Details

analyze987.0ms (2.4%)

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
12.5%	87.2%	0.3%	6
12.5%	87.2%	0.3%	7
12.5%	87.2%	0.3%	8
18.7%	81%	0.3%	9
18.7%	56.1%	25.2%	10
18.7%	56.1%	25.2%	11
18.7%	37.4%	43.9%	12
18.7%	37.4%	43.9%	13
18.7%	37.4%	43.9%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample4.4s (10.7%)

Results

2.4s	10104×	body	128	invalid
1.9s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify73.0ms (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

prune7.0ms (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
	21.3b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	1.4b	(/.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)

localize28.0ms (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))
✓	0.8b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.0b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.8s (6.7%)

Counts

4 → 176

Calls

4 calls:

1.3s	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
976.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
392.0ms	(*.f64 y (log.f64 z))
117.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite75.0ms (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:

22.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
20.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
13.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
7.0ms	(*.f64 y (log.f64 z))

simplify400.0ms (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

prune504.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	244	4	248
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	246	4	250

Error

0.0b

Counts

250 → 4

Alt Table

Status	Error	Program
	29.6b	(+.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y)) (.f64 (.f64 (log.f64 a) t) (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y))))
	18.0b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	17.7b	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)
▶	1.4b	(/.f64 (.f64 x (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))) y)

Compiler

Compiled 7250 to 3080 computations (57.5% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 y (log.f64 z))
✓	0.3b	(expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))))
	0.8b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.0b	(/.f64 (.f64 x (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))) y)

series3.4s (8.2%)

Counts

2 → 132

Calls

2 calls:

2.1s

(/.f64 (*.f64 x (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))) y)

1.2s

(expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

8.0ms

(/.f64 (*.f64 x (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))) y)

1.0ms

(expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))

simplify265.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

996×	`times-frac_binary64`
654×	`fma-def_binary64`
180×	`associate-r_binary64`
156×	`associate-l_binary64`
152×	`fma-neg_binary64`

Counts

166 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	5609
1	644	4605
2	2234	4533
3	4886	4533
4	4989	4533

prune480.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	240	4	244

Error

0.0b

Counts

244 → 4

Alt Table

Status	Error	Program
▶	18.0b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
✓	1.4b	(/.f64 (.f64 x (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))) y)
	21.3b	(.f64 (/.f64 x y) (.f64 (/.f64 (pow.f64 z y) a) (/.f64 (pow.f64 a t) (exp.f64 b))))
	18.2b	(/.f64 1 (/.f64 y (.f64 (.f64 (/.f64 (pow.f64 z y) a) (/.f64 (pow.f64 a t) (exp.f64 b))) x)))

Compiler

Compiled 7681 to 2968 computations (61.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 a (+.f64 t -1))
✓	0.5b	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
✓	0.5b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
✓	0.7b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))

series4.3s (10.4%)

Counts

4 → 192

Calls

4 calls:

2.4s	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
1.5s	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
355.0ms	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
65.0ms	(pow.f64 a (+.f64 t -1))

rewrite806.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

2141×	`times-frac_binary64`
946×	`add-sqr-sqrt_binary64`
892×	`*-un-lft-identity_binary64`
890×	`add-cube-cbrt_binary64`
622×	`unpow-prod-down_binary64`

Counts

4 → 985

Calls

4 calls:

213.0ms	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
28.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
8.0ms	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
6.0ms	(pow.f64 a (+.f64 t -1))

simplify2.0s (4.9%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-*r/_binary64`
605×	`*-commutative_binary64`
570×	`associate-/l/_binary64`
282×	`associate-/r/_binary64`
203×	`/-rgt-identity_binary64`

Counts

1177 → 1775

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1956	36831
1	4378	36375
2	4812	36315
3	4997	36315
4	4974	36315

prune5.3s (13%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1774	1	1775
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	1774	5	1779

