Details

analyze2.3s (22.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 28 to 19 computations (32.1% saved)

sample3.1s (31.9%)

Symmetry

(sort x y)

(sort z t)

Results

1.5s	7495×	body	128	invalid
1.5s	8256×	body	128	valid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify230.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1133×	`distribute-rgt-in_binary64`
1066×	`distribute-lft-in_binary64`
969×	`unsub-neg_binary64`
583×	`fma-def_binary64`
461×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	97	24
3	277	24
4	797	24
5	1809	24
6	2532	24
7	2783	24
8	3128	24
9	3409	24
10	3319	24
11	3327	24
12	3331	24
13	3461	24
14	3620	24
15	3621	24
16	3623	24
17	3623	24
18	5071	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

6.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 94 to 57 computations (39.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	8.6b	(.f64 (.f64 c (fma.f64 b c a)) i)

series89.0ms (0.9%)

Counts

4 → 228

Calls

4 calls:

52.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
19.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
10.0ms	(*.f64 c (fma.f64 b c a))
9.0ms	(fma.f64 x y (*.f64 z t))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 73

Calls

4 calls:

4.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
3.0ms	(*.f64 c (fma.f64 b c a))
3.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
563×	`distribute-rgt-in_binary64`
556×	`distribute-lft-in_binary64`
505×	`fma-def_binary64`
242×	`cancel-sign-sub-inv_binary64`

Counts

301 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	4992
1	327	4027
2	1091	3988
3	4531	3988
4	4933	3988

prune165.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	8	161

Error

0.0b

Counts

161 → 8

Alt Table

Status	Error	Program
	5.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (.f64 (fma.f64 c b a) (.f64 (cbrt.f64 i) (cbrt.f64 i)))) (cbrt.f64 i))))
	6.4b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))))
▶	5.3b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
	17.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c c) (*.f64 i b))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	32.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	22.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 c (fma.f64 b c a))) (.f64 c (fma.f64 b c a)))) i)))
	6.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c (.f64 (cbrt.f64 (fma.f64 b c a)) (cbrt.f64 (fma.f64 b c a)))) (cbrt.f64 (fma.f64 b c a))) i)))

Compiler

Compiled 4138 to 1147 computations (72.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
✓	0.0b	(fma.f64 t z (*.f64 y x))
✓	1.0b	(*.f64 i (fma.f64 c b a))
✓	4.5b	(.f64 c (.f64 i (fma.f64 c b a)))

series94.0ms (1%)

Counts

4 → 240

Calls

4 calls:

54.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
19.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
11.0ms	(*.f64 i (fma.f64 c b a))
9.0ms	(fma.f64 t z (*.f64 y x))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`fma-udef_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

4 → 81

Calls

4 calls:

4.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
3.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
3.0ms	(*.f64 i (fma.f64 c b a))
2.0ms	(fma.f64 t z (*.f64 y x))

simplify149.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
606×	`distribute-lft-in_binary64`
552×	`fma-def_binary64`
290×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

321 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	5146
1	339	4265
2	1166	4226
3	4533	4226
4	4990	4226
5	4926	4226

prune178.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	156	7	163

Error

0.0b

Counts

163 → 7

Alt Table

Status	Error	Program
▶	2.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
	19.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
	17.4b	(.f64 2 (-.f64 (fma.f64 y x (.f64 t z)) (.f64 (.f64 c c) (*.f64 i b))))
	5.7b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))))
	6.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	6.4b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 3951 to 1036 computations (73.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 t z (*.f64 y x))
✓	0.0b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))
✓	5.3b	(.f64 (.f64 c i) (fma.f64 c b a))

series76.0ms (0.8%)

Counts

2 → 144

Calls

2 calls:

58.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))
19.0ms	(.f64 (.f64 c i) (fma.f64 c b a))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`fma-udef_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(.f64 (.f64 c i) (fma.f64 c b a))
3.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))

simplify121.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
516×	`fma-def_binary64`
445×	`distribute-rgt-in_binary64`
436×	`distribute-lft-in_binary64`
295×	`*-commutative_binary64`

