Details

analyze3.4s (35.5%)

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)

sample364.0ms (3.8%)

Algorithm

1×

intervals

Symmetry

(sort y z t)

(sort a b)

Results

33.0ms	256×	body	128	valid
13.0ms	116×	body	128	invalid

Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify80.0ms (0.8%)

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

prune8.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 a 27) b))
	4.4b	(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)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
✓	0.2b	(.f64 (.f64 y 9) z)
✓	0.5b	(.f64 (.f64 a 27) b)
✓	7.4b	(.f64 (.f64 (*.f64 y 9) z) t)

series72.0ms (0.7%)

Counts

4 → 132

Calls

4 calls:

28.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
25.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
9.0ms	(.f64 (.f64 y 9) z)
9.0ms	(.f64 (.f64 a 27) b)

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
23×	`pow1_binary64`
12×	`cbrt-unprod_binary64`
12×	`prod-exp_binary64`

Counts

4 → 79

Calls

4 calls:

13.0ms	(.f64 (.f64 (*.f64 y 9) z) t)
7.0ms	(.f64 (.f64 y 9) z)
7.0ms	(.f64 (.f64 a 27) b)
7.0ms	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))

simplify172.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

543×	`distribute-rgt-neg-in_binary64`
369×	`fma-def_binary64`
365×	`associate-l_binary64`
300×	`fma-neg_binary64`
292×	`cancel-sign-sub-inv_binary64`

Counts

211 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	2455
1	372	2243
2	1621	2227
3	3117	2227
4	4841	2227
5	4894	2227

prune308.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	8	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Error

0.0b

Counts

129 → 8

Alt Table

Status	Error	Program
	3.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 a (.f64 27 b)))
▶	3.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 27 (.f64 a b)))
	20.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 y 9) z)) (sqrt.f64 (.f64 (.f64 y 9) z))) t)) (.f64 (*.f64 a 27) b))
	4.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))
	19.9b	(+.f64 (-.f64 (.f64 x 2) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 y 9) z) t) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (.f64 a 27) b))
	4.4b	(+.f64 (fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x)) (.f64 (.f64 a 27) b))
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
	13.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))

Compiler

Compiled 3283 to 2059 computations (37.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
	0.2b	(.f64 (.f64 y 9) z)
✓	0.2b	(.f64 27 (.f64 a b))
	7.4b	(.f64 (.f64 (*.f64 y 9) z) t)

series9.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

9.0ms

(*.f64 27 (*.f64 a b))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

8.0ms

(*.f64 27 (*.f64 a b))

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

495×	`associate-/l*_binary64`
484×	`cube-div_binary64`
484×	`log-div_binary64`
401×	`*-commutative_binary64`
334×	`associate-l_binary64`

Counts

20 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	210
1	84	174
2	255	174
3	647	174
4	824	174
5	953	174
6	1171	174
7	1550	174
8	2413	174
9	3887	174
10	5001	174

prune271.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Error

0.0b

Counts

125 → 7

Alt Table

Status	Error	Program
	20.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 y 9) z)) (sqrt.f64 (.f64 (.f64 y 9) z))) t)) (.f64 (*.f64 a 27) b))
	4.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))
	19.9b	(+.f64 (-.f64 (.f64 x 2) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 y 9) z) t) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (.f64 a 27) b))
	4.1b	(+.f64 (fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x)) (.f64 27 (.f64 a b)))
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
▶	3.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 a (.f64 27 b)))
	13.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))

Compiler

Compiled 3032 to 1795 computations (40.8% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t))
	0.2b	(.f64 (.f64 y 9) z)
✓	0.2b	(.f64 a (.f64 27 b))
	7.4b	(.f64 (.f64 (*.f64 y 9) z) t)

series14.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

14.0ms

(*.f64 a (*.f64 27 b))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

8.0ms

(*.f64 a (*.f64 27 b))

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Rules

525×	`associate-/r/_binary64`
451×	`associate-l_binary64`
384×	`associate-/l*_binary64`
370×	`*-commutative_binary64`
301×	`associate-r_binary64`

Counts

44 → 30

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	378
1	90	342
2	302	342
3	821	342
4	1011	342
5	1137	342
6	2002	342
7	4806	342
8	4922	342

prune253.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	127	7	134

Error

0.0b

Counts

134 → 7

Alt Table

Status	Error	Program
	20.8b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 y 9) z)) (sqrt.f64 (.f64 (.f64 y 9) z))) t)) (.f64 (*.f64 a 27) b))
	4.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))
	19.9b	(+.f64 (-.f64 (.f64 x 2) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 y 9) z) t) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 (.f64 (.f64 y 9) z) t)))) (.f64 (.f64 a 27) b))
▶	4.1b	(+.f64 (fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x)) (.f64 27 (.f64 a b)))
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
✓	3.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 a (.f64 27 b)))
	13.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))

