Details

analyze2.2s (28.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample2.0s (25.8%)

Symmetry

(sort y z t)

(sort a b)

Results

1.3s	8256×	body	128	valid
488.0ms	2996×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
641×	`fma-def_binary64`
213×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-neg-in_binary64`
157×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	115	21
3	308	21
4	552	21
5	902	21
6	1201	21
7	1433	21
8	1672	21
9	1787	21
10	1791	21
11	1791	21
12	1791	21
13	1674	21

prune7.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	3.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(.f64 (.f64 z t) -9)
✓	3.4b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series55.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

32.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
11.0ms	(.f64 (.f64 z t) -9)
7.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
4.0ms	(.f64 (.f64 a 27) b)

rewrite75.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
258×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
149×	`add-log-exp_binary64`

Counts

4 → 79

Calls

4 calls:

73.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
73.0ms	(.f64 (.f64 a 27) b)
73.0ms	(.f64 (.f64 z t) -9)
73.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	323	46
2	3607	46
3	4924	46
0	0	0
1	0	0

simplify174.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

741×	`fma-def_binary64`
713×	`fma-neg_binary64`
298×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Counts

235 → 93

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	2106
1	54	1992
2	120	1992
3	277	1992
4	478	1992
5	613	1992
6	879	1992
7	1175	1992
8	1476	1992
9	1604	1992
10	1747	1992
11	1781	1992
12	1781	1992
13	1781	1992
14	1666	1992

prune102.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	10	95

Error

0.0b

Counts

95 → 10

Alt Table

Status	Error	Program
	47.0b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b))) 3))
▶	3.7b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	31.8b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 2)
	3.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	4.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 3)
	18.9b	(+.f64 (.f64 27 (.f64 a b)) (*.f64 2 x))
✓	3.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	27.3b	(fma.f64 y (.f64 (.f64 z t) -9) (/.f64 (-.f64 (.f64 (.f64 x 2) (.f64 x 2)) (pow.f64 (.f64 (.f64 a 27) b) 2)) (-.f64 (.f64 x 2) (.f64 (.f64 a 27) b))))
	34.8b	(fma.f64 y (pow.f64 (sqrt.f64 (.f64 (.f64 z t) -9)) 2) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.0b	(fma.f64 y (pow.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) 3) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 2199 to 1383 computations (37.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 27 (.f64 a b)) (*.f64 2 x))
✓	0.3b	(.f64 9 (.f64 y (*.f64 t z)))
✓	0.3b	(.f64 27 (.f64 a b))
✓	8.6b	(.f64 y (.f64 t z))

series34.0ms (0.4%)

Counts

4 → 9

Calls

4 calls:

11.0ms	(.f64 9 (.f64 y (*.f64 t z)))
10.0ms	(+.f64 (.f64 27 (.f64 a b)) (*.f64 2 x))
9.0ms	(.f64 y (.f64 t z))
4.0ms	(.f64 27 (.f64 a b))

rewrite73.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

310×	`expm1-udef_binary64`
310×	`log1p-udef_binary64`
172×	`add-sqr-sqrt_binary64`
168×	`associate-r_binary64`
164×	`log1p-expm1-u_binary64`

Counts

4 → 84

Calls

4 calls:

71.0ms	(+.f64 (.f64 27 (.f64 a b)) (*.f64 2 x))
71.0ms	(.f64 9 (.f64 y (*.f64 t z)))
71.0ms	(.f64 27 (.f64 a b))
71.0ms	(.f64 y (.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	354	35
2	4133	35
3	4950	35
0	0	0
1	0	0

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Counts

93 → 85

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	51
1	14	51
2	20	51
3	20	51
4	20	51

prune110.0ms (1.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	85	10	95

Error

0.0b

Counts

95 → 10

Alt Table

Status	Error	Program
	31.8b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 2)
▶	3.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	4.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 3)
	18.9b	(+.f64 (.f64 27 (.f64 a b)) (*.f64 2 x))
✓	3.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	20.6b	(-.f64 (+.f64 (cbrt.f64 (.f64 19683 (pow.f64 (.f64 a b) 3))) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	27.3b	(fma.f64 y (.f64 (.f64 z t) -9) (/.f64 (-.f64 (.f64 (.f64 x 2) (.f64 x 2)) (pow.f64 (.f64 (.f64 a 27) b) 2)) (-.f64 (.f64 x 2) (.f64 (.f64 a 27) b))))
	34.8b	(fma.f64 y (pow.f64 (sqrt.f64 (.f64 (.f64 z t) -9)) 2) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.0b	(fma.f64 y (pow.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) 3) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
✓	3.7b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))

Compiler

Compiled 2329 to 1357 computations (41.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 (.f64 y 9) z)
	0.2b	(.f64 (.f64 a 27) b)
✓	6.0b	(.f64 (.f64 (*.f64 y 9) z) t)

series51.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

33.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
13.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
5.0ms	(.f64 (.f64 y 9) z)

rewrite89.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

350×	`log1p-udef_binary64`
194×	`add-sqr-sqrt_binary64`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`
183×	`add-log-exp_binary64`

Counts

3 → 75

Calls

3 calls:

88.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
88.0ms	(.f64 (.f64 y 9) z)
88.0ms	(.f64 (.f64 (*.f64 y 9) z) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	42
1	393	40
2	4954	40
3	5435	40
0	0	0
1	0	0

simplify166.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
713×	`fma-neg_binary64`
298×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Counts

