Details

analyze1.6s (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	96.6%	3.4%	6
0%	96.6%	3.4%	7
0%	95%	5%	8
0%	85.7%	14.3%	9
0%	64.3%	35.7%	10
0%	64.3%	35.7%	11
0.5%	49.2%	50.3%	12
0.7%	49%	50.3%	13
1%	47.6%	51.4%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.4s (24.9%)

Results

3.8s	22479×	body	128	invalid
1.5s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-/l/_binary64`
552×	`associate-/r/_binary64`
488×	`associate-*l/_binary64`
352×	`associate-*r/_binary64`
345×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	37	26
2	78	24
3	186	24
4	517	24
5	1664	24
6	4362	24
7	4750	24
8	5045	24

prune4.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.1b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 132 to 90 computations (31.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 t 1) (log.f64 a))
✓	0.3b	(*.f64 y (log.f64 z))
✓	1.0b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	1.2b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

series2.0s (9.3%)

Counts

4 → 176

Calls

4 calls:

1.2s	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
574.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
199.0ms	(*.f64 y (log.f64 z))
64.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
14×	`exp-sum_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 116

Calls

4 calls:

9.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
8.0ms	(*.f64 y (log.f64 z))
6.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
5.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

simplify231.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary64`
314×	`associate-r_binary64`
302×	`associate-l_binary64`
245×	`cancel-sign-sub-inv_binary64`
170×	`times-frac_binary64`

Counts

292 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	393	7243
1	895	6044
2	3341	5911
3	4549	5911
4	4999	5911
5	4924	5911

prune301.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	241	7	248
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	242	8	250

Error

0.0b

Counts

250 → 8

Alt Table

Status	Error	Program
	20.9b	(/.f64 (*.f64 x (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b))) y)
	18.8b	(.f64 x (/.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) y))
	21.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) (cbrt.f64 y)))
	25.0b	(/.f64 (.f64 x (cbrt.f64 (pow.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) 3))) y)
▶	18.1b	(/.f64 1 (/.f64 y (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x)))
	23.0b	(.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y))
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	28.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) (/.f64 x y))) (sqrt.f64 (.f64 (*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) (/.f64 x y))))

Compiler

Compiled 7422 to 3204 computations (56.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x)
✓	0.1b	(pow.f64 a (+.f64 t -1))
✓	0.1b	(/.f64 1 (/.f64 y (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x)))
✓	0.9b	(/.f64 y (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x))

series4.5s (20.8%)

Counts

4 → 240

Calls

4 calls:

1.6s	(/.f64 y (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x))
1.6s	(.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x)
1.4s	(/.f64 1 (/.f64 y (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x)))
27.0ms	(pow.f64 a (+.f64 t -1))

rewrite55.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`add-exp-log_binary64`
131×	`div-exp_binary64`
125×	`prod-exp_binary64`
47×	`add-cbrt-cube_binary64`
39×	`times-frac_binary64`

Counts

4 → 192

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 y (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x)))
8.0ms	(/.f64 y (.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x))
7.0ms	(.f64 (.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) x)
3.0ms	(pow.f64 a (+.f64 t -1))

simplify253.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

647×	`times-frac_binary64`
545×	`associate-/l*_binary64`
483×	`fma-def_binary64`
432×	`associate-/r*_binary64`
182×	`associate-*l/_binary64`

Counts

432 → 352

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	465	13175
1	1372	11951
2	4792	11939
3	5148	11939

prune320.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	348	4	352
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	354	6	360

Error

Counts

360 → 6

Alt Table

Status	Error	Program
	19.4b	(/.f64 1 (/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))))
	21.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) (cbrt.f64 y)))
	19.9b	(.f64 (exp.f64 (-.f64 (neg.f64 (.f64 y (neg.f64 (log.f64 z)))) b)) (/.f64 (pow.f64 a (-.f64 t 1)) (/.f64 y x)))
▶	17.5b	(/.f64 (.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	22.6b	(/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) (*.f64 y a)))

Compiler

Compiled 10699 to 5119 computations (52.2% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 a (-.f64 t 1))
✓	0.3b	(.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y)))
✓	1.3b	(/.f64 (.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y))) y)

series2.1s (9.8%)

Counts

3 → 136

Calls

3 calls:

1.1s	(/.f64 (.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y))) y)
1.0s	(.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y)))
28.0ms	(pow.f64 a (-.f64 t 1))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-exp-log_binary64`
42×	`prod-exp_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`unpow-prod-up_binary64`
26×	`*-un-lft-identity_binary64`

Counts

3 → 119

Calls

3 calls:

9.0ms	(.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y)))
8.0ms	(/.f64 (.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y))) y)
4.0ms	(pow.f64 a (-.f64 t 1))

simplify197.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
312×	`associate-r_binary64`
261×	`associate-l_binary64`
209×	`unswap-sqr_binary64`
205×	`associate-/l*_binary64`

