Details

analyze243.0ms (5.2%)

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
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.1s (23.2%)

Results

907.0ms	8256×	body	128	valid
150.0ms	1503×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
10×	`fma-def_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	10
2	35	10
3	41	10
4	39	10

prune4.0ms (0.1%)

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	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

Compiler

Compiled 40 to 27 computations (32.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.2b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

series26.0ms (0.6%)

Counts

2 → 50

Calls

2 calls:

14.0ms	(fma.f64 y (sqrt.f64 z) x)
12.0ms	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

rewrite45.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

650×	`log1p-expm1-u_binary64`
650×	`expm1-log1p-u_binary64`
347×	`log-prod_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`

Counts

2 → 51

Calls

2 calls:

44.0ms	(fma.f64 y (sqrt.f64 z) x)
44.0ms	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	157	17
2	1708	17
3	5198	17
0	0	0
1	0	0

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

10×	`fma-def_binary64`
7×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
2×	`+-commutative_binary64`

Counts

101 → 56

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	371
1	22	371
2	33	371
3	36	371
4	36	371

prune33.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	8	57

Error

0.3b

Counts

57 → 8

Alt Table

Status	Error	Program
	32.0b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)
	1.6b	(pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)
	29.7b	(*.f64 1/2 x)
✓	0.4b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	1.6b	(*.f64 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3))
	42.5b	(.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) (pow.f64 x 3)) (fma.f64 (.f64 y (sqrt.f64 z)) (.f64 y (sqrt.f64 z)) (-.f64 (.f64 x x) (.f64 (*.f64 y (sqrt.f64 z)) x)))))
▶	1.6b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	42.3b	(cbrt.f64 (pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3))

Compiler

Compiled 877 to 435 computations (50.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
✓	0.8b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series153.0ms (3.3%)

Counts

4 → 100

Calls

4 calls:

78.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
50.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
15.0ms	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
10.0ms	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))

rewrite51.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

857×	`log1p-expm1-u_binary64`
857×	`expm1-log1p-u_binary64`
104×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
98×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

50.0ms	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
50.0ms	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
50.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
50.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	222	38
2	2262	38
3	5274	38
0	0	0
1	0	0

simplify106.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

379×	`cancel-sign-sub-inv_binary64`
295×	`associate-/r/_binary64`
241×	`unswap-sqr_binary64`
236×	`associate-r_binary64`
195×	`associate-l_binary64`

Counts

178 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	3177
1	803	3115
2	2804	2874
3	4832	2614
4	4948	2614

prune190.0ms (4.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	222	7	229
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	224	13	237

Error

0.3b

Counts

237 → 13

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	2.4b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2)) 2)))
	31.4b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 2))))
	1.6b	(*.f64 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3))
	32.0b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)
▶	1.6b	(pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)
	29.7b	(*.f64 1/2 x)
	1.9b	(.f64 1/2 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	34.7b	(.f64 1/2 (.f64 (*.f64 (cbrt.f64 y) (pow.f64 z 1/6)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	33.1b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y))) 2)))
	42.5b	(.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) (pow.f64 x 3)) (fma.f64 (.f64 y (sqrt.f64 z)) (.f64 y (sqrt.f64 z)) (-.f64 (.f64 x x) (.f64 (*.f64 y (sqrt.f64 z)) x)))))
	12.6b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 4)))))
	25.2b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) 2)))

Compiler

Compiled 7952 to 4379 computations (44.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 z) x)
	0.2b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
✓	0.5b	(cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)

series1.6s (33.6%)

Counts

2 → 50

Calls

2 calls:

1.5s	(pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)
77.0ms	(cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))

rewrite46.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

822×	`log1p-expm1-u_binary64`
822×	`expm1-log1p-u_binary64`
96×	`add-sqr-sqrt_binary64`
91×	`add-cbrt-cube_binary64`
91×	`add-log-exp_binary64`

Counts

2 → 57

Calls

2 calls:

45.0ms	(cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))
44.0ms	(pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	206	22
2	2168	22
3	5031	22
0	0	0
1	0	0

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

912×	`associate-/l*_binary64`
614×	`fma-def_binary64`
226×	`associate-/r/_binary64`
195×	`associate-r_binary64`
191×	`cancel-sign-sub-inv_binary64`

