Details

analyze924.0ms (21.4%)

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 (30.8%)

Results

895.0ms	8256×	body	128	valid
250.0ms	2140×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
730×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
138×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	31	11
3	72	11
4	146	11
5	255	11
6	409	11
7	668	11
8	1099	11
9	1352	11
10	1478	11
11	1525	11
12	1531	11
13	1536	11
14	1536	11
15	1451	11

prune3.0ms (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

1.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	1.4b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

Compiler

Compiled 71 to 39 computations (45.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series16.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

15.0ms

(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 (1.5%)

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

prune23.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	26	5	31
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Error

0.0b

Counts

33 → 6

Alt Table

Status	Error	Program
	32.8b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	41.1b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 z t) (-.f64 y x) x) 3))
	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x)) (fma.f64 (-.f64 y x) (/.f64 z t) x)))
▶	7.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	32.8b	(/.f64 (-.f64 (.f64 y z) (.f64 z x)) t)

Compiler

Compiled 556 to 176 computations (68.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	0.0b	(/.f64 (-.f64 y x) t)
✓	7.0b	(*.f64 z (/.f64 (-.f64 y x) t))

series48.0ms (1.1%)

Counts

3 → 124

Calls

3 calls:

20.0ms	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
19.0ms	(*.f64 z (/.f64 (-.f64 y x) t))
9.0ms	(/.f64 (-.f64 y x) t)

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

3 → 94

Calls

3 calls:

8.0ms	(*.f64 z (/.f64 (-.f64 y x) t))
5.0ms	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
4.0ms	(/.f64 (-.f64 y x) t)

simplify98.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

409×	`distribute-rgt-in_binary64`
396×	`distribute-lft-in_binary64`
346×	`associate-*l/_binary64`
330×	`associate-*r/_binary64`
276×	`fma-def_binary64`

Counts

218 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2779
1	425	2436
2	1259	2427
3	4230	2427
4	4978	2427

prune79.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	4	0	4
Picked	0	1	1
Done	0	1	1
Total	136	5	141

Error

Counts

141 → 5

Alt Table

Status	Error	Program
▶	4.9b	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
✓	7.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	4.9b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t)) x)
	7.5b	(+.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (/.f64 (-.f64 y x) t))) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 2260 to 601 computations (73.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
✓	0.0b	(*.f64 z (-.f64 y x))
✓	5.9b	(.f64 (.f64 z (-.f64 y x)) (/.f64 1 t))

series47.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

21.0ms	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
19.0ms	(.f64 (.f64 z (-.f64 y x)) (/.f64 1 t))
6.0ms	(*.f64 z (-.f64 y x))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
27×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`

Counts

3 → 108

Calls

3 calls:

8.0ms	(.f64 (.f64 z (-.f64 y x)) (/.f64 1 t))
7.0ms	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
5.0ms	(*.f64 z (-.f64 y x))

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
526×	`distribute-rgt-in_binary64`
504×	`distribute-lft-in_binary64`
251×	`associate-l_binary64`
243×	`fma-neg_binary64`

Counts

228 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	3018
1	471	2466
2	1625	2403
3	4922	2403
4	4956	2403

prune103.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	164	5	169

Error

Counts

169 → 5

Alt Table

Status	Error	Program
✓	4.9b	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
✓	7.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
▶	4.9b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t)) x)
	7.5b	(+.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (/.f64 (-.f64 y x) t))) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 3171 to 1186 computations (62.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 (-.f64 y x)) t)
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
✓	0.5b	(cbrt.f64 (-.f64 y x))
✓	5.2b	(.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t))

series321.0ms (7.4%)

Counts

4 → 132

Calls

4 calls:

238.0ms	(/.f64 (cbrt.f64 (-.f64 y x)) t)
33.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
28.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t))
22.0ms	(cbrt.f64 (-.f64 y x))

rewrite50.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`
68×	`cbrt-prod_binary64`
48×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64`

Counts

4 → 197

Calls

4 calls:

16.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
4.0ms	(/.f64 (cbrt.f64 (-.f64 y x)) t)
2.0ms	(cbrt.f64 (-.f64 y x))

simplify180.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-r_binary64`
604×	`associate-l_binary64`
601×	`fma-def_binary64`
290×	`fma-neg_binary64`
196×	`associate-/l*_binary64`

Counts

329 → 347

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	468	7669
1	1278	6874
2	4748	6874
3	5302	6874

prune275.0ms (6.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	449	0	449
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	449	5	454

Error

Counts

454 → 5

Alt Table

Status	Error	Program
✓	4.9b	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
✓	7.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	4.9b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t)) x)
	7.5b	(+.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (/.f64 (-.f64 y x) t))) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 15071 to 5417 computations (64.1% saved)

regimes385.0ms (8.9%)

Accuracy

Total 1.8b remaining (98.7%)

Threshold costs 0b (0%)

Counts

63 → 3

Compiler

Compiled 6596 to 3772 computations (42.8% saved)

bsearch39.0ms (0.9%)

Steps

Iters	Range		Point
7	-1.7269616160348796e-261	-5.7553807379003056e-263	-9.888058153974043e-263
4	-1.4852138517364137e+63	-1.2180950005623508e+61	-1.7058464213464965e+61

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-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	23	53
1	30	53
2	34	53
3	36	53
4	37	53
5	36	53

end80.0ms (1.9%)

Compiler: Compiled 166 to 91 computations (45.2% saved)

Details

analyze924.0ms (21.4%)

sample1.3s (30.8%)

simplify68.0ms (1.6%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series16.0ms (0.4%)

rewrite1.0ms (0%)

simplify66.0ms (1.5%)

prune23.0ms (0.5%)

localize6.0ms (0.1%)

series48.0ms (1.1%)

rewrite23.0ms (0.5%)

simplify98.0ms (2.3%)

prune79.0ms (1.8%)

localize7.0ms (0.2%)

series47.0ms (1.1%)

rewrite29.0ms (0.7%)

simplify101.0ms (2.3%)

prune103.0ms (2.4%)

localize10.0ms (0.2%)

series321.0ms (7.4%)

rewrite50.0ms (1.2%)

simplify180.0ms (4.2%)

prune275.0ms (6.4%)

regimes385.0ms (8.9%)

bsearch39.0ms (0.9%)

simplify3.0ms (0.1%)

end80.0ms (1.9%)

Profiling