_binary64`
293×	`associate-/r*_binary64`

Counts

55 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	1240
1	53	1120
2	73	1120
3	100	1112
4	157	1112
5	256	1112
6	481	1112
7	1150	1112
8	2469	1112
9	4309	1112
10	4996	1112
11	4779	1112

prune50.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	57	3	60

Error

0.8b

Counts

60 → 3

Alt Table

Status	Error	Program
	1.7b	(exp.f64 (+.f64 (log.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (log.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))
	2.7b	(exp.f64 (+.f64 (log.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)))))) (log.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))
▶	0.8b	(expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))

Compiler

Compiled 1441 to 1061 computations (26.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.0b	(expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	0.0b	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.8b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

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

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
472×	`times-frac_binary64`
454×	`unswap-sqr_binary64`
398×	`unsub-neg_binary64`
339×	`fma-def_binary64`

Counts

23 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	453
1	30	418
2	41	418
3	60	418
4	88	418
5	132	418
6	221	418
7	441	418
8	979	418
9	2530	418
10	3734	418
11	4546	418
12	4798	418

prune89.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Error

0.8b

Counts

79 → 4

Alt Table

Status	Error	Program
	1.7b	(.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (sqrt.f64 (expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))))
	1.7b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))))
▶	0.8b	(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
	3.0b	(expm1.f64 (log1p.f64 (exp.f64 (+.f64 (log.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)))))) (log.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))))

Compiler

Compiled 2147 to 1623 computations (24.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
✓	0.0b	(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
✓	0.0b	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	0.8b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series3.3s (32.1%)

Counts

3 → 36

Calls

3 calls:

1.5s

(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))))

1.4s

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

461.0ms

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

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`exp-prod_binary64`
12×	`sqrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 58

Calls

3 calls:

3.0ms

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

2.0ms

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

0.0ms

(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))))

simplify186.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

430×	`exp-prod_binary64`
328×	`associate-l_binary64`
313×	`sqr-pow_binary64`
313×	`fma-def_binary64`
305×	`*-commutative_binary64`

Counts

94 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	3111
1	109	2970
2	238	2970
3	509	2970
4	1533	2970
5	3501	2970
6	4528	2970
7	4920	2970
8	4969	2970
9	4762	2970

prune124.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Error

0.8b

Counts

96 → 4

Alt Table

Status	Error	Program
	1.7b	(.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (sqrt.f64 (expm1.f64 (log1p.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))))
✓	0.8b	(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
	3.0b	(expm1.f64 (log1p.f64 (exp.f64 (+.f64 (log.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)))))) (log.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))))
	3.4b	(expm1.f64 (log1p.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))

Compiler

Compiled 4209 to 3188 computations (24.3% saved)

regimes290.0ms (2.8%)

Accuracy

Total 0.0b remaining (1.4%)

Threshold costs 0.0b (1.4%)

Counts

59 → 1

Compiler

Compiled 6270 to 4736 computations (24.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	53
1	22	53
2	23	53
3	21	53

end217.0ms (2.1%)

Compiler: Compiled 254 to 194 computations (23.6% saved)

Details

analyze1.2s (11.4%)

sample3.9s (38.4%)

simplify71.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify89.0ms (0.9%)

prune14.0ms (0.1%)

localize11.0ms (0.1%)

series432.0ms (4.2%)

rewrite4.0ms (0%)

simplify125.0ms (1.2%)

prune50.0ms (0.5%)

localize16.0ms (0.2%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify93.0ms (0.9%)

prune89.0ms (0.9%)

localize18.0ms (0.2%)

series3.3s (32.1%)

rewrite9.0ms (0.1%)

simplify186.0ms (1.8%)

prune124.0ms (1.2%)

regimes290.0ms (2.8%)

simplify3.0ms (0%)

end217.0ms (2.1%)

Profiling