Details

analyze1.3s (4.1%)

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)

sample6.2s (19.8%)

Results

4.5s	23063×	body	128	invalid
1.6s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify52.0ms (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

prune5.0ms (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
	23.3b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	1.6b	(/.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)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.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))
✓	0.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.3s (7.4%)

Counts

4 → 176

Calls

4 calls:

1.4s	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
656.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
229.0ms	(*.f64 y (log.f64 z))
65.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite34.0ms (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:

11.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
7.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
6.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
3.0ms	(*.f64 y (log.f64 z))

simplify215.0ms (0.7%)

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

prune256.0ms (0.8%)

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
	18.3b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	27.3b	(.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))) (sqrt.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))))
	18.2b	(/.f64 (.f64 x (.f64 (sqrt.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))) (sqrt.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))) y)
▶	1.7b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	18.2b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	18.9b	(/.f64 (*.f64 x (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b))) y)

Compiler

Compiled 7374 to 3170 computations (57% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (-.f64 t 1) (log.f64 a))
	0.3b	(*.f64 y (log.f64 z))
✓	0.9b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	1.0b	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

series3.0s (9.6%)

Counts

2 → 132

Calls

2 calls:

2.0s	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
1.0s	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

8.0ms	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
6.0ms	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

simplify195.0ms (0.6%)

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

prune267.0ms (0.9%)

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
	18.3b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	27.3b	(.f64 (sqrt.f64 (.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))) (sqrt.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))))
	22.5b	(/.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (/.f64 y x))
✓	1.7b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
▶	18.2b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	18.9b	(/.f64 (*.f64 x (/.f64 (pow.f64 a (+.f64 t -1)) (exp.f64 b))) y)

Compiler

Compiled 7750 to 2943 computations (62% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
✓	0.3b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
✓	0.3b	(/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))))
✓	0.9b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))

series4.0s (12.7%)

Counts

4 → 228

Calls

4 calls:

1.6s	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
1.1s	(/.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))))
194.0ms	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))

rewrite1.4s (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

11075×	`times-frac_binary64`
4410×	`*-un-lft-identity_binary64`
4410×	`add-sqr-sqrt_binary64`
4410×	`add-cube-cbrt_binary64`
2523×	`unpow-prod-down_binary64`

Counts

4 → 3611

Calls

4 calls:

103.0ms	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
33.0ms	(/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))))
16.0ms	(/.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)))

simplify2.7s (8.5%)

Algorithm

1×	egg-herbie

Counts

3839 → 3654

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5690	204461

prune3.8s (12.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	3651	3	3654
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	3656	4	3660

Error

Counts

3660 → 4

Alt Table

Status	Error	Program
	22.5b	(/.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (/.f64 y x))
▶	1.6b	(/.f64 x (/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))))
	18.2b	(/.f64 x (*.f64 (/.f64 y (pow.f64 z y)) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))))
	20.7b	(*.f64 (/.f64 1 (/.f64 1 (/.f64 1 (exp.f64 b)))) (/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 1 (pow.f64 a (+.f64 t -1)))))))

Compiler

Compiled 146932 to 62063 computations (57.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (log.f64 z) y)
✓	0.3b	(/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1))))))
✓	0.8b	(exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))
✓	0.9b	(/.f64 x (/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))))

series3.1s (9.8%)

Counts

4 → 200

Calls

4 calls:

1.4s	(/.f64 x (/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))))
803.0ms	(/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1))))))
642.0ms	(exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))
221.0ms	(*.f64 (log.f64 z) y)

rewrite93.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

279×	`times-frac_binary64`
158×	`add-sqr-sqrt_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
136×	`exp-sum_binary64`

Counts

4 → 279

Calls

4 calls:

12.0ms	(/.f64 x (/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))))
10.0ms	(/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1))))))
6.0ms	(exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))
3.0ms	(*.f64 (log.f64 z) y)

simplify395.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

404×	`associate-/r/_binary64`
282×	`associate-r_binary64`
281×	`*-commutative_binary64`
250×	`fma-neg_binary64`
246×	`associate-/l/_binary64`

Counts

479 → 547

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	636	16870
1	1308	14842
2	4416	14008
3	4978	14008
4	5008	14008

prune500.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	547	0	547
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	547	4	551

Error

Counts

551 → 4

Alt Table

Status	Error	Program
	22.5b	(/.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (/.f64 y x))
✓	1.6b	(/.f64 x (/.f64 y (exp.f64 (-.f64 (.f64 (log.f64 z) y) (-.f64 b (.f64 (log.f64 a) (+.f64 t -1)))))))
	18.2b	(/.f64 x (*.f64 (/.f64 y (pow.f64 z y)) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))))
	20.7b	(*.f64 (/.f64 1 (/.f64 1 (/.f64 1 (exp.f64 b)))) (/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 1 (pow.f64 a (+.f64 t -1)))))))

Compiler

Compiled 20279 to 8977 computations (55.7% saved)

regimes1.4s (4.4%)

Accuracy

Total 1.9b remaining (96.7%)

Threshold costs 0b (0%)

Counts

117 → 1

Compiler

Compiled 31655 to 21631 computations (31.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-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	19	31
1	30	31
2	34	31
3	36	31
4	37	31
5	35	31

end81.0ms (0.3%)

Compiler: Compiled 146 to 105 computations (28.1% saved)

Details

analyze1.3s (4.1%)

sample6.2s (19.8%)

simplify52.0ms (0.2%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series2.3s (7.4%)

rewrite34.0ms (0.1%)

simplify215.0ms (0.7%)

prune256.0ms (0.8%)

localize16.0ms (0%)

series3.0s (9.6%)

rewrite21.0ms (0.1%)

simplify195.0ms (0.6%)

prune267.0ms (0.9%)

localize13.0ms (0%)

series4.0s (12.7%)

rewrite1.4s (4.4%)

simplify2.7s (8.5%)

prune3.8s (12.3%)

localize16.0ms (0.1%)

series3.1s (9.8%)

rewrite93.0ms (0.3%)

simplify395.0ms (1.3%)

prune500.0ms (1.6%)

regimes1.4s (4.4%)

simplify3.0ms (0%)

end81.0ms (0.3%)

Profiling