Details

analyze5.9s (53.3%)

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)

sample1.7s (15.7%)

Symmetry

(sort y z t)

(sort a b)

Results

1.2s	8256×	body	128	valid
429.0ms	3123×	body	128	invalid

Compiler

Compiled 71 to 53 computations (25.4% saved)

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	39	23
2	123	21
3	423	21
4	908	21
5	1463	21
6	2155	21
7	2547	21
8	3019	21
9	3134	21
10	3138	21
11	3138	21
12	3138	21

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	3.1b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 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	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
✓	0.3b	(.f64 (.f64 a 27) b)
✓	0.4b	(.f64 (.f64 y 9) z)
✓	5.8b	(.f64 (.f64 (*.f64 y 9) z) t)

series50.0ms (0.5%)

Counts

4 → 156

Calls

4 calls:

29.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
11.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
5.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 y 9) z)

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

194×	`add-sqr-sqrt_binary64`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`
186×	`add-cbrt-cube_binary64`
183×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	49
1	397	47

Stop Event

1×	node limit

Counts

4 → 86

Calls

4 calls:

40.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
40.0ms	(.f64 (.f64 a 27) b)
40.0ms	(.f64 (.f64 y 9) z)
40.0ms	(.f64 (.f64 (*.f64 y 9) z) t)

simplify139.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
685×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`
178×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	2118
1	55	2004
2	138	2004
3	367	2004
4	696	2004
5	1082	2004
6	1534	2004
7	2117	2004
8	2583	2004
9	2888	2004
10	3207	2004
11	3241	2004
12	3241	2004
13	3241	2004

Stop Event

1×

saturated

Counts

242 → 102

prune113.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Error

0.0b

Counts

104 → 8

Alt Table

Status	Error	Program
	11.9b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 2)) (cbrt.f64 (.f64 a (.f64 27 b))) (-.f64 (.f64 x 2) (.f64 y (.f64 (.f64 9 z) t))))
	3.1b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
	2.8b	(fma.f64 27 (.f64 a b) (fma.f64 y (.f64 t (.f64 z -9)) (.f64 2 x)))
	4.0b	(.f64 (cbrt.f64 (fma.f64 a (.f64 27 b) (-.f64 (.f64 x 2) (.f64 y (.f64 (.f64 9 z) t))))) (pow.f64 (cbrt.f64 (fma.f64 a (.f64 27 b) (-.f64 (.f64 x 2) (.f64 y (.f64 (*.f64 9 z) t))))) 2))
▶	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	2.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
	3.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 a (.f64 27 b))) 3))
	18.5b	(fma.f64 b (.f64 27 a) (.f64 2 x))

Compiler

Compiled 2802 to 1930 computations (31.1% saved)

localize12.0ms (0.1%)

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 9 (.f64 y z))
	0.3b	(.f64 (.f64 a 27) b)
✓	5.8b	(.f64 (.f64 9 (*.f64 y z)) t)

series45.0ms (0.4%)

Counts

3 → 108

Calls

3 calls:

29.0ms	(+.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)
4.0ms	(.f64 9 (.f64 y z))

rewrite40.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

194×	`add-sqr-sqrt_binary64`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`
186×	`add-cbrt-cube_binary64`
183×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	42
1	397	38

Stop Event

1×	node limit

Counts

3 → 71

Calls

3 calls:

39.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
39.0ms	(.f64 9 (.f64 y z))
38.0ms	(.f64 (.f64 9 (*.f64 y z)) t)

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
699×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`
177×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	1782
1	50	1668
2	131	1668
3	374	1668
4	716	1668
5	1093	1668
6	1573	1668
7	2170	1668
8	2636	1668
9	2941	1668
10	3260	1668
11	3294	1668
12	3294	1668
13	3294	1668

Stop Event

1×

saturated

Counts

179 → 85

prune105.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	99	8	107

Error

0.0b

Counts

107 → 8

Alt Table

Status	Error	Program
	11.9b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 2)) (cbrt.f64 (.f64 a (.f64 27 b))) (-.f64 (.f64 x 2) (.f64 y (.f64 (.f64 9 z) t))))
	3.1b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
	2.8b	(fma.f64 27 (.f64 a b) (fma.f64 y (.f64 t (.f64 z -9)) (.f64 2 x)))
	4.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 a (.f64 27 b))) 2) (cbrt.f64 (.f64 a (.f64 27 b))) (fma.f64 x 2 (.f64 -9 (.f64 z (*.f64 y t)))))
✓	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	3.9b	(fma.f64 a (.f64 27 b) (fma.f64 x 2 (.f64 -9 (.f64 z (.f64 y t)))))
▶	2.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
	3.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 a (.f64 27 b))) 3))

Compiler

Compiled 2637 to 1609 computations (39% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
✓	0.2b	(.f64 9 (.f64 y (*.f64 t z)))
	0.3b	(.f64 (.f64 a 27) b)
✓	5.4b	(.f64 y (.f64 t z))

series54.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

36.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
9.0ms	(.f64 9 (.f64 y (*.f64 t z)))
8.0ms	(.f64 y (.f64 t z))

rewrite43.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

194×	`add-sqr-sqrt_binary64`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`
186×	`add-cbrt-cube_binary64`
183×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	42
1	398	38

Stop Event

1×	node limit

Counts

3 → 73

Calls

3 calls:

41.0ms	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
41.0ms	(.f64 9 (.f64 y (*.f64 t z)))
41.0ms	(.f64 y (.f64 t z))

