Details

analyze953.0ms (6.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (7.9%)

Results

928.0ms	8256×	body	128	valid
244.0ms	2192×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess42.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

458×	`div-sub_binary64`
436×	`unsub-neg_binary64`
432×	`fma-def_binary64`
326×	`cancel-sign-sub-inv_binary64`
310×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	91
1	69	77
2	166	77
3	466	77
4	1087	77
5	2421	77
6	4040	77
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
729×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
138×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	32	11
3	79	11
4	180	11
5	345	11
6	572	11
7	1043	11
8	1973	11
9	2951	11
10	3462	11
11	3509	11
12	3539	11
13	3544	11
14	3544	11

Stop Event

1×

saturated

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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series16.0ms (0.1%)

Counts

1 → 48

Calls

12 calls:

2.0ms	(fma.f64 (-.f64 y x) (/.f64 z t) x)	x	0
1.0ms	(fma.f64 (-.f64 y x) (/.f64 z t) x)	y	-inf
1.0ms	(fma.f64 (-.f64 y x) (/.f64 z t) x)	x	-inf
1.0ms	(fma.f64 (-.f64 y x) (/.f64 z t) x)	x	inf
1.0ms	(fma.f64 (-.f64 y x) (/.f64 z t) x)	z	-inf

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
197×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2476	11

Stop Event

1×	node limit

Counts

1 → 29

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
715×	`fma-neg_binary64`
244×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	69	561
2	162	552
3	383	552
4	825	480
5	1519	480
6	2510	480
7	3538	480
8	3588	480
9	3632	480
10	3690	480
11	3690	480

Stop Event

1×

saturated

Counts

77 → 42

prune26.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	37	5	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	6	43

Error

0.0b

Counts

43 → 6

Alt Table

Status	Error	Program
	36.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
	32.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)
▶	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
	29.6b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 y x) (/.f64 z t)) (.f64 (-.f64 y x) (/.f64 z t))) (.f64 x x)) (fma.f64 (-.f64 y x) (/.f64 z t) (neg.f64 x)))

Compiler

Compiled 730 to 237 computations (67.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series10.0s (66.6%)

Counts

2 → 40

Calls

24 calls:

2.5s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)	z	0
2.5s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)	t	inf
2.5s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)	t	-inf
2.2s	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)	x	0
267.0ms	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)	y	0

rewrite51.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`prod-diff_binary64`
207×	`fma-def_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
177×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	235	24
2	2954	24

Stop Event

1×	node limit

Counts

2 → 68

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

361×	`cancel-sign-sub-inv_binary64`
289×	`unswap-sqr_binary64`
193×	`associate-/r/_binary64`
183×	`associate-r_binary64`
170×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3553
1	685	3524
2	2714	3471

Stop Event

1×	node limit

Counts

108 → 103

prune99.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	142	9	151

Error

0.0b

Counts

151 → 9

Alt Table

Status	Error	Program
	36.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	1.7b	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)
	5.7b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
	1.7b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)
	30.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) 2)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	32.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)
✓	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

Compiler

Compiled 4225 to 1969 computations (53.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 z t)) 2)
✓	1.0b	(*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2))
✓	8.6b	(cbrt.f64 (/.f64 z t))

series647.0ms (4.3%)

Counts

4 → 54

Calls

36 calls:

47.0ms	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)	y	inf
40.0ms	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)	y	-inf
40.0ms	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)	y	0
38.0ms	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)	x	inf
38.0ms	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)	x	0

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

451×	`prod-diff_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
225×	`fma-def_binary64`
128×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	257	43
2	3334	41

Stop Event

1×	node limit

Counts

4 → 98

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary64`
512×	`fma-def_binary64`
362×	`associate-/r*_binary64`
267×	`fma-neg_binary64`
249×	`associate-/r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	1071
1	76	819
2	171	783
3	450	711
4	1607	675

Stop Event

1×	node limit

Counts

152 → 113

prune123.0ms (0.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	144	9	153

Error

0.0b

Counts

153 → 9

Alt Table

Status	Error	Program
	36.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	1.7b	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)
	5.7b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
▶	1.7b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)
	30.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) 2)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	32.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)
✓	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

Compiler

Compiled 2925 to 1033 computations (64.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 y x)) 2)
✓	0.6b	(cbrt.f64 (-.f64 y x))
✓	0.6b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)
✓	2.7b	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))

series715.0ms (4.7%)

Counts

4 → 84

Calls

36 calls:

209.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)	x	0
91.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)	y	0
25.0ms	(pow.f64 (cbrt.f64 (-.f64 y x)) 2)	y	0
25.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)	z	inf
23.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)	z	-inf

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

451×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
124×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	258	40
2	3375	40

Stop Event

1×	node limit

Counts

4 → 90

simplify57.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
457×	`cancel-sign-sub-inv_binary64`
375×	`times-frac_binary64`
227×	`associate-r_binary64`
205×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2574
1	693	2453
2	2556	2431

Stop Event

1×	node limit

Counts

174 → 161

prune175.0ms (1.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	202	9	211

Error

0.0b

Counts

211 → 9

Alt Table

Status	Error	Program
	5.6b	(+.f64 x (/.f64 (*.f64 z (-.f64 y x)) t))
✓	1.7b	(fma.f64 (*.f64 (-.f64 y x) (pow.f64 (cbrt.f64 (/.f64 z t)) 2)) (cbrt.f64 (/.f64 z t)) x)
	36.7b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.7b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
✓	1.7b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 y x)) 2) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)) x)
	30.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) 2)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	32.0b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 2)
✓	2.3b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

Compiler

Compiled 5901 to 2965 computations (49.8% saved)

regimes405.0ms (2.7%)

Accuracy

Total 2.1b remaining (99.4%)

Threshold costs 0b (0%)

Counts

67 → 1

Compiler

Compiled 7832 to 4690 computations (40.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	15	11
3	17	11
4	18	11

Stop Event

1×

saturated

end110.0ms (0.7%)

Stop Event

1×

fuel

Compiler

Compiled 185 to 106 computations (42.7% saved)

Details

analyze953.0ms (6.3%)

sample1.2s (7.9%)

preprocess42.0ms (0.3%)

simplify48.0ms (0.3%)

prune3.0ms (0%)

localize5.0ms (0%)

series16.0ms (0.1%)

rewrite42.0ms (0.3%)

simplify68.0ms (0.4%)

prune26.0ms (0.2%)

localize9.0ms (0.1%)

series10.0s (66.6%)

rewrite51.0ms (0.3%)

simplify71.0ms (0.5%)

prune99.0ms (0.7%)

localize9.0ms (0.1%)

series647.0ms (4.3%)

rewrite57.0ms (0.4%)

simplify40.0ms (0.3%)

prune123.0ms (0.8%)

localize13.0ms (0.1%)

series715.0ms (4.7%)

rewrite57.0ms (0.4%)

simplify57.0ms (0.4%)

prune175.0ms (1.2%)

regimes405.0ms (2.7%)

simplify3.0ms (0%)

end110.0ms (0.7%)

Profiling