Details

analyze48.0ms (0.3%)

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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	17.2%	14.1%	7
68.7%	10.1%	21.2%	8
68.7%	9%	22.3%	9
68.7%	5.3%	26%	10
68.7%	4.6%	26.7%	11
68.7%	2.7%	28.6%	12
68.7%	2.3%	29%	13
68.7%	1.4%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample816.0ms (4.6%)

Results

786.0ms	8256×	body	128	valid
3.0ms	36×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13
2	8	13

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series41.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

36.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

6.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-neg_binary64`
536×	`times-frac_binary64`
493×	`fma-def_binary64`
389×	`associate-/l*_binary64`
245×	`associate-/r*_binary64`

Counts

100 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1981
1	449	1869
2	1403	1853
3	4915	1853
4	5640	1853

prune96.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	2	109

Error

0.2b

Counts

109 → 2

Alt Table

Status	Error	Program
	19.2b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
▶	11.9b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 2255 to 839 computations (62.8% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))

series9.0ms (0%)

Counts

2 → 8

Calls

2 calls:

7.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 56

Calls

2 calls:

4.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
525×	`fma-def_binary64`
498×	`unswap-sqr_binary64`
428×	`associate-+l+_binary64`
349×	`cancel-sign-sub-inv_binary64`

Counts

64 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	733
1	185	669
2	382	663
3	887	653
4	2169	653
5	3922	653
6	5318	653

prune75.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	75	2	77

Error

0.2b

Counts

77 → 2

Alt Table

Status	Error	Program
	19.2b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
▶	12.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))

Status

Error

Program

19.2b

(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

▶

12.3b

(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))

Compiler

Compiled 946 to 689 computations (27.2% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))
	0.0b	(+.f64 1 (exp.f64 b))
	0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))
✓	0.6b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))

series23.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

16.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))
7.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`sqrt-prod_binary64`
130×	`add-sqr-sqrt_binary64`
117×	`*-un-lft-identity_binary64`
106×	`times-frac_binary64`
50×	`add-cube-cbrt_binary64`

Counts

2 → 174

Calls

2 calls:

21.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))
4.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))

simplify188.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
547×	`fma-def_binary64`
522×	`cancel-sign-sub-inv_binary64`
241×	`associate-l_binary64`
237×	`associate-/l/_binary64`

Counts

190 → 198

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	2887
1	290	2705
2	788	2662
3	2304	2577
4	3991	2571
5	4772	2571
6	4971	2571
7	4899	2571

prune447.0ms (2.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	392	1	393
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	393	2	395

Error

0.2b

Counts

395 → 2

Alt Table

Status	Error	Program
	19.2b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
▶	12.7b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))

Status

Error

Program

19.2b

(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

▶

12.7b

(*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))

Compiler

Compiled 8658 to 6561 computations (24.2% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))
✓	0.5b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))
✓	0.6b	(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))
✓	0.6b	(cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))

series796.0ms (4.5%)

Counts

3 → 36

Calls

3 calls:

348.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))

231.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))

217.0ms

(cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))

rewrite99.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`cbrt-prod_binary64`
138×	`sqrt-prod_binary64`
121×	`pow1_binary64`
120×	`add-sqr-sqrt_binary64`
116×	`*-un-lft-identity_binary64`

Counts

3 → 253

Calls

3 calls:

31.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))

24.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))

4.0ms

(cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))

simplify241.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-neg_binary64`
725×	`times-frac_binary64`
475×	`cancel-sign-sub-inv_binary64`
261×	`*-commutative_binary64`
259×	`fma-def_binary64`

Counts

289 → 284

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	211	6226
1	388	5887
2	1113	5574
3	2389	5458
4	4380	5070
5	4795	5046
6	4914	5046

prune2.2s (12.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1093	1	1094
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	1094	2	1096

Error

0.2b

Counts

1096 → 2

Alt Table

Status	Error	Program
	19.2b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
	13.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))))

Status

Error

Program

19.2b

(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

13.0b

(*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))) (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))) (*.f64 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))))))))

Compiler

Compiled 66038 to 51464 computations (22.1% saved)

regimes12.4s (69.5%)

Accuracy

Total 0.4b remaining (63.2%)

Threshold costs 0.4b (63.2%)

Counts

1314 → 1

Compiler

Compiled 366608 to 295306 computations (19.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end137.0ms (0.8%)

Compiler: Compiled 140 to 107 computations (23.6% saved)

Details

analyze48.0ms (0.3%)

sample816.0ms (4.6%)

simplify6.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0%)

series41.0ms (0.2%)

rewrite13.0ms (0.1%)

simplify83.0ms (0.5%)

prune96.0ms (0.5%)

localize6.0ms (0%)

series9.0ms (0%)

rewrite8.0ms (0%)

simplify76.0ms (0.4%)

prune75.0ms (0.4%)

localize5.0ms (0%)

series23.0ms (0.1%)

rewrite47.0ms (0.3%)

simplify188.0ms (1.1%)

prune447.0ms (2.5%)

localize9.0ms (0%)

series796.0ms (4.5%)

rewrite99.0ms (0.6%)

simplify241.0ms (1.4%)

prune2.2s (12.1%)

regimes12.4s (69.5%)

simplify2.0ms (0%)

end137.0ms (0.8%)

Profiling