Details

analyze1.7s (18.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.7s (18.7%)

Symmetry

(sort x y)

(sort z t)

Results

1.1s	8256×	body	128	valid
471.0ms	3302×	body	128	invalid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify210.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

2966×	`fma-def_binary64`
757×	`fma-neg_binary64`
541×	`cancel-sign-sub-inv_binary64`
473×	`associate-/l/_binary64`
472×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	31	17
2	103	17
3	318	17
4	794	17
5	1526	17
6	2054	17
7	2281	17
8	2975	17
9	3540	17
10	3954	17
11	4158	17
12	4097	17
13	4108	17
14	4118	17
15	4462	17
16	4531	17
17	4536	17
18	4536	17
19	6474	17

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

7.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.3b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
▶	7.2b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

Compiler

Compiled 100 to 69 computations (31% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
✓	0.2b	(.f64 (.f64 z 9) t)
✓	6.7b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

series61.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

44.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
13.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
5.0ms	(.f64 (.f64 z 9) t)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

7.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
4.0ms	(.f64 (.f64 z 9) t)
3.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

470×	`fma-def_binary64`
445×	`*-commutative_binary64`
325×	`div-sub_binary64`
307×	`associate-/l*_binary64`
287×	`fma-neg_binary64`

Counts

194 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	2790
1	396	2561
2	1506	2551
3	4128	2551
4	5247	2551

prune139.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	12	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Error

6.8b

Counts

117 → 13

Alt Table

Status	Error	Program
	7.3b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
▶	7.1b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	36.9b	(exp.f64 (log.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
	33.5b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	35.1b	(.f64 (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
	32.0b	(.f64 1/2 (/.f64 (.f64 y x) a))
	7.3b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
	35.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2)) 3))
	8.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2)))
	46.3b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
	33.4b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
	8.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
	7.2b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))

Compiler

Compiled 2911 to 1693 computations (41.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
✓	0.2b	(.f64 z (.f64 9 t))
✓	6.7b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))

series62.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

44.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
13.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
6.0ms	(.f64 z (.f64 9 t))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
4.0ms	(.f64 z (.f64 9 t))
4.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

423×	`fma-def_binary64`
421×	`*-commutative_binary64`
320×	`div-sub_binary64`
286×	`associate-/l*_binary64`
251×	`fma-neg_binary64`

Counts

194 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2786
1	388	2556
2	1391	2549
3	3885	2549
4	4952	2549

prune115.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	114	14	128

Error

6.8b

Counts

128 → 14

Alt Table

Status	Error	Program
	7.3b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	37.3b	(/.f64 (/.f64 (fma.f64 y (.f64 y (.f64 x x)) (.f64 (.f64 (.f64 t z) (.f64 t z)) -81)) (fma.f64 z (.f64 t 9) (.f64 y x))) (*.f64 a 2))
	7.6b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (.f64 9 t)))) (.f64 a 2))
	36.9b	(exp.f64 (log.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
	46.3b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
	7.2b	(.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (/.f64 1/2 a))
	33.5b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	35.1b	(.f64 (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
	32.0b	(.f64 1/2 (/.f64 (.f64 y x) a))
	35.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2)) 3))
	8.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2)))
	33.4b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
	8.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
▶	7.2b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))

Compiler

Compiled 3006 to 1742 computations (42% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))
✓	0.3b	(.f64 9/2 (/.f64 (.f64 t z) a))
✓	4.6b	(/.f64 (*.f64 t z) a)
✓	6.3b	(/.f64 (*.f64 y x) a)

series92.0ms (1%)

Counts

4 → 24

Calls

4 calls:

44.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))
17.0ms	(.f64 9/2 (/.f64 (.f64 t z) a))
15.0ms	(/.f64 (*.f64 y x) a)
15.0ms	(/.f64 (*.f64 t z) a)

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 93

Calls

4 calls:

6.0ms	(/.f64 (*.f64 y x) a)
6.0ms	(.f64 9/2 (/.f64 (.f64 t z) a))
5.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (.f64 t z) a)))
4.0ms	(/.f64 (*.f64 t z) a)

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
581×	`fma-def_binary64`
359×	`*-commutative_binary64`
335×	`associate-/l/_binary64`
254×	`associate-/r*_binary64`

Counts

117 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1744
1	423	1541
2	1523	1530
3	4162	1530
4	4941	1530

prune151.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	125	9	134
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	137	11	148

