Details

analyze1.9s (19.4%)

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
1.1%	98.6%	0.3%	12
1.9%	97.8%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.4s (14.1%)

Results

1.3s	8254×	body	128	valid
1.0ms	1×	body	2048	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 83 to 50 computations (39.8% saved)

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

765×	`sub-neg_binary64`
731×	`fma-neg_binary64`
652×	`neg-mul-1_binary64`
505×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	37	29
2	85	29
3	194	27
4	486	27
5	1003	27
6	1920	27
7	3406	27
8	4078	27
9	4431	27
10	4919	27
11	5085	27

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

24.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.3b	(/.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

Compiler

Compiled 100 to 55 computations (45% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 t y) a)
✓	1.6b	(+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a))
✓	3.1b	(-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b))
✓	22.6b	(/.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

series199.0ms (2%)

Counts

4 → 240

Calls

4 calls:

145.0ms	(/.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))
28.0ms	(-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b))
19.0ms	(+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a))
6.0ms	(*.f64 (+.f64 t y) a)

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
13×	`distribute-lft-out_binary64`

Counts

4 → 105

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))
7.0ms	(-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b))
5.0ms	(+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a))
4.0ms	(*.f64 (+.f64 t y) a)

simplify184.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-/l*_binary64`
298×	`+-commutative_binary64`
292×	`fma-def_binary64`
269×	`distribute-rgt-in_binary64`
247×	`distribute-lft-in_binary64`

Counts

345 → 284

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	774	12872
1	2277	12422
2	5030	12422

prune268.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	273	11	284
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	274	11	285

Error

3.9b

Counts

285 → 11

Alt Table

Status	Error	Program
	28.7b	(-.f64 (+.f64 a z) b)
	24.3b	(.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (.f64 y b)) (/.f64 1 (+.f64 (+.f64 x t) y)))
	42.6b	(*.f64 (/.f64 a (+.f64 y (+.f64 t x))) (+.f64 y t))
	44.1b	z
	42.9b	a
	43.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 x t) y))) (/.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (.f64 y b)) (sqrt.f64 (+.f64 (+.f64 x t) y))))
	40.7b	(/.f64 (fma.f64 a t (*.f64 y (-.f64 a b))) (+.f64 y (+.f64 t x)))
	24.4b	(/.f64 1 (/.f64 (+.f64 (+.f64 x t) y) (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b))))
	24.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 y (+.f64 t x))) (cbrt.f64 (+.f64 y (+.f64 t x))))) (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (*.f64 y (-.f64 a b)))) (cbrt.f64 (+.f64 y (+.f64 t x)))))
	25.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (.f64 y (-.f64 a b)))) (+.f64 y (+.f64 t x)))) (cbrt.f64 (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (.f64 y (-.f64 a b)))) (+.f64 y (+.f64 t x))))) (cbrt.f64 (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (*.f64 y (-.f64 a b)))) (+.f64 y (+.f64 t x)))))
▶	24.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 z x) (+.f64 y (+.f64 t x))) (/.f64 (.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))

Compiler

Compiled 13538 to 3558 computations (73.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.3b	(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))
✓	7.7b	(/.f64 (*.f64 y z) (+.f64 y (+.f64 t x)))
✓	9.3b	(/.f64 (*.f64 a y) (+.f64 y (+.f64 t x)))
✓	9.5b	(/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))

series218.0ms (2.2%)

Counts

4 → 144

Calls

4 calls:

59.0ms	(/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))
53.0ms	(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))
53.0ms	(/.f64 (*.f64 a y) (+.f64 y (+.f64 t x)))
52.0ms	(/.f64 (*.f64 y z) (+.f64 y (+.f64 t x)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`distribute-lft-out_binary64`
24×	`add-cbrt-cube_binary64`
24×	`add-exp-log_binary64`
20×	`associate-/r*_binary64`

Counts

4 → 116

Calls

4 calls:

6.0ms	(/.f64 (*.f64 a y) (+.f64 y (+.f64 t x)))
6.0ms	(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))
6.0ms	(/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))
6.0ms	(/.f64 (*.f64 y z) (+.f64 y (+.f64 t x)))