Counts

107 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2377
1	588	2295
2	2084	2132
3	5100	2132

prune123.0ms (2.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	168	13	181

Error

0.0b

Counts

181 → 13

Alt Table

Status	Error	Program
	35.5b	(pow.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6))) 3)
	33.1b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y))) 2)))
	31.4b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 2))))
	1.6b	(*.f64 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3))
	32.0b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)
	1.8b	(pow.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)
	2.4b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))) 2) 3) (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))
▶	1.5b	(*.f64 (pow.f64 (cbrt.f64 1/2) 3) (fma.f64 y (sqrt.f64 z) x))
✓	0.4b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	1.6b	(.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)))
	1.6b	(.f64 (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2))
	42.5b	(.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) (pow.f64 x 3)) (fma.f64 (.f64 y (sqrt.f64 z)) (.f64 y (sqrt.f64 z)) (-.f64 (.f64 x x) (.f64 (*.f64 y (sqrt.f64 z)) x)))))
	25.2b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) 2)))

Compiler

Compiled 4322 to 2746 computations (36.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.2b	(*.f64 (pow.f64 (cbrt.f64 1/2) 3) (fma.f64 y (sqrt.f64 z) x))
✓	1.0b	(pow.f64 (cbrt.f64 1/2) 3)

series14.0ms (0.3%)

Counts

2 → 25

Calls

2 calls:

14.0ms	(*.f64 (pow.f64 (cbrt.f64 1/2) 3) (fma.f64 y (sqrt.f64 z) x))
0.0ms	(pow.f64 (cbrt.f64 1/2) 3)

rewrite45.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
96×	`add-sqr-sqrt_binary64`
92×	`add-log-exp_binary64`
91×	`add-cbrt-cube_binary64`

Counts

2 → 17

Calls

2 calls:

44.0ms	(*.f64 (pow.f64 (cbrt.f64 1/2) 3) (fma.f64 y (sqrt.f64 z) x))
44.0ms	(pow.f64 (cbrt.f64 1/2) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	11
1	205	11
2	2114	11
3	4914	11
0	0	0
1	0	0

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`fma-def_binary64`
8×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
2×	`+-commutative_binary64`

Counts

42 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	259
1	22	223
2	33	223
3	36	223
4	36	223

prune31.0ms (0.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	51	14	65

Error

0.0b

Counts

65 → 14

Alt Table

Status	Error	Program
	35.5b	(pow.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6))) 3)
	33.1b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y))) 2)))
	31.4b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 2))))
	1.6b	(*.f64 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3))
	32.0b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)
	1.8b	(pow.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)
	2.4b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))) 2) 3) (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))
✓	1.5b	(*.f64 (pow.f64 (cbrt.f64 1/2) 3) (fma.f64 y (sqrt.f64 z) x))
✓	0.4b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	1.6b	(.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)))
	1.6b	(.f64 (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2))
	42.5b	(.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) (pow.f64 x 3)) (fma.f64 (.f64 y (sqrt.f64 z)) (.f64 y (sqrt.f64 z)) (-.f64 (.f64 x x) (.f64 (*.f64 y (sqrt.f64 z)) x)))))
	1.8b	(*.f64 (pow.f64 (cbrt.f64 1/2) 3) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3))
	25.2b	(.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) 2)))

Compiler

Compiled 927 to 518 computations (44.1% saved)

regimes571.0ms (12.2%)

Accuracy

Total 0.1b remaining (72.7%)

Threshold costs 0.1b (72.7%)

Counts

73 → 1

Compiler

Compiled 9103 to 6425 computations (29.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
2	9	10

end212.0ms (4.5%)

Compiler: Compiled 282 to 191 computations (32.3% saved)

Details

analyze243.0ms (5.2%)

sample1.1s (23.2%)

simplify6.0ms (0.1%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series26.0ms (0.6%)

rewrite45.0ms (1%)

simplify14.0ms (0.3%)

prune33.0ms (0.7%)

localize9.0ms (0.2%)

series153.0ms (3.3%)

rewrite51.0ms (1.1%)

simplify106.0ms (2.3%)

prune190.0ms (4.1%)

localize8.0ms (0.2%)

series1.6s (33.6%)

rewrite46.0ms (1%)

simplify75.0ms (1.6%)

prune123.0ms (2.6%)

localize10.0ms (0.2%)

series14.0ms (0.3%)

rewrite45.0ms (1%)

simplify11.0ms (0.2%)

prune31.0ms (0.7%)

regimes571.0ms (12.2%)

simplify2.0ms (0%)

end212.0ms (4.5%)

Profiling