Details

analyze1.2s (2.3%)

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)

sample5.5s (10.8%)

Results

4.0s	21999×	body	128	invalid
1.5s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify53.0ms (0.1%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.1b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	2.5b	(/.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)

localize15.0ms (0%)

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))
✓	0.9b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.8b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.6s (5%)

Counts

4 → 176

Calls

4 calls:

1.7s	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
621.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
204.0ms	(*.f64 y (log.f64 z))
63.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite35.0ms (0.1%)

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:

10.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
10.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
6.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
3.0ms	(*.f64 y (log.f64 z))

simplify222.0ms (0.4%)

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

prune275.0ms (0.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	242	6	248
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	244	6	250

Error

0.0b

Counts

250 → 6

Alt Table

Status	Error	Program
	16.5b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	17.6b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
	16.6b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	24.3b	(+.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y)) (fma.f64 1/2 (.f64 (.f64 t (.f64 t (.f64 x (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b)))))) (/.f64 (pow.f64 (log.f64 a) 2) y)) (.f64 (.f64 (log.f64 a) t) (.f64 (/.f64 (pow.f64 z y) (*.f64 a (exp.f64 b))) (/.f64 x y)))))
	21.2b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))) (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y)))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))))
▶	2.5b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 7466 to 3198 computations (57.2% saved)

localize22.0ms (0%)

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	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.8b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.8s (5.4%)

Counts

2 → 132

Calls

2 calls:

1.8s	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
959.0ms	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64`
14×	`unpow-prod-up_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

7.0ms	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
5.0ms	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

simplify186.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
362×	`fma-neg_binary64`
218×	`associate-r_binary64`
190×	`associate-l_binary64`
187×	`cancel-sign-sub-inv_binary64`

Counts

196 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	309	6432
1	775	5429
2	2686	5090
3	4508	5076
4	4983	5076
5	4987	5076

prune287.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	260	6	266

Error

Counts

266 → 6

Alt Table

Status	Error	Program
	18.0b	(/.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (/.f64 y x))
▶	16.5b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	17.6b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
	16.6b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	21.2b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))) (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y)))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))))
✓	2.5b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 7798 to 2965 computations (62% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 a (+.f64 t -1))
✓	0.5b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
✓	0.6b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
✓	0.7b	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))

series2.7s (5.3%)

Counts

4 → 192

Calls

4 calls:

1.5s	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
1.0s	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
196.0ms	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
29.0ms	(pow.f64 a (+.f64 t -1))

rewrite1.4s (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

9016×	`times-frac_binary64`
3564×	`*-un-lft-identity_binary64`
3563×	`add-sqr-sqrt_binary64`
3562×	`add-cube-cbrt_binary64`
1938×	`unpow-prod-down_binary64`

Counts

4 → 2797

Calls

4 calls:

94.0ms	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
14.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
4.0ms	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
3.0ms	(pow.f64 a (+.f64 t -1))

simplify1.8s (3.6%)

Algorithm

1×	egg-herbie

Counts

2989 → 2835

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5443	161965

prune4.0s (7.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	2835	0	2835
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	2835	6	2841

Error

Counts

2841 → 6

Alt Table

Status	Error	Program
	18.0b	(/.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (/.f64 y x))
✓	16.5b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	17.6b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
▶	16.6b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	21.2b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))) (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y)))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))))
✓	2.5b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 115737 to 48730 computations (57.9% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(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 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
✓	0.8b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))

series1.3s (2.6%)

Counts

1 → 72

Calls

1 calls:

1.3s	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))

rewrite300.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

1729×	`times-frac_binary64`
745×	`add-sqr-sqrt_binary64`
690×	`*-un-lft-identity_binary64`
690×	`add-cube-cbrt_binary64`
607×	`associate-r_binary64`

Counts

1 → 654

Calls

1 calls:

110.0ms

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

simplify485.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

772×	`associate-/r*_binary64`
610×	`associate-*r/_binary64`
564×	`associate-/l/_binary64`
552×	`*-commutative_binary64`
304×	`associate-/r/_binary64`

Counts

726 → 1157

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1634	22825
1	3690	22522
2	4981	22522

prune2.4s (4.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1515	0	1515
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1515	6	1521

Error

Counts

1521 → 6

Alt Table

Status	Error	Program
	18.0b	(/.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (/.f64 y x))
✓	16.5b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	17.6b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
✓	16.6b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	21.2b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))) (cbrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y)))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))))
✓	2.5b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

Compiler

Compiled 55750 to 23526 computations (57.8% saved)

regimes23.6s (45.9%)

Accuracy

Total 2.0b remaining (97%)

Threshold costs 0b (0%)

Counts

1158 → 1

Compiler

Compiled 551240 to 342358 computations (37.9% saved)

simplify2.0ms (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

end171.0ms (0.3%)

Compiler: Compiled 218 to 143 computations (34.4% saved)

Details

analyze1.2s (2.3%)

sample5.5s (10.8%)

simplify53.0ms (0.1%)

prune4.0ms (0%)

localize15.0ms (0%)

series2.6s (5%)

rewrite35.0ms (0.1%)

simplify222.0ms (0.4%)

prune275.0ms (0.5%)

localize22.0ms (0%)

series2.8s (5.4%)

rewrite17.0ms (0%)

simplify186.0ms (0.4%)

prune287.0ms (0.6%)

localize11.0ms (0%)

series2.7s (5.3%)

rewrite1.4s (2.6%)

simplify1.8s (3.6%)

prune4.0s (7.8%)

localize11.0ms (0%)

series1.3s (2.6%)

rewrite300.0ms (0.6%)

simplify485.0ms (0.9%)

prune2.4s (4.7%)

regimes23.6s (45.9%)

simplify2.0ms (0%)

end171.0ms (0.3%)

Profiling