Details

analyze835.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
28.1%	71.8%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.7%	52.2%	0.1%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample4.3s (42.8%)

Results

2.5s	4018×	body	8192	exit
816.0ms	6788×	body	128	valid
499.0ms	4107×	body	128	invalid
224.0ms	731×	body	512	valid
150.0ms	716×	body	256	valid
8.0ms	21×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

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

14.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	14.6b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	4.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series50.0ms (0.5%)

Counts

3 → 52

Calls

3 calls:

19.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
16.0ms	(/.f64 x (exp.f64 wj))
15.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 100

Calls

3 calls:

17.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
10.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms	(/.f64 x (exp.f64 wj))

simplify108.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-neg_binary64`
444×	`fma-def_binary64`
331×	`distribute-rgt-in_binary64`
292×	`associate--l+_binary64`
278×	`distribute-lft-in_binary64`

Counts

152 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3154
1	583	3016
2	1604	2995
3	4798	2993
4	5298	2993

prune124.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	153	3	156

Error

0.0b

Counts

156 → 3

Alt Table

Status	Error	Program
	15.3b	(.f64 (.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
▶	0.6b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	14.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 3298 to 1431 computations (56.6% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	0.1b	(*.f64 8/3 (pow.f64 wj 3))
✓	6.7b	(.f64 x (.f64 wj wj))

series42.0ms (0.4%)

Counts

3 → 48

Calls

3 calls:

30.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
8.0ms	(.f64 x (.f64 wj wj))
4.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`
13×	`add-exp-log_binary64`

Counts

3 → 86

Calls

3 calls:

5.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
5.0ms	(*.f64 8/3 (pow.f64 wj 3))
4.0ms	(.f64 x (.f64 wj wj))

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
521×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
479×	`fma-neg_binary64`
401×	`cancel-sign-sub-inv_binary64`

Counts

134 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	3193
1	405	2774
2	1425	2483
3	4969	2402
4	5173	2402

prune188.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	145	5	150

Error

0.0b

Counts

150 → 5

Alt Table

Status	Error	Program
	40.2b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))) 3))
✓	14.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	15.3b	(.f64 (.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
✓	0.6b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	33.4b	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))

Compiler

Compiled 5602 to 3085 computations (44.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
✓	0.4b	(*.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
✓	0.5b	(cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
	4.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series1.6s (16.4%)

Counts

3 → 72

Calls

3 calls:

1.4s

(*.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

209.0ms

(cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

21.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

rewrite127.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
33×	`cbrt-prod_binary64`
32×	`frac-times_binary64`

Counts

3 → 136

Calls

3 calls:

55.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

31.0ms

(*.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

14.0ms

(cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

simplify331.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

499×	`*-commutative_binary64`
339×	`fma-def_binary64`
312×	`associate-+r+_binary64`
257×	`associate-/l*_binary64`
251×	`associate-*r/_binary64`

Counts

208 → 260

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1383	31787
1	5146	31787

prune1.1s (10.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	511	1	512
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	512	5	517

Error

0.0b

Counts

517 → 5

Alt Table

Status	Error	Program
	40.2b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))) 3))
✓	14.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	57.1b	(.f64 (.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (exp.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))
✓	0.6b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
▶	33.4b	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))

Compiler

Compiled 70130 to 38589 computations (45% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))
✓	0.2b	(fma.f64 x 8/3 1)
✓	2.9b	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
✓	5.9b	(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))

series49.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

25.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
12.0ms	(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))
10.0ms	(.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))
2.0ms	(fma.f64 x 8/3 1)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

10.0ms	(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))
5.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
4.0ms	(.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))
0.0ms	(fma.f64 x 8/3 1)

simplify136.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

638×	`cancel-sign-sub-inv_binary64`
401×	`exp-prod_binary64`
292×	`fma-neg_binary64`
286×	`associate-+l+_binary64`
276×	`associate-l_binary64`

Counts

170 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	3286
1	444	2750
2	1930	2727
3	4400	2703
4	4999	2703
5	4952	2703

prune126.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	166	5	171

Error

0.0b

Counts

171 → 5

Alt Table

Status	Error	Program
✓	0.6b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	33.4b	(.f64 (.f64 (cbrt.f64 (exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))) (cbrt.f64 (exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))))) (cbrt.f64 (exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))))
	34.6b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (-.f64 (fma.f64 wj (.f64 x (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3))))) (cbrt.f64 (log.f64 (-.f64 (fma.f64 wj (.f64 x (fma.f64 wj 5/2 -2)) (fma.f64 wj wj x)) (.f64 (fma.f64 8/3 x 1) (pow.f64 wj 3))))))) (cbrt.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))))
	57.1b	(.f64 (.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (exp.f64 (cbrt.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))
✓	14.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 5301 to 3286 computations (38% saved)

regimes410.0ms (4.1%)

Accuracy

Total 1.5b remaining (92.3%)

Threshold costs 0b (0%)

Counts

113 → 1

Compiler

Compiled 8433 to 5412 computations (35.8% saved)

simplify3.0ms (0%)

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	15	31
1	20	31
2	25	31
3	27	31
4	28	31
5	28	31

end167.0ms (1.7%)

Compiler: Compiled 288 to 182 computations (36.8% saved)

Details

analyze835.0ms (8.4%)

sample4.3s (42.8%)

simplify81.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series50.0ms (0.5%)

rewrite38.0ms (0.4%)

simplify108.0ms (1.1%)

prune124.0ms (1.2%)

localize14.0ms (0.1%)

series42.0ms (0.4%)

rewrite19.0ms (0.2%)

simplify107.0ms (1.1%)

prune188.0ms (1.9%)

localize13.0ms (0.1%)

series1.6s (16.4%)

rewrite127.0ms (1.3%)

simplify331.0ms (3.3%)

prune1.1s (10.6%)

localize19.0ms (0.2%)

series49.0ms (0.5%)

rewrite23.0ms (0.2%)

simplify136.0ms (1.4%)

prune126.0ms (1.3%)

regimes410.0ms (4.1%)

simplify3.0ms (0%)

end167.0ms (1.7%)

Profiling