Counts

189 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	3996
1	308	3155
2	1033	3116
3	3628	3108
4	4843	3108
5	4797	3108

prune101.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	125	7	132

Error

0.0b

Counts

132 → 7

Alt Table

Status	Error	Program
✓	2.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
	19.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
	17.4b	(.f64 2 (-.f64 (fma.f64 y x (.f64 t z)) (.f64 (.f64 c c) (*.f64 i b))))
▶	5.7b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))))
	6.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	6.4b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 3218 to 857 computations (73.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 i) (cbrt.f64 i))
✓	0.6b	(cbrt.f64 i)
✓	1.2b	(*.f64 (cbrt.f64 i) (fma.f64 c b a))
✓	4.5b	(.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))

series332.0ms (3.4%)

Counts

4 → 120

Calls

4 calls:

172.0ms	(*.f64 (cbrt.f64 i) (fma.f64 c b a))
89.0ms	(cbrt.f64 i)
36.0ms	(*.f64 (cbrt.f64 i) (cbrt.f64 i))
34.0ms	(.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64`
29×	`add-sqr-sqrt_binary64`
26×	`add-exp-log_binary64`
23×	`cbrt-prod_binary64`
17×	`*-un-lft-identity_binary64`

Counts

4 → 118

Calls

4 calls:

9.0ms	(.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))
5.0ms	(*.f64 (cbrt.f64 i) (cbrt.f64 i))
3.0ms	(*.f64 (cbrt.f64 i) (fma.f64 c b a))
1.0ms	(cbrt.f64 i)

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

776×	`distribute-rgt-in_binary64`
764×	`distribute-lft-in_binary64`
352×	`associate-l_binary64`
350×	`associate-r_binary64`
261×	`unswap-sqr_binary64`

Counts

238 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2987
1	347	2433
2	1485	2380
3	5076	2380

prune214.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	216	7	223

Error

0.0b

Counts

223 → 7

Alt Table

Status	Error	Program
✓	2.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
	19.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
	17.4b	(.f64 2 (-.f64 (fma.f64 y x (.f64 t z)) (.f64 (.f64 c c) (*.f64 i b))))
✓	5.7b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))))
	6.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	6.4b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))) (cbrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 6440 to 1735 computations (73.1% saved)

regimes2.2s (22.5%)

Accuracy

Total 0.8b remaining (96.4%)

Threshold costs 0.8b (96.4%)

Counts

103 → 3

Compiler

Compiled 43340 to 28072 computations (35.2% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

29×	`*-commutative_binary64`
22×	`+-commutative_binary64`
19×	`sub-neg_binary64`
18×	`distribute-rgt-neg-in_binary64`
16×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	142
1	70	142
2	105	142
3	133	142
4	173	142
5	193	142
6	201	142
7	203	142
8	203	142

end152.0ms (1.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 852 to 363 computations (57.4% saved)

Iter	Nodes	Cost
0	40	142
1	70	142
2	105	142
3	133	142
4	173	142
5	193	142
6	201	142
7	203	142
8	203	142

Iter	Nodes	Cost
0	40	142
1	70	142
2	105	142
3	133	142
4	173	142
5	193	142
6	201	142
7	203	142
8	203	142

Details

analyze2.3s (22.9%)

sample3.1s (31.9%)

simplify230.0ms (2.3%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series89.0ms (0.9%)

rewrite14.0ms (0.1%)

simplify115.0ms (1.2%)

prune165.0ms (1.7%)

localize13.0ms (0.1%)

series94.0ms (1%)

rewrite15.0ms (0.2%)

simplify149.0ms (1.5%)

prune178.0ms (1.8%)

localize12.0ms (0.1%)

series76.0ms (0.8%)

rewrite9.0ms (0.1%)

simplify121.0ms (1.2%)

prune101.0ms (1%)

localize16.0ms (0.2%)

series332.0ms (3.4%)

rewrite25.0ms (0.3%)

simplify79.0ms (0.8%)

prune214.0ms (2.2%)

regimes2.2s (22.5%)

bsearch6.0ms (0.1%)

simplify8.0ms (0.1%)

end152.0ms (1.5%)

Profiling

Iter	Nodes	Cost
0	40	142
1	70	142
2	105	142
3	133	142
4	173	142
5	193	142
6	201	142
7	203	142
8	203	142