Details

analyze1.2s (16.5%)

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)

sample3.8s (53.2%)

Results

2.4s	4120×	body	2048	valid
859.0ms	2060×	body	1024	valid
314.0ms	1005×	body	512	valid
117.0ms	548×	body	256	valid
78.0ms	520×	body	128	valid
2.0ms	3×	body	4096	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify73.0ms (1%)

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

0.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.7b	(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))
✓	0.7b	(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)))

simplify72.0ms (1%)

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

prune52.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	4	61

Error

0.7b

Counts

61 → 4

Alt Table

Status	Error	Program
▶	0.7b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.8b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	1.6b	(.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)))))
	2.2b	(.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)))))

Compiler

Compiled 1351 to 976 computations (27.8% saved)

localize10.0ms (0.1%)

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))))
✓	0.1b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series449.0ms (6.2%)

Counts

2 → 24

Calls

2 calls:

447.0ms	(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)))))

rewrite1.0ms (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	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
0.0ms	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

simplify104.0ms (1.4%)

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

prune89.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	92	5	97

Error

0.7b

Counts

97 → 5

Alt Table

Status	Error	Program
	0.9b	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
	0.7b	(expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (sqrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	3.3b	(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)))))))
	2.2b	(.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)))))
▶	0.7b	(exp.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))

Compiler

Compiled 2262 to 1681 computations (25.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
✓	0.0b	(exp.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	0.1b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series561.0ms (7.8%)

Counts

2 → 24

Calls

2 calls:

557.0ms

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

4.0ms

(exp.f64 (log.f64 (expm1.f64 (log1p.f64 (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

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

1.0ms

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

simplify108.0ms (1.5%)

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 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	1240
1	54	1120
2	74	1120
3	101	1112
4	158	1112
5	257	1112
6	482	1112
7	1151	1112
8	2470	1112
9	4310	1112
10	4997	1112
11	4780	1112

prune83.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Error

0.7b

Counts

91 → 5

Alt Table

Status	Error	Program
	2.2b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	3.3b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))) (cbrt.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
▶	0.7b	(expm1.f64 (log1p.f64 (exp.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))))
	0.9b	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
	3.3b	(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)))))))

Compiler

Compiled 2407 to 1819 computations (24.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	0.1b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
✓	0.1b	(expm1.f64 (log1p.f64 (exp.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))))
	0.7b	(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 (expm1.f64 (log1p.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 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))))

simplify88.0ms (1.2%)

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 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	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

prune68.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Error

0.7b

Counts

87 → 4

Alt Table

Status	Error	Program
	3.3b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))) (cbrt.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
	0.9b	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (*.f64 v v) -1))))
	3.3b	(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)))))))
	2.2b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (exp.f64 (log.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 (exp.f64 (log.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 (exp.f64 (log.f64 (expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))))))

Compiler

Compiled 2250 to 1736 computations (22.8% saved)

regimes205.0ms (2.8%)

Accuracy

Total 0.0b remaining (2%)

Threshold costs 0.0b (2%)

Counts

50 → 1

Compiler

Compiled 5185 to 3903 computations (24.7% 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	32
1	22	32
2	23	32
3	21	32

end170.0ms (2.3%)

Compiler: Compiled 210 to 164 computations (21.9% saved)

Details

analyze1.2s (16.5%)

sample3.8s (53.2%)

simplify73.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series5.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify72.0ms (1%)

prune52.0ms (0.7%)

localize10.0ms (0.1%)

series449.0ms (6.2%)

rewrite1.0ms (0%)

simplify104.0ms (1.4%)

prune89.0ms (1.2%)

localize13.0ms (0.2%)

series561.0ms (7.8%)

rewrite4.0ms (0.1%)

simplify108.0ms (1.5%)

prune83.0ms (1.1%)

localize18.0ms (0.2%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify88.0ms (1.2%)

prune68.0ms (0.9%)

regimes205.0ms (2.8%)

simplify3.0ms (0%)

end170.0ms (2.3%)

Profiling