Details

analyze1.9s (24.6%)

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)

sample1.9s (24.6%)

Symmetry

(sort y z t)

(sort a b)

Results

1.2s	8256×	body	128	valid
424.0ms	2985×	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

prune4.0ms (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	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 126 to 90 computations (28.6% saved)

localize10.0ms (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 z t) -9)
✓	0.2b	(.f64 (.f64 a 27) b)
✓	2.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

series52.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

31.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
12.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))
4.0ms	(.f64 (.f64 a 27) b)
4.0ms	(.f64 (.f64 z t) -9)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
6×	`associate-r_binary64`
6×	`cbrt-unprod_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(.f64 (.f64 z t) -9)
4.0ms	(.f64 (.f64 a 27) b)
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))
0.0ms	(fma.f64 x 2 (.f64 (.f64 a 27) b))

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

868×	`unswap-sqr_binary64`
419×	`*-commutative_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
310×	`fma-def_binary64`

Counts

216 → 107

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	122	2976
1	250	2724
2	873	2724
3	1485	2724
4	2922	2724
5	5289	2724

prune110.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Error

0.0b

Counts

109 → 7

Alt Table

Status	Error	Program
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
▶	2.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
	28.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
	2.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a 27) b)) (cbrt.f64 (.f64 (.f64 a 27) b))) (cbrt.f64 (.f64 (.f64 a 27) b)))))
	3.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b))))) (cbrt.f64 (fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 a 27) b)))))
	2.2b	(fma.f64 y (.f64 (.f64 (.f64 z t) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 2530 to 1482 computations (41.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
✓	0.2b	(.f64 (.f64 y (*.f64 t z)) -9)
✓	7.3b	(.f64 y (.f64 t z))

series66.0ms (0.9%)

Counts

4 → 156

Calls

4 calls:

35.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))
13.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
10.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
8.0ms	(.f64 y (.f64 t z))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(.f64 (.f64 y (*.f64 t z)) -9)
3.0ms	(.f64 y (.f64 t z))
3.0ms	(fma.f64 2 x (.f64 (.f64 y (*.f64 t z)) -9))
0.0ms	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 y (.f64 t z)) -9)))

simplify110.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

507×	`distribute-rgt-in_binary64`
501×	`distribute-lft-in_binary64`
416×	`fma-def_binary64`
360×	`*-commutative_binary64`
190×	`associate-+l+_binary64`

Counts

219 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	3305
1	213	3114
2	739	3114
3	1576	3114
4	4976	3114
5	4981	3114

prune104.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

0.0b

Counts

101 → 7

Alt Table

Status	Error	Program
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
▶	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	28.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
	2.2b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))))
	2.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a 27) b)) (cbrt.f64 (.f64 (.f64 a 27) b))) (cbrt.f64 (.f64 (.f64 a 27) b)))))
	3.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	2.2b	(fma.f64 y (.f64 (.f64 (.f64 z t) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 2309 to 1154 computations (50% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (.f64 a (.f64 27 b)))
	0.2b	(.f64 (.f64 z t) -9)
✓	0.2b	(.f64 a (.f64 27 b))
✓	2.0b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))

series42.0ms (0.5%)

Counts

3 → 132

Calls

3 calls:

28.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
9.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))
4.0ms	(.f64 a (.f64 27 b))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 40

Calls

3 calls:

3.0ms	(.f64 a (.f64 27 b))
0.0ms	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
0.0ms	(fma.f64 x 2 (.f64 a (.f64 27 b)))

simplify100.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

576×	`distribute-lft-in_binary64`
576×	`distribute-rgt-in_binary64`
548×	`associate-l_binary64`
426×	`fma-def_binary64`
385×	`associate-r_binary64`

Counts

172 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	2594
1	159	2378
2	475	2378
3	1528	2378
4	4509	2378
5	5090	2378

prune105.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	106	8	114

Error

Counts

114 → 8

Alt Table

Status	Error	Program
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
✓	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	28.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
▶	2.2b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))))
	3.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	48.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (*.f64 27 b)))))
	2.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (cbrt.f64 a) (.f64 27 b)))))
	2.2b	(fma.f64 y (.f64 (.f64 (.f64 z t) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 2487 to 1456 computations (41.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))))
✓	0.2b	(.f64 (.f64 (.f64 y (.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))
✓	0.3b	(.f64 (.f64 y (.f64 t z)) (.f64 (cbrt.f64 -9) (cbrt.f64 -9)))
	7.3b	(.f64 y (.f64 t z))

series553.0ms (7.2%)

Counts

3 → 144

Calls

3 calls:

226.0ms

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

189.0ms

(*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)))

137.0ms

(*.f64 (*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-exp-log_binary64`
53×	`pow1_binary64`
37×	`cbrt-unprod_binary64`
37×	`prod-exp_binary64`
37×	`pow-prod-down_binary64`

Counts

3 → 78

Calls

3 calls:

11.0ms

(*.f64 (*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))

9.0ms

(*.f64 (*.f64 y (*.f64 t z)) (*.f64 (cbrt.f64 -9) (cbrt.f64 -9)))

0.0ms

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

simplify120.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
675×	`*-commutative_binary64`
337×	`associate-l_binary64`
254×	`associate-r_binary64`
249×	`exp-prod_binary64`

Counts

222 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	3816
1	278	3407
2	1210	3407
3	2610	3405
4	4753	3405
5	4953	3405

prune134.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	128	8	136

Error

Counts

136 → 8

Alt Table

Status	Error	Program
	3.7b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
✓	2.1b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 a (.f64 27 b))))
	28.2b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 (.f64 (.f64 a 27) b)) (sqrt.f64 (.f64 (*.f64 a 27) b)))))
✓	2.2b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9))))
	3.9b	(fma.f64 27 (.f64 a b) (fma.f64 2 x (.f64 (.f64 (.f64 y t) z) -9)))
	48.8b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (*.f64 27 b)))))
	2.5b	(fma.f64 y (.f64 (.f64 z t) -9) (fma.f64 x 2 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (cbrt.f64 a) (.f64 27 b)))))
	2.2b	(fma.f64 y (.f64 (.f64 (.f64 z t) (.f64 (cbrt.f64 -9) (cbrt.f64 -9))) (cbrt.f64 -9)) (fma.f64 x 2 (.f64 (.f64 a 27) b)))

Compiler

Compiled 3693 to 2175 computations (41.1% saved)

regimes1.4s (17.9%)

Accuracy

Total 0.6b remaining (96.3%)

Threshold costs 0.6b (96.3%)

Counts

57 → 2

Compiler

Compiled 20494 to 14731 computations (28.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 8 computations (11.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	53
1	40	53
2	40	53

end753.0ms (9.8%)

Compiler: Compiled 461 to 327 computations (29.1% saved)

Details

analyze1.9s (24.6%)

sample1.9s (24.6%)

simplify71.0ms (0.9%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series52.0ms (0.7%)

rewrite10.0ms (0.1%)

simplify99.0ms (1.3%)

prune110.0ms (1.4%)

localize12.0ms (0.2%)

series66.0ms (0.9%)

rewrite14.0ms (0.2%)

simplify110.0ms (1.4%)

prune104.0ms (1.4%)

localize10.0ms (0.1%)

series42.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify100.0ms (1.3%)

prune105.0ms (1.4%)

localize13.0ms (0.2%)

series553.0ms (7.2%)

rewrite29.0ms (0.4%)

simplify120.0ms (1.6%)

prune134.0ms (1.7%)

regimes1.4s (17.9%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end753.0ms (9.8%)

Profiling