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	1422
1	50	1308
2	131	1308
3	373	1308
4	711	1308
5	1087	1308
6	1566	1308
7	2180	1308
8	2648	1308
9	2953	1308
10	3272	1308
11	3306	1308
12	3306	1308
13	3306	1308

Stop Event

1×

saturated

Counts

145 → 85

prune105.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	99	8	107

Error

0.0b

Counts

107 → 8

Alt Table

Status	Error	Program
	11.9b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 2)) (cbrt.f64 (.f64 a (.f64 27 b))) (-.f64 (.f64 x 2) (.f64 y (.f64 (.f64 9 z) t))))
	3.1b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
▶	2.8b	(fma.f64 27 (.f64 a b) (fma.f64 y (.f64 t (.f64 z -9)) (.f64 2 x)))
	4.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 a (.f64 27 b))) 2) (cbrt.f64 (.f64 a (.f64 27 b))) (fma.f64 x 2 (.f64 -9 (.f64 z (*.f64 y t)))))
✓	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	3.9b	(fma.f64 a (.f64 27 b) (fma.f64 x 2 (.f64 -9 (.f64 z (.f64 y t)))))
✓	2.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
	3.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 a (.f64 27 b))) 3))

Compiler

Compiled 2624 to 1510 computations (42.5% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 y (.f64 t (.f64 z -9)) (.f64 2 x)))
✓	0.2b	(.f64 t (.f64 z -9))
✓	3.0b	(fma.f64 y (.f64 t (.f64 z -9)) (*.f64 2 x))

series55.0ms (0.5%)

Counts

3 → 144

Calls

3 calls:

39.0ms	(fma.f64 27 (.f64 a b) (fma.f64 y (.f64 t (.f64 z -9)) (.f64 2 x)))
12.0ms	(fma.f64 y (.f64 t (.f64 z -9)) (*.f64 2 x))
4.0ms	(.f64 t (.f64 z -9))

rewrite62.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

286×	`expm1-udef_binary64`
286×	`log1p-udef_binary64`
228×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
148×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	321	42
2	3695	42

Stop Event

1×	node limit

Counts

3 → 62

Calls

3 calls:

61.0ms	(fma.f64 27 (.f64 a b) (fma.f64 y (.f64 t (.f64 z -9)) (.f64 2 x)))
61.0ms	(.f64 t (.f64 z -9))
61.0ms	(fma.f64 y (.f64 t (.f64 z -9)) (*.f64 2 x))

simplify151.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
685×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
178×	`distribute-rgt-neg-in_binary64`
119×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	2256
1	54	2070
2	139	2070
3	374	2070
4	706	2070
5	1095	2070
6	1549	2070
7	2132	2070
8	2596	2070
9	2901	2070
10	3220	2070
11	3254	2070
12	3254	2070
13	3254	2070

Stop Event

1×

saturated

Counts

206 → 77

prune77.0ms (0.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	77	8	85

Error

0.0b

Counts

85 → 8

Alt Table

Status	Error	Program
	11.9b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 a (.f64 27 b)) 2)) (cbrt.f64 (.f64 a (.f64 27 b))) (-.f64 (.f64 x 2) (.f64 y (.f64 (.f64 9 z) t))))
	3.1b	(fma.f64 x 2 (fma.f64 y (.f64 z (.f64 t -9)) (.f64 a (.f64 27 b))))
✓	2.8b	(fma.f64 27 (.f64 a b) (fma.f64 y (.f64 t (.f64 z -9)) (.f64 2 x)))
	4.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 a (.f64 27 b))) 2) (cbrt.f64 (.f64 a (.f64 27 b))) (fma.f64 x 2 (.f64 -9 (.f64 z (*.f64 y t)))))
✓	2.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	3.9b	(fma.f64 a (.f64 27 b) (fma.f64 x 2 (.f64 -9 (.f64 z (.f64 y t)))))
✓	2.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 9 (.f64 y (.f64 t z)))) (.f64 (.f64 a 27) b))
	3.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (pow.f64 (cbrt.f64 (.f64 a (.f64 27 b))) 3))

Compiler

Compiled 1691 to 1035 computations (38.8% saved)

regimes1.2s (11%)

Accuracy

Total 0.7b remaining (97.6%)

Threshold costs 0.7b (97.6%)

Counts

55 → 2

Compiler

Compiled 19524 to 14487 computations (25.8% saved)

bsearch6.0ms (0.1%)

Steps

Iters	Range		Point
1	1.517347032896308e-188	9.233386814591935e-187	1.184025489070519e-187

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	48
1	34	48

Stop Event

1×

saturated

end760.0ms (6.9%)

Compiler: Compiled 438 to 308 computations (29.7% saved)

Details

analyze5.9s (53.3%)

sample1.7s (15.7%)

simplify52.0ms (0.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series50.0ms (0.5%)

rewrite42.0ms (0.4%)

simplify139.0ms (1.3%)

prune113.0ms (1%)

localize12.0ms (0.1%)

series45.0ms (0.4%)

rewrite40.0ms (0.4%)

simplify128.0ms (1.2%)

prune105.0ms (1%)

localize15.0ms (0.1%)

series54.0ms (0.5%)

rewrite43.0ms (0.4%)

simplify106.0ms (1%)

prune105.0ms (1%)

localize13.0ms (0.1%)

series55.0ms (0.5%)

rewrite62.0ms (0.6%)

simplify151.0ms (1.4%)

prune77.0ms (0.7%)

regimes1.2s (11%)

bsearch6.0ms (0.1%)

simplify2.0ms (0%)

end760.0ms (6.9%)

Profiling