Details

analyze1.4s (0.9%)

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
6.2%	90.4%	3.4%	6
6.2%	90.4%	3.4%	7
6.2%	88.8%	5%	8
7.8%	77.9%	14.3%	9
7.8%	56.5%	35.7%	10
7.8%	56.5%	35.7%	11
8.1%	41.5%	50.3%	12
8.3%	41.4%	50.3%	13
8.4%	40.2%	51.4%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample161.0ms (0.1%)

Algorithm

1×

intervals

Results

46.0ms	478×	body	128	nan
27.0ms	256×	body	128	valid
27.0ms	262×	body	128	invalid

Compiler

Compiled 55 to 41 computations (25.5% saved)

simplify63.0ms (0%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	22.1b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	2.9b	(/.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%)

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	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	2.2b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.2s (1.5%)

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)
624.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
219.0ms	(*.f64 y (log.f64 z))
66.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite34.0ms (0%)

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)
6.0ms	(*.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))

simplify236.0ms (0.2%)

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

prune280.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	241	7	248
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	243	7	250

Error

0.2b

Counts

250 → 7

Alt Table

Status	Error	Program
▶	2.9b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	17.3b	(/.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x) y)
	42.3b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))) (sqrt.f64 y))
	16.3b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	16.3b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	32.9b	(+.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (/.f64 x y)) (+.f64 (.f64 (.f64 (log.f64 a) t) (.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 1/6 (.f64 (.f64 (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))) (.f64 x (pow.f64 t 3))) (/.f64 (pow.f64 (log.f64 a) 3) y))))))
	26.4b	(.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))))

Compiler

Compiled 7526 to 3234 computations (57% 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))
✓	1.1b	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	2.2b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.9s (2%)

Counts

2 → 132

Calls

2 calls:

1.9s	(/.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))

rewrite42.0ms (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:

20.0ms	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
11.0ms	(pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))

simplify543.0ms (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

prune712.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	260	7	267

Error

0.2b

Counts

267 → 7

Alt Table

Status	Error	Program
✓	2.9b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	17.3b	(/.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x) y)
	42.3b	(/.f64 (*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))) (sqrt.f64 y))
▶	16.3b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	16.3b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	22.1b	(.f64 (/.f64 x y) (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y)))
	26.4b	(.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))))

Compiler

Compiled 7818 to 2983 computations (61.8% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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))))))

series5.5s (3.7%)

Counts

4 → 216

Calls

4 calls:

2.6s	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
1.5s	(/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))))
1.3s	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
29.0ms	(pow.f64 a (+.f64 t -1))

rewrite1.3s (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

11051×	`times-frac_binary64`
4397×	`*-un-lft-identity_binary64`
4396×	`add-sqr-sqrt_binary64`
4395×	`add-cube-cbrt_binary64`
2514×	`unpow-prod-down_binary64`

Counts

4 → 3582

Calls

4 calls:

102.0ms	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
35.0ms	(/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))))
13.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
3.0ms	(pow.f64 a (+.f64 t -1))

simplify2.4s (1.6%)

Algorithm

1×	egg-herbie

Counts

3798 → 3621

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5670	203167

prune5.2s (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	3620	1	3621
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	3621	7	3628

Error

Counts

3628 → 7

Alt Table

Status	Error	Program
	22.1b	(.f64 (/.f64 x y) (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y)))
▶	15.7b	(*.f64 (/.f64 1 (/.f64 1 (/.f64 1 (/.f64 1 (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))) (/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))))
✓	2.9b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	17.3b	(/.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x) y)
✓	16.3b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	16.3b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	26.4b	(.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))))

Compiler

Compiled 146121 to 61713 computations (57.8% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1))))
✓	0.3b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1))))))
✓	0.3b	(pow.f64 (sqrt.f64 a) (+.f64 t -1))
✓	0.5b	(*.f64 (/.f64 1 (/.f64 1 (/.f64 1 (/.f64 1 (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))) (/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))))

series3.8s (2.5%)

Counts

4 → 180

Calls

4 calls:

1.5s	(*.f64 (/.f64 1 (/.f64 1 (/.f64 1 (/.f64 1 (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))) (/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))))
1.4s	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1))))))
847.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1))))
29.0ms	(pow.f64 (sqrt.f64 a) (+.f64 t -1))

rewrite32.8s (21.9%)

Algorithm

1×	rewrite-expression-head

Rules

35092×	`times-frac_binary64`
24393×	`div-exp_binary64`
21769×	`add-exp-log_binary64`
19253×	`add-sqr-sqrt_binary64`
12590×	`*-un-lft-identity_binary64`

Counts

4 → 12746

Calls

4 calls:

21.0s	(*.f64 (/.f64 1 (/.f64 1 (/.f64 1 (/.f64 1 (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))) (/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))))
174.0ms	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1))))))
30.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1))))
4.0ms	(pow.f64 (sqrt.f64 a) (+.f64 t -1))

simplify15.1s (10.1%)

Algorithm

1×	egg-herbie

Counts

12926 → 10229

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8685	838937

prune17.0s (11.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	10260	0	10260
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	10260	7	10267

Error

Counts

10267 → 7

Alt Table

Status	Error	Program
	22.1b	(.f64 (/.f64 x y) (.f64 (/.f64 (pow.f64 a t) (*.f64 a (exp.f64 b))) (pow.f64 z y)))
✓	15.7b	(*.f64 (/.f64 1 (/.f64 1 (/.f64 1 (/.f64 1 (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))) (/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 (sqrt.f64 a) (+.f64 t -1)))))))
✓	2.9b	(/.f64 (.f64 x (pow.f64 (E.f64) (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	17.3b	(/.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x) y)
✓	16.3b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
	16.3b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	26.4b	(.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))))

Compiler

Compiled 583087 to 325876 computations (44.1% saved)

regimes3.3s (2.2%)

Accuracy

Total 1.9b remaining (99.1%)

Threshold costs 0b (0%)

Counts

227 → 3

Compiler

Compiled 88067 to 57962 computations (34.2% saved)

bsearch7.0ms (0%)

Steps

Iters	Range		Point
1	-178.77550545307847	-168.27729092774317	-176.15095182174466
0	-512.192791003153	-503.89186203592266	-507.9941287687496

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	30	98
1	45	98
2	49	98
3	51	98
4	52	98
5	50	98

end1.0ms (0%)

Compiler: Compiled 68 to 41 computations (39.7% saved)

sample54.9s (36.6%)

Algorithm

1×

intervals

Results

1.4s	14508×	body	128	nan
880.0ms	8000×	body	128	valid
812.0ms	7354×	body	128	invalid

Compiler

Compiled 474 to 310 computations (34.6% saved)

Details

analyze1.4s (0.9%)

sample161.0ms (0.1%)

simplify63.0ms (0%)

prune5.0ms (0%)

localize16.0ms (0%)

series2.2s (1.5%)

rewrite34.0ms (0%)

simplify236.0ms (0.2%)

prune280.0ms (0.2%)

localize15.0ms (0%)

series2.9s (2%)

rewrite42.0ms (0%)

simplify543.0ms (0.4%)

prune712.0ms (0.5%)

localize24.0ms (0%)

series5.5s (3.7%)

rewrite1.3s (0.9%)

simplify2.4s (1.6%)

prune5.2s (3.5%)

localize19.0ms (0%)

series3.8s (2.5%)

rewrite32.8s (21.9%)

simplify15.1s (10.1%)

prune17.0s (11.3%)

regimes3.3s (2.2%)

bsearch7.0ms (0%)

simplify5.0ms (0%)

end1.0ms (0%)

sample54.9s (36.6%)

Profiling