Details

analyze1.2s (19.1%)

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)

sample3.8s (61.2%)

Results

2.3s	4127×	body	2048	valid
844.0ms	2037×	body	1024	valid
324.0ms	1035×	body	512	valid
111.0ms	506×	body	256	valid
72.0ms	549×	body	128	valid
1.0ms	2×	body	4096	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

685×	`div-sub_binary64`
303×	`associate-/r*_binary64`
302×	`fma-def_binary64`
296×	`fma-neg_binary64`
220×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	76	17
3	215	17
4	640	17
5	1828	17
6	4394	17

Stop Event

1×	node limit

Counts

1 → 2

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 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)))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
3.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))

rewrite51.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

891×	`log1p-expm1-u_binary64`
891×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`
91×	`add-cbrt-cube_binary64`
90×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	199	32
2	2345	32

Stop Event

1×	node limit

Counts

2 → 67

Calls

2 calls:

49.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
49.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

649×	`cancel-sign-sub-inv_binary64`
494×	`fma-def_binary64`
285×	`unswap-sqr_binary64`
207×	`distribute-neg-frac_binary64`
189×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	380
1	114	362
2	326	359
3	976	359
4	3116	359

Stop Event

1×	node limit

Counts

91 → 83

prune76.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Error

0.7b

Counts

84 → 4

Alt Table

Status	Error	Program
▶	0.8b	(acos.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1))))
	1.7b	(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)
	2.6b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
	0.9b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Compiler

Compiled 2645 to 1934 computations (26.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (fma.f64 v v -1))
✓	0.0b	(.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1)))
✓	0.7b	(acos.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1))))

series7.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1)))
2.0ms	(/.f64 1 (fma.f64 v v -1))
2.0ms	(acos.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1))))

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

474×	`log-prod_binary64`
268×	`pow2_binary64`
189×	`pow1/3_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	221	40
2	2564	40

Stop Event

1×	node limit

Counts

3 → 101

Calls

3 calls:

46.0ms	(/.f64 1 (fma.f64 v v -1))
46.0ms	(.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1)))
46.0ms	(acos.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1))))

simplify31.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
356×	`fma-neg_binary64`
306×	`associate-l_binary64`
245×	`cancel-sign-sub-inv_binary64`
209×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	590
1	156	566
2	477	559
3	1494	559

Stop Event

1×	node limit

Counts

137 → 131

prune105.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Error

0.7b

Counts

135 → 4

Alt Table

Status	Error	Program
✓	0.8b	(acos.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1))))
	1.7b	(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)
	2.6b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) 2) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2))))
▶	0.9b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Compiler

Compiled 3111 to 2307 computations (25.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(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))

rewrite38.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`log1p-expm1-u_binary64`
667×	`expm1-log1p-u_binary64`
152×	`prod-diff_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	164	14
2	1805	14

Stop Event

1×	node limit

Counts

1 → 35

Calls

1 calls:

37.0ms

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

35 → 35

prune50.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	34	5	39

Error

0.7b

Counts

39 → 5

Alt Table

Status	Error	Program
✓	0.8b	(acos.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1))))
	2.4b	(fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	2.6b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) 2) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2))))
▶	1.8b	(pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3)
	61.9b	(/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (fma.f64 (PI.f64) 1/2 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))

Compiler

Compiled 1556 to 1177 computations (24.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
✓	1.0b	(cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
✓	1.5b	(pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3)

series90.0ms (1.5%)

Counts

2 → 24

Calls

2 calls:

52.0ms	(pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3)
38.0ms	(cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

819×	`log1p-expm1-u_binary64`
819×	`expm1-log1p-u_binary64`
180×	`prod-diff_binary64`
94×	`add-sqr-sqrt_binary64`
92×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	224	30
2	2271	30

Stop Event

1×	node limit

Counts

2 → 60

Calls

2 calls:

44.0ms	(cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
44.0ms	(pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3)

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-def_binary64`
704×	`unswap-sqr_binary64`
603×	`associate-l_binary64`
402×	`associate-r_binary64`
211×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	360
1	23	360
2	43	360
3	89	360
4	202	360
5	645	360
6	2400	360
7	4873	360

Stop Event

1×	node limit

Counts

84 → 61

prune90.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	93	8	101

Error

0.7b

Counts

101 → 8

Alt Table

Status	Error	Program
	2.4b	(fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) (cbrt.f64 (.f64 (PI.f64) 1/2))) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	2.4b	(pow.f64 (-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))) 1) 3)
✓	0.8b	(acos.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 1 (fma.f64 v v -1))))
	2.4b	(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (.f64 (PI.f64) 1/2)) (sqrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))) 3)
	2.4b	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) 3) 3)
	2.4b	(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 2)) 3) (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	2.6b	(+.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) 1/2)) 2) (cbrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2))))
	61.9b	(/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (fma.f64 (PI.f64) 1/2 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))

Compiler

Compiled 3455 to 2663 computations (22.9% saved)

regimes230.0ms (3.8%)

Accuracy

Total 0.0b remaining (5.3%)

Threshold costs 0.0b (5.3%)

Counts

50 → 1

Compiler

Compiled 6126 to 4649 computations (24.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	15	20

Stop Event

1×

saturated

end210.0ms (3.4%)

Compiler: Compiled 305 to 236 computations (22.6% saved)

Details

analyze1.2s (19.1%)

sample3.8s (61.2%)

simplify26.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series7.0ms (0.1%)

rewrite51.0ms (0.8%)

simplify28.0ms (0.5%)

prune76.0ms (1.2%)

localize8.0ms (0.1%)

series7.0ms (0.1%)

rewrite48.0ms (0.8%)

simplify31.0ms (0.5%)

prune105.0ms (1.7%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite38.0ms (0.6%)

simplify6.0ms (0.1%)

prune50.0ms (0.8%)

localize8.0ms (0.1%)

series90.0ms (1.5%)

rewrite46.0ms (0.7%)

simplify39.0ms (0.6%)

prune90.0ms (1.5%)

regimes230.0ms (3.8%)

simplify2.0ms (0%)

end210.0ms (3.4%)

Profiling