207 → 89

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	1950
1	55	1836
2	119	1836
3	276	1836
4	479	1836
5	613	1836
6	879	1836
7	1175	1836
8	1476	1836
9	1604	1836
10	1747	1836
11	1781	1836
12	1781	1836
13	1781	1836
14	1666	1836

prune128.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	104	11	115

Error

0.0b

Counts

115 → 11

Alt Table

Status	Error	Program
	27.3b	(fma.f64 y (.f64 (.f64 z t) -9) (/.f64 (-.f64 (.f64 (.f64 x 2) (.f64 x 2)) (pow.f64 (.f64 (.f64 a 27) b) 2)) (-.f64 (.f64 x 2) (.f64 (.f64 a 27) b))))
	32.3b	(pow.f64 (sqrt.f64 (fma.f64 (.f64 a 27) b (-.f64 (.f64 x 2) (.f64 (.f64 (*.f64 y 9) z) t)))) 2)
✓	3.7b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	22.6b	(fma.f64 (.f64 y (.f64 t z)) -9 (*.f64 2 x))
✓	3.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.1b	(fma.f64 a (.f64 27 b) (-.f64 (.f64 x 2) (.f64 (.f64 (*.f64 y 9) z) t)))
	20.6b	(-.f64 (+.f64 (cbrt.f64 (.f64 19683 (pow.f64 (.f64 a b) 3))) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	34.8b	(fma.f64 y (pow.f64 (sqrt.f64 (.f64 (.f64 z t) -9)) 2) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.0b	(fma.f64 y (pow.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) 3) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 3)
▶	3.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 2933 to 2020 computations (31.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	0.2b	(.f64 (.f64 a 27) b)
✓	0.2b	(.f64 9 (.f64 y z))
✓	6.0b	(.f64 (.f64 9 (*.f64 y z)) t)

series49.0ms (0.6%)

Counts

3 → 108

Calls

3 calls:

32.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
11.0ms	(.f64 (.f64 9 (*.f64 y z)) t)
7.0ms	(.f64 9 (.f64 y z))

rewrite97.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

350×	`log1p-udef_binary64`
194×	`add-sqr-sqrt_binary64`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`
183×	`add-log-exp_binary64`

Counts

3 → 73

Calls

3 calls:

95.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
95.0ms	(.f64 9 (.f64 y z))
95.0ms	(.f64 (.f64 9 (*.f64 y z)) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	42
1	393	38
2	4953	38
3	5432	38
0	0	0
1	0	0

simplify160.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
713×	`fma-neg_binary64`
298×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Counts

181 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	1782
1	50	1668
2	113	1668
3	275	1668
4	478	1668
5	613	1668
6	879	1668
7	1175	1668
8	1476	1668
9	1604	1668
10	1747	1668
11	1781	1668
12	1781	1668
13	1781	1668
14	1666	1668

prune108.0ms (1.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	102	11	113

Error

0.0b

Counts

113 → 11

Alt Table

Status	Error	Program
	27.3b	(fma.f64 y (.f64 (.f64 z t) -9) (/.f64 (-.f64 (.f64 (.f64 x 2) (.f64 x 2)) (pow.f64 (.f64 (.f64 a 27) b) 2)) (-.f64 (.f64 x 2) (.f64 (.f64 a 27) b))))
	32.3b	(pow.f64 (sqrt.f64 (fma.f64 (.f64 a 27) b (-.f64 (.f64 x 2) (.f64 (.f64 (*.f64 y 9) z) t)))) 2)
✓	3.7b	(-.f64 (+.f64 (.f64 27 (.f64 a b)) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	22.6b	(fma.f64 (.f64 y (.f64 t z)) -9 (*.f64 2 x))
✓	3.7b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.1b	(fma.f64 a (.f64 27 b) (-.f64 (.f64 x 2) (.f64 (.f64 (*.f64 y 9) z) t)))
	20.6b	(-.f64 (+.f64 (cbrt.f64 (.f64 19683 (pow.f64 (.f64 a b) 3))) (.f64 2 x)) (.f64 9 (.f64 y (.f64 t z))))
	34.8b	(fma.f64 y (pow.f64 (sqrt.f64 (.f64 (.f64 z t) -9)) 2) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.0b	(fma.f64 y (pow.f64 (cbrt.f64 (.f64 (.f64 z t) -9)) 3) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
	4.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) 3)
✓	3.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))

Compiler

Compiled 2591 to 1578 computations (39.1% saved)

regimes1.1s (13.8%)

Accuracy

Total 0.6b remaining (96.2%)

Threshold costs 0.6b (96.2%)

Counts

44 → 2

Compiler

Compiled 16034 to 11854 computations (26.1% saved)

bsearch17.0ms (0.2%)

Steps

Iters	Range		Point
2	3.00375305902273e-179	3.8989756550983054e-175	3.322523053190084e-178

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	50
1	42	50
2	50	50
3	60	50
4	73	50
5	82	50
6	88	50
7	90	50
8	89	50

end872.0ms (11.2%)

Compiler: Compiled 512 to 366 computations (28.5% saved)

Details

analyze2.2s (28.3%)

sample2.0s (25.8%)

simplify71.0ms (0.9%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

series55.0ms (0.7%)

rewrite75.0ms (1%)

simplify174.0ms (2.2%)

prune102.0ms (1.3%)

localize11.0ms (0.1%)

series34.0ms (0.4%)

rewrite73.0ms (0.9%)

simplify8.0ms (0.1%)

prune110.0ms (1.4%)

localize11.0ms (0.1%)

series51.0ms (0.7%)

rewrite89.0ms (1.1%)

simplify166.0ms (2.1%)

prune128.0ms (1.6%)

localize13.0ms (0.2%)

series49.0ms (0.6%)

rewrite97.0ms (1.2%)

simplify160.0ms (2.1%)

prune108.0ms (1.4%)

regimes1.1s (13.8%)

bsearch17.0ms (0.2%)

simplify4.0ms (0.1%)

end872.0ms (11.2%)

Profiling