Details

analyze984.0ms (13.2%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
24%	75.2%	0.8%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.6s (20.8%)

Results

1.1s	8256×	body	128	valid
231.0ms	2099×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	11

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	6.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	6.7b	(/.f64 (*.f64 y (-.f64 z x)) t)

series41.0ms (0.5%)

Counts

2 → 80

Calls

2 calls:

22.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
19.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
3.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Rules

440×	`associate-/l*_binary64`
432×	`distribute-rgt-in_binary64`
413×	`distribute-lft-in_binary64`
377×	`associate-*l/_binary64`
356×	`times-frac_binary64`

Counts

122 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1685
1	307	1432
2	989	1336
3	4641	1336
4	4987	1336

prune66.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Error

Counts

83 → 5

Alt Table

Status	Error	Program
	6.1b	(+.f64 (/.f64 (*.f64 y (-.f64 z x)) t) x)
	6.8b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
▶	1.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	1.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	30.6b	(+.f64 x (/.f64 (.f64 y (-.f64 (.f64 z z) (.f64 x x))) (.f64 t (+.f64 z x))))

Compiler

Compiled 1357 to 388 computations (71.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series17.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

17.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune17.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Error

Counts

29 → 5

Alt Table

Status	Error	Program
	6.1b	(+.f64 (/.f64 (*.f64 y (-.f64 z x)) t) x)
	6.8b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	1.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
▶	1.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	30.6b	(+.f64 x (/.f64 (.f64 y (-.f64 (.f64 z z) (.f64 x x))) (.f64 t (+.f64 z x))))

Compiler

Compiled 431 to 148 computations (65.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
✓	6.8b	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
✓	7.5b	(*.f64 (/.f64 y t) (-.f64 z x))

series2.7s (36.6%)

Counts

4 → 192

Calls

4 calls:

1.3s	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
1.3s	(.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
60.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
19.0ms	(*.f64 (/.f64 y t) (-.f64 z x))

rewrite151.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

605×	`cbrt-div_binary64`
594×	`frac-times_binary64`
284×	`associate-*r/_binary64`
244×	`flip--_binary64`
244×	`flip3--_binary64`

Counts

4 → 400

Calls

4 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
9.0ms	(*.f64 (/.f64 y t) (-.f64 z x))
6.0ms	(.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
4.0ms	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))

simplify461.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-def_binary64`
476×	`*-commutative_binary64`
359×	`associate-l_binary64`
354×	`times-frac_binary64`
263×	`associate-/r*_binary64`

Counts

592 → 650

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	980	24883
1	1977	24485
2	4889	24469
3	5277	24469

prune706.0ms (9.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1004	0	1004
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1004	5	1009

Error

Counts

1009 → 5

Alt Table

Status	Error	Program
▶	6.1b	(+.f64 (/.f64 (*.f64 y (-.f64 z x)) t) x)
	6.8b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	1.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	1.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	30.6b	(+.f64 x (/.f64 (.f64 y (-.f64 (.f64 z z) (.f64 x x))) (.f64 t (+.f64 z x))))

Compiler

Compiled 47067 to 11796 computations (74.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y (-.f64 z x)) t) x)
	6.7b	(/.f64 (*.f64 y (-.f64 z x)) t)

series24.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

24.0ms

(+.f64 (/.f64 (*.f64 y (-.f64 z x)) t) x)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`fma-def_binary64`
5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`times-frac_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 21

Calls

1 calls:

6.0ms

(+.f64 (/.f64 (*.f64 y (-.f64 z x)) t) x)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
607×	`div-sub_binary64`
563×	`associate-*l/_binary64`
379×	`fma-neg_binary64`
361×	`associate-/l*_binary64`

Counts

69 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1089
1	156	840
2	393	724
3	1415	722
4	4438	722
5	6062	722

prune53.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Error

Counts

93 → 5

Alt Table

Status	Error	Program
✓	6.1b	(+.f64 (/.f64 (*.f64 y (-.f64 z x)) t) x)
	6.8b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	1.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	1.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	30.6b	(+.f64 x (/.f64 (.f64 y (-.f64 (.f64 z z) (.f64 x x))) (.f64 t (+.f64 z x))))

Compiler

Compiled 1351 to 346 computations (74.4% saved)

regimes258.0ms (3.5%)

Accuracy

Total 2.1b remaining (98.9%)

Threshold costs 0b (0%)

Counts

52 → 1

Compiler

Compiled 4476 to 2593 computations (42.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end65.0ms (0.9%)

Compiler: Compiled 115 to 60 computations (47.8% saved)

Details

analyze984.0ms (13.2%)

sample1.6s (20.8%)

simplify68.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series41.0ms (0.5%)

rewrite11.0ms (0.2%)

simplify74.0ms (1%)

prune66.0ms (0.9%)

localize6.0ms (0.1%)

series17.0ms (0.2%)

rewrite1.0ms (0%)

simplify69.0ms (0.9%)

prune17.0ms (0.2%)

localize10.0ms (0.1%)

series2.7s (36.6%)

rewrite151.0ms (2%)

simplify461.0ms (6.2%)

prune706.0ms (9.5%)

localize8.0ms (0.1%)

series24.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify65.0ms (0.9%)

prune53.0ms (0.7%)

regimes258.0ms (3.5%)

simplify2.0ms (0%)

end65.0ms (0.9%)

Profiling