Details

analyze1.3s (18.5%)

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)

sample4.1s (60.8%)

Results

2.4s	4052×	body	2048	valid
922.0ms	2123×	body	1024	valid
345.0ms	1020×	body	512	valid
241.0ms	534×	body	256	valid
112.0ms	525×	body	128	valid
1.0ms	2×	body	4096	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify70.0ms (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

0.4b

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)

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))
✓	0.4b	(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)))

simplify75.0ms (1.1%)

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

prune97.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	3	61

Error

0.4b

Counts

61 → 3

Alt Table

Status	Error	Program
▶	0.5b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	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)))))
	1.4b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))

Compiler

Compiled 1297 to 938 computations (27.7% saved)

localize33.0ms (0.5%)

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))

series2.0ms (0%)

Counts

1 → 0

Calls

1 calls:

2.0ms

(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))

simplify121.0ms (1.8%)

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

prune16.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	9	2	11
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	11	3	14

Error

0.4b

Counts

14 → 3

Alt Table

Status	Error	Program
▶	0.5b	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	1.4b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))
	2.1b	(.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))))

Compiler

Compiled 325 to 245 computations (24.6% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
✓	0.4b	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series6.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
2.0ms	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

2 → 82

Calls

2 calls:

7.0ms	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
0.0ms	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

simplify174.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-def_binary64`
349×	`distribute-rgt-in_binary64`
328×	`unsub-neg_binary64`
317×	`fma-neg_binary64`
288×	`distribute-lft-in_binary64`

Counts

94 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	3370
1	215	2716
2	598	2070
3	1781	2070
4	4258	2055
5	4987	2055
6	4859	2055

prune126.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	98	4	102

Error

0.4b

Counts

102 → 4

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	2.8b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))))
▶	1.4b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))
	2.1b	(.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))))

Compiler

Compiled 5092 to 3789 computations (25.6% 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))
	0.4b	(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)

series16.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(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))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 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)

simplify134.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

72 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	1816
1	92	1621
2	256	1605
3	1130	1605
4	2164	1602
5	4057	1602
6	4481	1602
7	4915	1602
8	4871	1602

prune84.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	116	5	121

Error

0.4b

Counts

121 → 5

Alt Table

Status	Error	Program
✓	0.5b	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	1.9b	(cbrt.f64 (pow.f64 (.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))))) 3))
	1.9b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 3))) (cbrt.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) 3)))) (cbrt.f64 (cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))))
	2.8b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))))
✓	1.4b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))

Compiler

Compiled 3028 to 2277 computations (24.8% saved)

regimes187.0ms (2.7%)

Accuracy

Total 0.0b remaining (1.8%)

Threshold costs 0.0b (1.8%)

Counts

33 → 1

Compiler

Compiled 4234 to 3179 computations (24.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	19	24
2	22	24
3	24	24
4	25	24
5	24	24

end192.0ms (2.8%)

Compiler: Compiled 287 to 217 computations (24.4% saved)

Details

analyze1.3s (18.5%)

sample4.1s (60.8%)

simplify70.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series5.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify75.0ms (1.1%)

prune97.0ms (1.4%)

localize33.0ms (0.5%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify121.0ms (1.8%)

prune16.0ms (0.2%)

localize10.0ms (0.2%)

series6.0ms (0.1%)

rewrite18.0ms (0.3%)

simplify174.0ms (2.6%)

prune126.0ms (1.9%)

localize10.0ms (0.1%)

series16.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify134.0ms (2%)

prune84.0ms (1.2%)

regimes187.0ms (2.7%)

simplify3.0ms (0%)

end192.0ms (2.8%)

Profiling