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

928×	`associate-/l*_binary64`
273×	`associate-/r/_binary64`
230×	`sub-neg_binary64`
219×	`associate-/l/_binary64`
188×	`+-commutative_binary64`

Counts

260 → 337

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	737	10472
1	2276	10144
2	5042	10144

prune318.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	337	11	348

Error

2.0b

Counts

348 → 11

Alt Table

Status	Error	Program
	40.7b	(/.f64 (fma.f64 a t (*.f64 y (-.f64 a b))) (+.f64 y (+.f64 t x)))
	21.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (.f64 z (/.f64 x (+.f64 y (+.f64 t x)))) (/.f64 (.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
	42.6b	(*.f64 (/.f64 a (+.f64 y (+.f64 t x))) (+.f64 y t))
	44.1b	z
	42.9b	a
	43.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 x t) y))) (/.f64 (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (.f64 y b)) (sqrt.f64 (+.f64 (+.f64 x t) y))))
	28.7b	(-.f64 (+.f64 a z) b)
	24.4b	(/.f64 1 (/.f64 (+.f64 (+.f64 x t) y) (-.f64 (+.f64 (.f64 (+.f64 x y) z) (.f64 (+.f64 t y) a)) (*.f64 y b))))
▶	21.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 z x) (+.f64 y (+.f64 t x))) (/.f64 (.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b)))
	24.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 y (+.f64 t x))) (cbrt.f64 (+.f64 y (+.f64 t x))))) (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (*.f64 y (-.f64 a b)))) (cbrt.f64 (+.f64 y (+.f64 t x)))))
	25.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (.f64 y (-.f64 a b)))) (+.f64 y (+.f64 t x)))) (cbrt.f64 (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (.f64 y (-.f64 a b)))) (+.f64 y (+.f64 t x))))) (cbrt.f64 (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (*.f64 y (-.f64 a b)))) (+.f64 y (+.f64 t x)))))

Compiler

Compiled 24109 to 4824 computations (80% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.3b	(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))
	7.7b	(/.f64 (*.f64 y z) (+.f64 y (+.f64 t x)))
✓	8.4b	(/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b))
	9.3b	(/.f64 (*.f64 a y) (+.f64 y (+.f64 t x)))

series52.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

52.0ms

(/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`*-un-lft-identity_binary64`
117×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
57×	`add-cube-cbrt_binary64`
36×	`distribute-lft-out_binary64`

Counts

1 → 96

Calls

1 calls:

9.0ms

(/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b))

simplify123.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

337×	`cancel-sign-sub-inv_binary64`
290×	`times-frac_binary64`
287×	`fma-neg_binary64`
259×	`associate-/l*_binary64`
183×	`sub-neg_binary64`

Counts

144 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	4674
1	853	4562
2	3518	4541
3	4933	4541
4	5000	4541

prune413.0ms (4.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	412	3	415
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	417	9	426

Error

0.9b

Counts

426 → 9

Alt Table

Status	Error	Program
▶	17.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 t x)) y)) (+.f64 (/.f64 (.f64 z x) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b)))
	40.7b	(/.f64 (fma.f64 a t (*.f64 y (-.f64 a b))) (+.f64 y (+.f64 t x)))
	21.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (.f64 z (/.f64 x (+.f64 y (+.f64 t x)))) (/.f64 (.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
	42.6b	(*.f64 (/.f64 a (+.f64 y (+.f64 t x))) (+.f64 y t))
	44.1b	z
	28.7b	(-.f64 (+.f64 a z) b)
	20.1b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 z x) (+.f64 y (+.f64 t x))) (/.f64 (.f64 a t) (+.f64 y (+.f64 t x)))))) (*.f64 (/.f64 y (+.f64 y (+.f64 t x))) b))
	24.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 y (+.f64 t x))) (cbrt.f64 (+.f64 y (+.f64 t x))))) (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (*.f64 y (-.f64 a b)))) (cbrt.f64 (+.f64 y (+.f64 t x)))))
	18.1b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 z (/.f64 (+.f64 y (+.f64 t x)) x)) (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b)))

