Details

analyze568.0ms (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
6.2%	79.6%	14.2%	8
7.8%	75.7%	16.5%	9
11.7%	68.6%	19.6%	10
20.3%	49.3%	30.4%	11
22.2%	44.4%	33.4%	12
25.2%	37.3%	37.5%	13
28%	27.3%	44.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.4s (22.5%)

Results

841.0ms	8256×	body	128	valid
500.0ms	4574×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1052×	`fma-def_binary64`
290×	`unswap-sqr_binary64`
257×	`*-commutative_binary64`
210×	`distribute-rgt-in_binary64`
206×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	19	12
2	46	12
3	112	12
4	251	12
5	454	12
6	809	12
7	2311	12
8	3475	12
9	4680	12

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.0b	(/.f64 (cosh.f64 x) (*.f64 x (/.f64 z y)))
	7.2b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 63 to 38 computations (39.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (cosh.f64 x) (*.f64 x (/.f64 z y)))
✓	6.6b	(*.f64 x (/.f64 z y))

series63.0ms (1%)

Counts

2 → 72

Calls

2 calls:

51.0ms	(/.f64 (cosh.f64 x) (*.f64 x (/.f64 z y)))
12.0ms	(*.f64 x (/.f64 z y))

rewrite51.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`log-prod_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`
162×	`pow3_binary64`
160×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	177	19
2	2636	19

Stop Event

1×	node limit

Counts

2 → 76

Calls

2 calls:

50.0ms	(/.f64 (cosh.f64 x) (*.f64 x (/.f64 z y)))
50.0ms	(*.f64 x (/.f64 z y))

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
407×	`associate-/r/_binary64`
383×	`associate-/r*_binary64`
323×	`associate-*l/_binary64`
259×	`associate-/l*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	1089
1	151	1021
2	376	1021
3	884	1017
4	2451	1005

Stop Event

1×	node limit

Counts

148 → 90

prune84.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Error

0.2b

Counts

92 → 7

Alt Table

Status	Error	Program
▶	6.8b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
	7.1b	(/.f64 (cosh.f64 x) (*.f64 z (/.f64 x y)))
	7.8b	(+.f64 (/.f64 y (.f64 z x)) (.f64 (/.f64 y z) (+.f64 (.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (.f64 1/720 (pow.f64 x 5))))))
	32.6b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)) 2)
	7.2b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
	7.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)
	8.5b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) (pow.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) 2)) (cbrt.f64 (.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)))

Compiler

Compiled 1425 to 524 computations (63.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
✓	6.5b	(/.f64 (/.f64 y z) x)

series70.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

54.0ms	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
15.0ms	(/.f64 (/.f64 y z) x)

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
177×	`pow1/3_binary64`
170×	`log-div_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	176	19
2	2618	19

Stop Event

1×	node limit

Counts

2 → 89

Calls

2 calls:

45.0ms	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
45.0ms	(/.f64 (/.f64 y z) x)

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-def_binary64`
406×	`associate-/r/_binary64`
384×	`associate-/r*_binary64`
324×	`associate-*l/_binary64`
259×	`associate-/l*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	48	1089
1	150	1021
2	375	1021
3	884	1017
4	2455	1005

Stop Event

1×	node limit

Counts

161 → 101

prune106.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	101	7	108

Error

0.2b

Counts

108 → 7

Alt Table

Status	Error	Program
	32.7b	(.f64 (cosh.f64 x) (.f64 (/.f64 (sqrt.f64 y) x) (/.f64 (sqrt.f64 y) z)))
	7.8b	(+.f64 (/.f64 y (.f64 z x)) (.f64 (/.f64 y z) (+.f64 (.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (.f64 1/720 (pow.f64 x 5))))))
	7.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)
▶	6.9b	(/.f64 1 (/.f64 x (*.f64 (/.f64 y z) (cosh.f64 x))))
	7.2b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
✓	6.8b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
	8.5b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) (pow.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) 2)) (cbrt.f64 (.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)))

Compiler

Compiled 1569 to 638 computations (59.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 y z) (cosh.f64 x))
✓	0.3b	(/.f64 1 (/.f64 x (*.f64 (/.f64 y z) (cosh.f64 x))))
✓	6.6b	(/.f64 x (*.f64 (/.f64 y z) (cosh.f64 x)))

series221.0ms (3.5%)

Counts

3 → 108

Calls

3 calls:

105.0ms	(/.f64 x (*.f64 (/.f64 y z) (cosh.f64 x)))
60.0ms	(*.f64 (/.f64 y z) (cosh.f64 x))
57.0ms	(/.f64 1 (/.f64 x (*.f64 (/.f64 y z) (cosh.f64 x))))

rewrite60.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

612×	`log-prod_binary64`
199×	`log-div_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
176×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	217	33
2	3126	33

Stop Event

1×	node limit

Counts

3 → 132

Calls

3 calls:

