Details

analyze1.1s (13%)

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
22.8%	77%	0.2%	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)

sample1.3s (15.4%)

Results

920.0ms	8256×	body	128	valid
234.0ms	2043×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	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
▶	1.3b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	6.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series17.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

17.0ms

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

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune19.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	29	4	33

Error

0.0b

Counts

33 → 4

Alt Table

Status	Error	Program
	2.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
▶	1.3b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
	35.6b	(/.f64 (-.f64 (.f64 y z) (.f64 z x)) t)
	36.2b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 498 to 147 computations (70.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
✓	6.3b	(*.f64 (-.f64 y x) (/.f64 z t))

series39.0ms (0.5%)

Counts

2 → 96

Calls

2 calls:

20.0ms	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
19.0ms	(*.f64 (-.f64 y x) (/.f64 z t))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
10×	`times-frac_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

7.0ms	(*.f64 (-.f64 y x) (/.f64 z t))
6.0ms	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

417×	`associate-l_binary64`
395×	`distribute-rgt-in_binary64`
376×	`distribute-lft-in_binary64`
352×	`associate-r_binary64`
351×	`fma-neg_binary64`

Counts

150 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2201
1	369	1746
2	1183	1737
3	4199	1737
4	4679	1737
5	5004	1737

prune52.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

Counts

102 → 7

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
	25.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (sqrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))) x)
	35.6b	(/.f64 (-.f64 (.f64 y z) (.f64 z x)) t)
▶	1.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t)))) (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))) x)
	36.2b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	6.7b	(+.f64 (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)) x)
	34.0b	(+.f64 (.f64 (.f64 (-.f64 y x) (sqrt.f64 z)) (/.f64 (sqrt.f64 z) t)) x)

Compiler

Compiled 1763 to 508 computations (71.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t)))) (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))))
✓	5.6b	(cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))
	6.3b	(*.f64 (-.f64 y x) (/.f64 z t))

series1.9s (22.9%)

Counts

3 → 144

Calls

3 calls:

1.2s

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

646.0ms

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

61.0ms

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

rewrite128.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

605×	`cbrt-div_binary64`
592×	`frac-times_binary64`
312×	`associate-*l/_binary64`
242×	`flip--_binary64`
242×	`flip3--_binary64`

Counts

3 → 334

Calls

3 calls:

14.0ms

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

6.0ms

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

4.0ms

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

simplify336.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-l_binary64`
435×	`*-commutative_binary64`
409×	`associate-r_binary64`
224×	`times-frac_binary64`
185×	`fma-def_binary64`

Counts

478 → 588

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	866	23451
1	1767	22977
2	5003	22977

prune630.0ms (7.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	953	1	954
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	954	7	961

Error

Counts

961 → 7

Alt Table

Status	Error	Program
	35.6b	(/.f64 (-.f64 (.f64 y z) (.f64 z x)) t)
▶	1.8b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3) x)
✓	1.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t)))) (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))) x)
✓	1.3b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
	36.2b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)
	6.7b	(+.f64 (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)) x)
	34.0b	(+.f64 (.f64 (.f64 (-.f64 y x) (sqrt.f64 z)) (/.f64 (sqrt.f64 z) t)) x)

Compiler

Compiled 43754 to 11228 computations (74.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3) x)
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3)
	5.6b	(cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))
	6.3b	(*.f64 (-.f64 y x) (/.f64 z t))

series2.0s (23.8%)

Counts

2 → 96

Calls

2 calls:

1.9s	(pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3)
49.0ms	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3) x)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`fma-def_binary64`
10×	`*-un-lft-identity_binary64`
8×	`cube-prod_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`unpow-prod-down_binary64`

Counts

2 → 61

Calls

2 calls:

7.0ms	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3) x)
3.0ms	(pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3)

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

438×	`fma-def_binary64`
425×	`unswap-sqr_binary64`
374×	`times-frac_binary64`
347×	`log-prod_binary64`
275×	`fma-neg_binary64`

Counts

157 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2936
1	589	2425
2	1988	2331
3	4618	2331
4	5094	2331

prune185.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	273	7	280

Error

Counts

280 → 7

Alt Table

Status	Error	Program
	35.6b	(/.f64 (-.f64 (.f64 y z) (.f64 z x)) t)
✓	1.8b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t))) 3) x)
✓	1.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (cbrt.f64 (.f64 (-.f64 y x) (/.f64 z t)))) (cbrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))) x)
✓	1.3b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
	8.2b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
	6.7b	(+.f64 (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)) x)
	34.0b	(+.f64 (.f64 (.f64 (-.f64 y x) (sqrt.f64 z)) (/.f64 (sqrt.f64 z) t)) x)

Compiler

Compiled 6424 to 2827 computations (56% saved)

regimes188.0ms (2.3%)

Accuracy

Total 2.0b remaining (99.3%)

Threshold costs 0b (0%)

Counts

42 → 1

Compiler

Compiled 4036 to 2113 computations (47.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	18	13
3	20	13
4	21	13
5	21	13

end84.0ms (1%)

Compiler: Compiled 144 to 81 computations (43.8% saved)

Details

analyze1.1s (13%)

sample1.3s (15.4%)

simplify74.0ms (0.9%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series17.0ms (0.2%)

rewrite1.0ms (0%)

simplify66.0ms (0.8%)

prune19.0ms (0.2%)

localize6.0ms (0.1%)

series39.0ms (0.5%)

rewrite15.0ms (0.2%)

simplify92.0ms (1.1%)

prune52.0ms (0.6%)

localize9.0ms (0.1%)

series1.9s (22.9%)

rewrite128.0ms (1.5%)

simplify336.0ms (4.1%)

prune630.0ms (7.6%)

localize9.0ms (0.1%)

series2.0s (23.8%)

rewrite12.0ms (0.1%)

simplify97.0ms (1.2%)

prune185.0ms (2.2%)

regimes188.0ms (2.3%)

simplify2.0ms (0%)

end84.0ms (1%)

Profiling