Compiler

Compiled 28851 to 5115 computations (82.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.7b	(/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))
	7.3b	(/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))
	7.7b	(/.f64 (*.f64 y z) (+.f64 y (+.f64 t x)))
	8.4b	(/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b))

series49.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

49.0ms

(/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
6×	`distribute-lft-out_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

6.0ms

(/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

420×	`fma-neg_binary64`
399×	`times-frac_binary64`
346×	`cancel-sign-sub-inv_binary64`
270×	`associate-/l*_binary64`
222×	`neg-mul-1_binary64`

Counts

65 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	2621
1	751	2528
2	3342	2450
3	4590	2450
4	5020	2450

prune446.0ms (4.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	408	2	410
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	410	9	419

Error

0.5b

Counts

419 → 9

Alt Table

Status	Error	Program
	40.7b	(/.f64 (fma.f64 a t (*.f64 y (-.f64 a b))) (+.f64 y (+.f64 t x)))
	21.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (.f64 z (/.f64 x (+.f64 y (+.f64 t x)))) (/.f64 (.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))
	42.6b	(*.f64 (/.f64 a (+.f64 y (+.f64 t x))) (+.f64 y t))
	44.1b	z
	15.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 t x)) y)) (+.f64 (/.f64 (.f64 z x) (+.f64 y (+.f64 t x))) (/.f64 (.f64 a t) (+.f64 y (+.f64 t x)))))) (.f64 (/.f64 y (+.f64 y (+.f64 t x))) b))
	28.7b	(-.f64 (+.f64 a z) b)
	11.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 a (/.f64 (+.f64 y (+.f64 t x)) y)) (+.f64 (/.f64 (.f64 z x) (+.f64 y (+.f64 t x))) (/.f64 a (/.f64 (+.f64 y (+.f64 t x)) t))))) (/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b)))
	24.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 y (+.f64 t x))) (cbrt.f64 (+.f64 y (+.f64 t x))))) (/.f64 (fma.f64 z (+.f64 y x) (fma.f64 a t (*.f64 y (-.f64 a b)))) (cbrt.f64 (+.f64 y (+.f64 t x)))))
	18.1b	(-.f64 (+.f64 (/.f64 (.f64 y z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (.f64 a y) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 z (/.f64 (+.f64 y (+.f64 t x)) x)) (/.f64 (*.f64 a t) (+.f64 y (+.f64 t x)))))) (/.f64 y (/.f64 (+.f64 y (+.f64 t x)) b)))

Compiler

Compiled 28090 to 4912 computations (82.5% saved)

regimes3.8s (37.4%)

Accuracy

Total 7.1b remaining (84.3%)

Threshold costs 0b (0%)

Counts

263 → 3

Compiler

Compiled 75302 to 35258 computations (53.2% saved)

bsearch14.0ms (0.1%)

Compiler: Compiled 27 to 16 computations (40.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
12×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	159
1	68	159
2	88	159
3	98	159
4	103	159
5	103	159

end130.0ms (1.3%)

Compiler: Compiled 543 to 220 computations (59.5% saved)

Details

analyze1.9s (19.4%)

sample1.4s (14.1%)

simplify94.0ms (0.9%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series199.0ms (2%)

rewrite38.0ms (0.4%)

simplify184.0ms (1.8%)

prune268.0ms (2.7%)

localize21.0ms (0.2%)

series218.0ms (2.2%)

rewrite29.0ms (0.3%)

simplify146.0ms (1.5%)

prune318.0ms (3.2%)

localize19.0ms (0.2%)

series52.0ms (0.5%)

rewrite20.0ms (0.2%)

simplify123.0ms (1.2%)

prune413.0ms (4.1%)

localize19.0ms (0.2%)

series49.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify87.0ms (0.9%)

prune446.0ms (4.4%)

regimes3.8s (37.4%)

bsearch14.0ms (0.1%)

simplify6.0ms (0.1%)

end130.0ms (1.3%)

Profiling