Compiler

Compiled 3214 to 2007 computations (37.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x)) (.f64 27 (.f64 a b)))
✓	0.1b	(fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x))
	0.2b	(.f64 27 (.f64 a b))
✓	5.8b	(.f64 y (.f64 t z))

series114.0ms (1.2%)

Counts

3 → 120

Calls

3 calls:

65.0ms	(+.f64 (fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x)) (.f64 27 (.f64 a b)))
31.0ms	(fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x))
18.0ms	(.f64 y (.f64 t z))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

7.0ms	(.f64 y (.f64 t z))
4.0ms	(+.f64 (fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x)) (.f64 27 (.f64 a b)))
1.0ms	(fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x))

simplify194.0ms (2%)

Algorithm

1×	egg-herbie

Rules

471×	`fma-neg_binary64`
421×	`cancel-sign-sub-inv_binary64`
305×	`*-commutative_binary64`
296×	`fma-def_binary64`
257×	`exp-prod_binary64`

Counts

167 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	2975
1	231	2671
2	762	2657
3	2374	2657
4	4296	2657
5	5013	2657

prune169.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Error

Counts

104 → 7

Alt Table

Status	Error	Program
	37.1b	(/.f64 (fma.f64 -729 (.f64 (.f64 a b) (.f64 a b)) (.f64 (+.f64 x (fma.f64 y (.f64 (.f64 t z) -9) x)) (+.f64 x (fma.f64 y (.f64 (.f64 t z) -9) x)))) (fma.f64 (.f64 a b) -27 (+.f64 x (fma.f64 y (.f64 (*.f64 t z) -9) x))))
	3.7b	(+.f64 (fma.f64 (.f64 (.f64 y t) z) -9 (+.f64 x x)) (.f64 27 (.f64 a b)))
✓	4.1b	(+.f64 (fma.f64 (.f64 y (.f64 t z)) -9 (+.f64 x x)) (.f64 27 (.f64 a b)))
	4.2b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 9 (.f64 y z)) t)) (.f64 (.f64 a 27) b))
✓	3.9b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 y 9) z) t)) (.f64 a (.f64 27 b)))
	13.3b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 (.f64 (.f64 y 9) z) (sqrt.f64 t)) (sqrt.f64 t))) (.f64 (*.f64 a 27) b))
	4.4b	(+.f64 (-.f64 (.f64 x 2) (.f64 (.f64 y 9) (.f64 z t))) (.f64 (.f64 a 27) b))

Compiler

Compiled 2392 to 1025 computations (57.1% saved)

regimes1.9s (19.9%)

Accuracy

Total 0.6b remaining (96.8%)

Threshold costs 0.6b (96.8%)

Counts

50 → 2

Compiler

Compiled 19415 to 14038 computations (27.7% saved)

bsearch28.0ms (0.3%)

Steps

Iters	Range		Point
6	-2.171906031616654e-16	-4.559594630918193e-21	-7.30141131545903e-21

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	52
1	45	52
2	61	52
3	77	52
4	87	52
5	92	52
6	93	52
7	92	52

end78.0ms (0.8%)

Remove: (sort a b)
Compiler: Compiled 294 to 203 computations (31% saved)

sample1.8s (18.8%)

Algorithm

1×

intervals

Results

519.0ms	8000×	body	128	valid
211.0ms	3108×	body	128	invalid

Compiler

Compiled 264 to 180 computations (31.8% saved)

Details

analyze3.4s (35.5%)

sample364.0ms (3.8%)

simplify80.0ms (0.8%)

prune8.0ms (0.1%)

localize23.0ms (0.2%)

series72.0ms (0.7%)

rewrite42.0ms (0.4%)

simplify172.0ms (1.8%)

prune308.0ms (3.2%)

localize23.0ms (0.2%)

series9.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify91.0ms (0.9%)

prune271.0ms (2.8%)

localize28.0ms (0.3%)

series14.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify95.0ms (1%)

prune253.0ms (2.6%)

localize22.0ms (0.2%)

series114.0ms (1.2%)

rewrite15.0ms (0.2%)

simplify194.0ms (2%)

prune169.0ms (1.7%)

regimes1.9s (19.9%)

bsearch28.0ms (0.3%)

simplify4.0ms (0%)

end78.0ms (0.8%)

sample1.8s (18.8%)

Profiling