Error

0.8b

Counts

148 → 11

Alt Table

Status	Error	Program
	7.2b	(.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (/.f64 1/2 a))
	7.5b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 t z) a)) (cbrt.f64 (/.f64 (.f64 t z) a))) (cbrt.f64 (/.f64 (.f64 t z) a)))))
	9.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
▶	5.4b	(-.f64 (.f64 1/2 (/.f64 (.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))) (.f64 9/2 (/.f64 (*.f64 t z) a)))
	7.3b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	7.1b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (/.f64 (.f64 9/2 (.f64 t z)) a))
	9.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 (.f64 t 9/2) (/.f64 z a)))
	7.4b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 (sqrt.f64 9/2) (.f64 (sqrt.f64 9/2) (/.f64 (*.f64 t z) a))))
	7.5b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (/.f64 (.f64 t z) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))))
	7.2b	(-.f64 (.f64 1/2 (/.f64 y (/.f64 a x))) (.f64 9/2 (/.f64 (*.f64 t z) a)))
	7.2b	(-.f64 (.f64 1/2 (.f64 y (/.f64 x a))) (.f64 9/2 (/.f64 (.f64 t z) a)))

Compiler

Compiled 3304 to 1446 computations (56.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 a)
✓	1.2b	(/.f64 (.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))
✓	1.4b	(.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))))
	4.6b	(/.f64 (*.f64 t z) a)

series1.2s (13.6%)

Counts

3 → 84

Calls

3 calls:

1.1s	(.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))))
45.0ms	(/.f64 (.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))
34.0ms	(cbrt.f64 a)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

7.0ms	(/.f64 (.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))
7.0ms	(.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))))
1.0ms	(cbrt.f64 a)

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/r*_binary64`
583×	`associate-/l/_binary64`
402×	`associate-/r/_binary64`
288×	`*-commutative_binary64`
261×	`log-div_binary64`

Counts

161 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	2447
1	288	1740
2	1257	1735
3	3968	1727
4	4769	1727
5	4973	1727
6	4982	1727

prune200.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	190	10	200

Error

0.0b

Counts

200 → 10

Alt Table

Status	Error	Program
	4.1b	(-.f64 (.f64 1/2 (/.f64 (.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))) (.f64 9/2 (/.f64 (.f64 z (/.f64 t (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))))
	9.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 (.f64 t 9/2) (/.f64 z a)))
	5.6b	(-.f64 (.f64 1/2 (/.f64 x (/.f64 a y))) (.f64 9/2 (/.f64 (*.f64 t z) a)))
	7.2b	(.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (/.f64 1/2 a))
	7.5b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 t z) a)) (cbrt.f64 (/.f64 (.f64 t z) a))) (cbrt.f64 (/.f64 (.f64 t z) a)))))
	7.3b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	7.1b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (/.f64 (.f64 9/2 (.f64 t z)) a))
	6.5b	(-.f64 (.f64 1/2 (/.f64 (.f64 x (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))) (.f64 9/2 (/.f64 t (/.f64 a z))))
	7.5b	(-.f64 (.f64 1/2 (/.f64 (.f64 y x) a)) (.f64 9/2 (/.f64 (/.f64 (.f64 t z) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))))
	7.2b	(-.f64 (.f64 1/2 (/.f64 y (/.f64 a x))) (.f64 9/2 (/.f64 (*.f64 t z) a)))

Compiler

Compiled 5252 to 1907 computations (63.7% saved)

regimes2.4s (26.3%)

Accuracy

Total 3.1b remaining (95.6%)

Threshold costs 0b (0%)

Counts

114 → 3

Compiler

Compiled 37212 to 25071 computations (32.6% saved)

bsearch4.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-neg-in_binary64`
9×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	109
1	70	109
2	96	109
3	115	109
4	133	109
5	139	109
6	140	109
7	138	109

end467.0ms (5.2%)

Compiler: Compiled 708 to 434 computations (38.7% saved)

Details

analyze1.7s (18.6%)

sample1.7s (18.7%)

simplify210.0ms (2.3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series61.0ms (0.7%)

rewrite17.0ms (0.2%)

simplify100.0ms (1.1%)

prune139.0ms (1.6%)

localize9.0ms (0.1%)

series62.0ms (0.7%)

rewrite16.0ms (0.2%)

simplify99.0ms (1.1%)

prune115.0ms (1.3%)

localize11.0ms (0.1%)

series92.0ms (1%)

rewrite26.0ms (0.3%)

simplify76.0ms (0.9%)

prune151.0ms (1.7%)

localize14.0ms (0.2%)

series1.2s (13.6%)

rewrite19.0ms (0.2%)

simplify124.0ms (1.4%)

prune200.0ms (2.2%)

regimes2.4s (26.3%)

bsearch4.0ms (0%)

simplify8.0ms (0.1%)

end467.0ms (5.2%)

Profiling