Error

Counts

1779 → 5

Alt Table

Status	Error	Program
✓	18.0b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
▶	18.1b	(.f64 (.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1)))) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))) y))
✓	1.4b	(/.f64 (.f64 x (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))) y)
	21.3b	(.f64 (/.f64 x y) (.f64 (/.f64 (pow.f64 z y) a) (/.f64 (pow.f64 a t) (exp.f64 b))))
	18.2b	(/.f64 1 (/.f64 y (.f64 (.f64 (/.f64 (pow.f64 z y) a) (/.f64 (pow.f64 a t) (exp.f64 b))) x)))

Compiler

Compiled 63844 to 27004 computations (57.7% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1))))
✓	0.5b	(/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))
✓	0.5b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1)))))
✓	1.0b	(.f64 (.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1)))) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))) y))

series4.8s (11.8%)

Counts

4 → 204

Calls

4 calls:

2.3s	(.f64 (.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1)))) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))) y))
1.7s	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1)))))
433.0ms	(/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))
358.0ms	(*.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1))))

rewrite902.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

2818×	`times-frac_binary64`
1221×	`add-sqr-sqrt_binary64`
1214×	`*-un-lft-identity_binary64`
1214×	`add-cube-cbrt_binary64`
819×	`associate-r_binary64`

Counts

4 → 1265

Calls

4 calls:

210.0ms	(.f64 (.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1)))) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))) y))
18.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1)))))
16.0ms	(*.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1))))
11.0ms	(/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))

simplify2.1s (5.2%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-*r/_binary64`
633×	`associate-/l/_binary64`
589×	`associate-l_binary64`
322×	`associate-/r/_binary64`
222×	`/-rgt-identity_binary64`

Counts

1469 → 2037

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2218	57705
1	5124	57705

prune4.9s (11.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	2037	0	2037
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	2037	5	2042

Error

Counts

2042 → 5

Alt Table

Status	Error	Program
✓	18.0b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
✓	18.1b	(.f64 (.f64 x (sqrt.f64 (pow.f64 a (-.f64 t 1)))) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (sqrt.f64 (pow.f64 a (+.f64 t -1))))) y))
✓	1.4b	(/.f64 (.f64 x (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))))) y)
	21.3b	(.f64 (/.f64 x y) (.f64 (/.f64 (pow.f64 z y) a) (/.f64 (pow.f64 a t) (exp.f64 b))))
	18.2b	(/.f64 1 (/.f64 y (.f64 (.f64 (/.f64 (pow.f64 z y) a) (/.f64 (pow.f64 a t) (exp.f64 b))) x)))

Compiler

Compiled 92279 to 45651 computations (50.5% saved)

regimes2.3s (5.6%)

Accuracy

Total 0.9b remaining (99%)

Threshold costs 0.9b (99%)

Counts

127 → 1

Compiler

Compiled 35845 to 24143 computations (32.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	28	28
2	32	28
3	34	28
4	35	28
5	33	28

end131.0ms (0.3%)

Compiler: Compiled 172 to 119 computations (30.8% saved)

Details

analyze987.0ms (2.4%)

sample4.4s (10.7%)

simplify73.0ms (0.2%)

prune7.0ms (0%)

localize28.0ms (0.1%)

series2.8s (6.7%)

rewrite75.0ms (0.2%)

simplify400.0ms (1%)

prune504.0ms (1.2%)

localize36.0ms (0.1%)

series3.4s (8.2%)

rewrite13.0ms (0%)

simplify265.0ms (0.6%)

prune480.0ms (1.2%)

localize25.0ms (0.1%)

series4.3s (10.4%)

rewrite806.0ms (2%)

simplify2.0s (4.9%)

prune5.3s (13%)

localize34.0ms (0.1%)

series4.8s (11.8%)

rewrite902.0ms (2.2%)

simplify2.1s (5.2%)

prune4.9s (11.9%)

regimes2.3s (5.6%)

simplify5.0ms (0%)

end131.0ms (0.3%)

Profiling