Counts

255 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	271	4980
1	731	4679
2	2835	4480
3	4668	4434
4	4953	4434
5	4991	4434
6	5007	4434

prune217.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	207	6	213

Error

Counts

213 → 6

Alt Table

Status	Error	Program
▶	19.4b	(/.f64 1 (/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))))
	21.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) (cbrt.f64 y)))
	19.9b	(.f64 (exp.f64 (-.f64 (neg.f64 (.f64 y (neg.f64 (log.f64 z)))) b)) (/.f64 (pow.f64 a (-.f64 t 1)) (/.f64 y x)))
✓	17.5b	(/.f64 (.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	22.6b	(/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) (*.f64 y a)))

Compiler

Compiled 5080 to 2451 computations (51.8% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))
✓	0.0b	(*.f64 (exp.f64 b) a)
✓	0.2b	(/.f64 1 (/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))))
✓	1.4b	(/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a)))

series1.8s (8.3%)

Counts

4 → 184

Calls

4 calls:

618.0ms	(/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a)))
613.0ms	(/.f64 1 (/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))))
583.0ms	(/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))
5.0ms	(*.f64 (exp.f64 b) a)

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-exp-log_binary64`
152×	`times-frac_binary64`
96×	`div-exp_binary64`
75×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`

Counts

4 → 231

Calls

4 calls:

9.0ms	(/.f64 1 (/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))))
7.0ms	(/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a)))
7.0ms	(/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))
3.0ms	(*.f64 (exp.f64 b) a)

simplify203.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

592×	`times-frac_binary64`
445×	`associate-/l*_binary64`
345×	`associate-/r*_binary64`
330×	`associate-r_binary64`
296×	`fma-def_binary64`

Counts

415 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	388	10464
1	1038	9326
2	4530	9223
3	5058	9223

prune290.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	365	6	371

Error

Counts

371 → 6

Alt Table

Status	Error	Program
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	18.8b	(.f64 (/.f64 x (.f64 a y)) (exp.f64 (-.f64 (neg.f64 (*.f64 y (neg.f64 (log.f64 z)))) b)))
✓	19.4b	(/.f64 1 (/.f64 y (/.f64 (.f64 x (pow.f64 z y)) (.f64 (exp.f64 b) a))))
	21.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (*.f64 (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b)) (pow.f64 z y)) (cbrt.f64 y)))
	19.9b	(.f64 (exp.f64 (-.f64 (neg.f64 (.f64 y (neg.f64 (log.f64 z)))) b)) (/.f64 (pow.f64 a (-.f64 t 1)) (/.f64 y x)))
✓	17.5b	(/.f64 (.f64 (pow.f64 a (-.f64 t 1)) (.f64 x (pow.f64 z y))) y)

Compiler

Compiled 9191 to 2327 computations (74.7% saved)

regimes1.9s (8.6%)

Accuracy

Total 0.9b remaining (92.4%)

Threshold costs 0.9b (92.4%)

Counts

144 → 3

Compiler

Compiled 36995 to 25697 computations (30.5% saved)

bsearch5.0ms (0%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

22×	`distribute-rgt-neg-in_binary64`
20×	`cancel-sign-sub-inv_binary64`
18×	`distribute-lft-neg-in_binary64`
14×	`*-commutative_binary64`
14×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	100
1	64	96
2	83	96
3	107	96
4	118	96
5	126	96
6	131	96
7	143	96
8	151	96
9	158	96
10	160	96
11	156	96

end112.0ms (0.5%)

Compiler: Compiled 276 to 179 computations (35.1% saved)

Iter	Nodes	Cost
0	40	100
1	64	96
2	83	96
3	107	96
4	118	96
5	126	96
6	131	96
7	143	96
8	151	96
9	158	96
10	160	96
11	156	96

Iter	Nodes	Cost
0	40	100
1	64	96
2	83	96
3	107	96
4	118	96
5	126	96
6	131	96
7	143	96
8	151	96
9	158	96
10	160	96
11	156	96

Details

analyze1.6s (7.4%)

sample5.4s (24.9%)

simplify50.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series2.0s (9.3%)

rewrite34.0ms (0.2%)

simplify231.0ms (1.1%)

prune301.0ms (1.4%)

localize15.0ms (0.1%)

series4.5s (20.8%)

rewrite55.0ms (0.3%)

simplify253.0ms (1.2%)

prune320.0ms (1.5%)

localize9.0ms (0%)

series2.1s (9.8%)

rewrite29.0ms (0.1%)

simplify197.0ms (0.9%)

prune217.0ms (1%)

localize9.0ms (0%)

series1.8s (8.3%)

rewrite52.0ms (0.2%)

simplify203.0ms (0.9%)

prune290.0ms (1.3%)

regimes1.9s (8.6%)

bsearch5.0ms (0%)

simplify8.0ms (0%)

end112.0ms (0.5%)

Profiling

Iter	Nodes	Cost
0	40	100
1	64	96
2	83	96
3	107	96
4	118	96
5	126	96
6	131	96
7	143	96
8	151	96
9	158	96
10	160	96
11	156	96