58.0ms	(*.f64 (/.f64 y z) (cosh.f64 x))
58.0ms	(/.f64 1 (/.f64 x (*.f64 (/.f64 y z) (cosh.f64 x))))
58.0ms	(/.f64 x (*.f64 (/.f64 y z) (cosh.f64 x)))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
513×	`fma-def_binary64`
465×	`associate-/r/_binary64`
235×	`associate-/l/_binary64`
205×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	2385
1	298	2239
2	801	2217
3	2400	2195

Stop Event

1×	node limit

Counts

240 → 170

prune142.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	170	7	177

Error

0.2b

Counts

177 → 7

Alt Table

Status	Error	Program
	7.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)
	7.8b	(+.f64 (/.f64 y (.f64 z x)) (fma.f64 1/2 (.f64 x (/.f64 y z)) (.f64 (/.f64 y z) (+.f64 (.f64 (pow.f64 x 3) 1/24) (*.f64 (pow.f64 x 5) 1/720)))))
	32.7b	(.f64 (cosh.f64 x) (.f64 (/.f64 (sqrt.f64 y) x) (/.f64 (sqrt.f64 y) z)))
	7.2b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
▶	7.2b	(/.f64 1 (/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z)))))
✓	6.8b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
	8.5b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) (pow.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) 2)) (cbrt.f64 (.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)))

Compiler

Compiled 2957 to 1220 computations (58.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/24 (pow.f64 x 4))
✓	0.3b	(/.f64 1 (/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z)))))
✓	1.8b	(.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6))))
✓	6.6b	(/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z))))

series516.0ms (8.2%)

Counts

4 → 108

Calls

4 calls:

344.0ms	(/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z))))
114.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z)))))
56.0ms	(.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6))))
3.0ms	(*.f64 1/24 (pow.f64 x 4))

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

242×	`add-sqr-sqrt_binary64`
239×	`log1p-expm1-u_binary64`
239×	`expm1-log1p-u_binary64`
237×	`add-cbrt-cube_binary64`
231×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	110
1	516	110

Stop Event

1×	node limit

Counts

4 → 69

Calls

4 calls:

41.0ms	(*.f64 1/24 (pow.f64 x 4))
41.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z)))))
41.0ms	(.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6))))
41.0ms	(/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z))))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

364×	`cancel-sign-sub-inv_binary64`
273×	`fma-neg_binary64`
262×	`times-frac_binary64`
259×	`fma-def_binary64`
206×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	3324
1	352	3304
2	958	3194
3	3082	3112

Stop Event

1×	node limit

Counts

177 → 117

prune114.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	116	8	124

Error

0.2b

Counts

124 → 8

Alt Table

Status	Error	Program
	7.2b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
	63.3b	(/.f64 1 (*.f64 (/.f64 z y) (+.f64 (/.f64 720 (pow.f64 x 5)) (/.f64 -21600 (pow.f64 x 7)))))
	7.8b	(/.f64 (.f64 y (+.f64 (fma.f64 x (.f64 x 1/2) (.f64 1/720 (pow.f64 x 6))) (+.f64 (.f64 1/24 (pow.f64 x 4)) 1))) (*.f64 z x))
	8.5b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) (pow.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) 2)) (cbrt.f64 (.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)))
	32.7b	(.f64 (cosh.f64 x) (.f64 (/.f64 (sqrt.f64 y) x) (/.f64 (sqrt.f64 y) z)))
✓	7.2b	(/.f64 1 (/.f64 x (+.f64 (.f64 (/.f64 y z) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 1/720 (pow.f64 x 6)))) (fma.f64 (/.f64 y z) (*.f64 1/24 (pow.f64 x 4)) (/.f64 y z)))))
	7.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 x z)) y)
✓	6.8b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))

Compiler

Compiled 3762 to 2143 computations (43% saved)

regimes2.3s (37.3%)

Accuracy

Total 0.4b remaining (78.7%)

Threshold costs 0.4b (78.7%)

Counts

223 → 3

Compiler

Compiled 19074 to 12844 computations (32.7% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	110
1	42	110

Stop Event

1×

saturated

end139.0ms (2.2%)

Compiler: Compiled 311 to 197 computations (36.7% saved)

Details

analyze568.0ms (9%)

sample1.4s (22.5%)

simplify34.0ms (0.5%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series63.0ms (1%)

rewrite51.0ms (0.8%)

simplify40.0ms (0.6%)

prune84.0ms (1.3%)

localize6.0ms (0.1%)

series70.0ms (1.1%)

rewrite46.0ms (0.7%)

simplify42.0ms (0.7%)

prune106.0ms (1.7%)

localize7.0ms (0.1%)

series221.0ms (3.5%)

rewrite60.0ms (1%)

simplify64.0ms (1%)

prune142.0ms (2.3%)

localize18.0ms (0.3%)

series516.0ms (8.2%)

rewrite43.0ms (0.7%)

simplify77.0ms (1.2%)

prune114.0ms (1.8%)

regimes2.3s (37.3%)

bsearch6.0ms (0.1%)

simplify3.0ms (0.1%)

end139.0ms (2.2%)

Profiling