Details

analyze4.1s (24.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.5%	0.5%	0
0%	99.5%	0.5%	1
0%	99.5%	0.5%	2
0%	99.5%	0.5%	3
0%	99.5%	0.5%	4
0%	99.5%	0.5%	5
0%	99.5%	0.5%	6
0%	99.5%	0.5%	7
0%	99.5%	0.5%	8
0%	99.5%	0.5%	9
0%	99.5%	0.5%	10
0%	99.5%	0.5%	11
0%	99.5%	0.5%	12
0%	99.5%	0.5%	13
0%	99.5%	0.5%	14

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample5.6s (32.7%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results

2.7s	8256×	body	128	valid
2.7s	8412×	body	128	invalid

Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify469.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

6437×	`fma-neg_binary64`
684×	`unsub-neg_binary64`
621×	`distribute-rgt-neg-in_binary64`
515×	`distribute-rgt-in_binary64`
434×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	43
1	77	37
2	255	35
3	773	35
4	1711	35
5	2777	35
6	3474	35
7	3470	35
8	3493	35
9	3516	35
10	3534	35
11	3534	35
12	3526	35
13	3549	35
14	3549	35
15	3549	35
16	3639	35
17	4131	35
18	3675	35
19	3675	35
20	3675	35
21	9384	35

prune9.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
▶	3.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Status

Error

Program

6.4b

(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))

▶

3.4b

(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

Compiler

Compiled 218 to 148 computations (32.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x 18) y)
✓	0.2b	(.f64 (.f64 j 27) k)
✓	5.4b	(.f64 (.f64 (*.f64 x 18) y) z)
✓	5.6b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)

series97.0ms (0.6%)

Counts

4 → 132

Calls

4 calls:

47.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
30.0ms	(.f64 (.f64 (*.f64 x 18) y) z)
11.0ms	(.f64 (.f64 j 27) k)
9.0ms	(.f64 (.f64 x 18) y)

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-cbrt-cube_binary64`
37×	`add-exp-log_binary64`
37×	`pow1_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`

Counts

4 → 89

Calls

4 calls:

13.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
10.0ms	(.f64 (.f64 j 27) k)
9.0ms	(.f64 (.f64 (*.f64 x 18) y) z)
7.0ms	(.f64 (.f64 x 18) y)

simplify205.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

708×	`unswap-sqr_binary64`
612×	`sqr-pow_binary64`
463×	`associate-l_binary64`
289×	`associate-r_binary64`
215×	`pow-sqr_binary64`

Counts

221 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	150	2582
1	351	2318
2	1407	2318
3	1831	2318
4	2585	2318
5	3963	2318
6	5760	2318

prune361.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	122	7	129

Error

0.0b

Counts

129 → 7

Alt Table

Status	Error	Program
	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
▶	3.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 j (*.f64 27 k)))
	14.7b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) (sqrt.f64 z)) (sqrt.f64 z)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (.f64 j 27) k))
	3.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 x 18) y) (.f64 z t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Compiler

Compiled 5242 to 3065 computations (41.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 j (.f64 27 k))
	0.2b	(.f64 (.f64 x 18) y)
	5.4b	(.f64 (.f64 (*.f64 x 18) y) z)
	5.6b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)

series5.0ms (0%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f64 j (*.f64 27 k))

rewrite5.0ms (0%)

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:

4.0ms

(*.f64 j (*.f64 27 k))

simplify107.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

525×	`associate-/r/_binary64`
451×	`associate-l_binary64`
384×	`associate-/l*_binary64`
372×	`*-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

prune432.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	126	8	134

Error

0.0b

Counts

134 → 8

Alt Table

Status	Error	Program
	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
✓	3.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 j (*.f64 27 k)))
	14.7b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) (sqrt.f64 z)) (sqrt.f64 z)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (.f64 j 27) k))
▶	3.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 x 18) y) (.f64 z t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	47.3b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (sqrt.f64 j) (.f64 (sqrt.f64 j) (.f64 27 k))))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Compiler

Compiled 5291 to 3097 computations (41.5% saved)

localize49.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 t)
✓	0.9b	(.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	4.9b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
	5.4b	(.f64 (.f64 (*.f64 x 18) y) z)

series1.9s (10.9%)

Counts

3 → 108

Calls

3 calls:

1.7s	(.f64 (.f64 (.f64 (.f64 x 18) y) z) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
75.0ms	(.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
60.0ms	(cbrt.f64 t)

rewrite71.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64`
77×	`pow1_binary64`
57×	`cbrt-unprod_binary64`
57×	`prod-exp_binary64`
57×	`pow-prod-down_binary64`

Counts

3 → 93

Calls

3 calls:

30.0ms	(.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
18.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
1.0ms	(cbrt.f64 t)

simplify303.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
627×	`unswap-sqr_binary64`
482×	`associate-l_binary64`
351×	`associate-r_binary64`
308×	`log-prod_binary64`

Counts

201 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	147	3624
1	338	2988
2	1532	2869
3	2412	2867
4	4209	2866
5	4941	2866
6	4949	2866

prune537.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	179	8	187

Error

0.0b

Counts

187 → 8

Alt Table

Status	Error	Program
	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
✓	3.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 j (*.f64 27 k)))
	14.7b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) (sqrt.f64 z)) (sqrt.f64 z)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (.f64 j 27) k))
✓	3.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 x 18) y) (.f64 z t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	47.3b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (sqrt.f64 j) (.f64 (sqrt.f64 j) (.f64 27 k))))
▶	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Compiler

Compiled 8509 to 4399 computations (48.3% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 j 27) k)
✓	0.2b	(.f64 18 (.f64 y (*.f64 z x)))
✓	5.6b	(.f64 (.f64 18 (.f64 y (.f64 z x))) t)
✓	6.9b	(.f64 y (.f64 z x))

series91.0ms (0.5%)

Counts

3 → 48

Calls

3 calls:

53.0ms	(.f64 (.f64 18 (.f64 y (.f64 z x))) t)
22.0ms	(.f64 18 (.f64 y (*.f64 z x)))
16.0ms	(.f64 y (.f64 z x))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
31×	`pow1_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`

Counts

3 → 69

Calls

3 calls:

14.0ms	(.f64 (.f64 18 (.f64 y (.f64 z x))) t)
9.0ms	(.f64 18 (.f64 y (*.f64 z x)))
8.0ms	(.f64 y (.f64 z x))

simplify173.0ms (1%)

Algorithm

1×	egg-herbie

Rules

632×	`unswap-sqr_binary64`
527×	`*-commutative_binary64`
465×	`sqr-pow_binary64`
240×	`associate-l_binary64`
221×	`associate-r_binary64`

Counts

117 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	98	1685
1	228	1448
2	897	1448
3	1596	1448
4	2251	1448
5	3516	1448
6	5204	1448

prune352.0ms (2.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	105	8	113

Error

0.0b

Counts

113 → 8

Alt Table

Status	Error	Program
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 (.f64 y z) x)) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.4b	(fma.f64 x (fma.f64 18 (.f64 y (.f64 z t)) (.f64 i -4)) (fma.f64 a (.f64 t -4) (fma.f64 -27 (.f64 j k) (.f64 b c))))
✓	3.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 j (*.f64 27 k)))
✓	3.5b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 x 18) y) (.f64 z t)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	47.3b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (sqrt.f64 j) (.f64 (sqrt.f64 j) (.f64 27 k))))
✓	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Compiler

Compiled 4224 to 2251 computations (46.7% saved)

regimes1.0s (5.9%)

Accuracy

Total 1.7b remaining (98.2%)

Threshold costs 0b (0%)

Counts

14 → 3

Compiler

Compiled 10818 to 7626 computations (29.5% saved)

bsearch269.0ms (1.6%)

Steps

Iters	Range		Point
7	2.2711776306426844e-11	8.285429727123158e-10	6.816993419378373e-11
6	-2.4708176279044213e+57	-2.0828193279613255e+53	-1.3998370911959288e+54

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
16×	`+-commutative_binary64`
15×	`sub-neg_binary64`
12×	`distribute-rgt-neg-in_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	95
1	82	95
2	125	95
3	149	95
4	167	95
5	173	95
6	171	95

end777.0ms (4.5%)

Remove

(sort j k)

(sort b c)

Compiler

Compiled 1083 to 722 computations (33.3% saved)

Details

analyze4.1s (24.1%)

sample5.6s (32.7%)

simplify469.0ms (2.7%)

prune9.0ms (0.1%)

localize34.0ms (0.2%)

series97.0ms (0.6%)

rewrite48.0ms (0.3%)

simplify205.0ms (1.2%)

prune361.0ms (2.1%)

localize23.0ms (0.1%)

series5.0ms (0%)

rewrite5.0ms (0%)

simplify107.0ms (0.6%)

prune432.0ms (2.5%)

localize49.0ms (0.3%)

series1.9s (10.9%)

rewrite71.0ms (0.4%)

simplify303.0ms (1.8%)

prune537.0ms (3.1%)

localize42.0ms (0.2%)

series91.0ms (0.5%)

rewrite41.0ms (0.2%)

simplify173.0ms (1%)

prune352.0ms (2.1%)

regimes1.0s (5.9%)

bsearch269.0ms (1.6%)

simplify12.0ms (0.1%)

end777.0ms (4.5%)

Profiling