Details

analyze1.2s (1.7%)

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)

sample6.4s (9%)

Results

4.7s	22212×	body	128	invalid
1.6s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify50.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.8b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	23.4b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x 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))
✓	1.2b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series2.2s (3.1%)

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)
637.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
211.0ms	(*.f64 y (log.f64 z))
63.0ms	(*.f64 (-.f64 t 1) (log.f64 a))

rewrite44.0ms (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:

21.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
7.0ms	(*.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))

simplify212.0ms (0.3%)

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

prune311.0ms (0.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	239	9	248
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	240	10	250

Error

0.1b

Counts

250 → 10

Alt Table

Status	Error	Program
✓	2.8b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	21.2b	(/.f64 (.f64 x (.f64 (+.f64 (.f64 (log.f64 a) t) 1) (/.f64 (pow.f64 z y) (.f64 a (exp.f64 b))))) y)
	18.5b	(/.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)
	29.9b	(exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y))))
	18.5b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
▶	18.2b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
	23.6b	(.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))))
	29.4b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (/.f64 x y)) 3))
	18.6b	(/.f64 (.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))) (cbrt.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))))) (cbrt.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))) y)
	25.1b	(+.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))))

Compiler

Compiled 7674 to 3341 computations (56.5% saved)

localize11.0ms (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 a (+.f64 t -1))))
✓	0.3b	(pow.f64 a (+.f64 t -1))
✓	0.6b	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
✓	1.5b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))

series2.6s (3.7%)

Counts

4 → 192

Calls

4 calls:

1.4s	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
976.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
214.0ms	(/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))
27.0ms	(pow.f64 a (+.f64 t -1))

rewrite423.0ms (0.6%)

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:

112.0ms	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) y))
18.0ms	(/.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))

simplify1.1s (1.5%)

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

prune3.0s (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1771	4	1775
Fresh	6	2	8
Picked	1	0	1
Done	0	1	1
Total	1778	7	1785

Error

0.0b

Counts

1785 → 7

Alt Table

Status	Error	Program
	31.3b	(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 a) 2) (.f64 (pow.f64 t 2) (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) (.f64 a y)))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 (log.f64 z) y)) x) (.f64 (exp.f64 b) (.f64 a y))) (/.f64 (.f64 (log.f64 a) (.f64 t (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) (*.f64 a y)))))
	25.1b	(+.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))))
▶	18.1b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1))) y))
✓	2.8b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	18.5b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
	18.5b	(.f64 (.f64 x (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))) (/.f64 1 y))
	18.3b	(.f64 x (/.f64 (/.f64 (pow.f64 z y) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (pow.f64 a (+.f64 t -1))) (cbrt.f64 (pow.f64 a (+.f64 t -1))))) (/.f64 (exp.f64 b) (cbrt.f64 (pow.f64 a (+.f64 t -1)))))) y))

Compiler

Compiled 64094 to 27130 computations (57.7% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1))
✓	0.3b	(/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))
✓	0.6b	(/.f64 (exp.f64 b) (pow.f64 a t))
✓	1.5b	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1))) y))

series3.1s (4.3%)

Counts

4 → 204

Calls

4 calls:

1.6s	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1))) y))
1.1s	(/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))
191.0ms	(/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1))
181.0ms	(/.f64 (exp.f64 b) (pow.f64 a t))

rewrite3.6s (5.1%)

Algorithm

1×	rewrite-expression-head

Rules

18679×	`times-frac_binary64`
7407×	`add-sqr-sqrt_binary64`
7217×	`*-un-lft-identity_binary64`
7217×	`add-cube-cbrt_binary64`
6361×	`unpow-prod-down_binary64`

Counts

4 → 5685

Calls

4 calls:

706.0ms	(*.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1))) y))
47.0ms	(/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))
12.0ms	(/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1))
4.0ms	(/.f64 (exp.f64 b) (pow.f64 a t))

simplify5.6s (7.9%)

Algorithm

1×	egg-herbie

Counts

5889 → 6413

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8959	250967

prune9.6s (13.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	6409	4	6413
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	6413	7	6420

Error

Counts

6420 → 7

Alt Table

Status	Error	Program
	20.9b	(/.f64 (.f64 (exp.f64 (.f64 (log.f64 a) t)) x) (.f64 (exp.f64 b) (.f64 a y)))
	25.1b	(+.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))))
▶	13.1b	(.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (.f64 (log.f64 a) t))) (pow.f64 a -1))) y))
✓	2.8b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	18.5b	(.f64 (.f64 x (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))) (/.f64 1 y))
	18.5b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
	17.1b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) (/.f64 (sqrt.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))) (cbrt.f64 y)))

Compiler

Compiled 283091 to 106268 computations (62.5% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) (pow.f64 a -1))
✓	0.3b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) (pow.f64 a -1)))
✓	0.3b	(*.f64 (log.f64 a) t)
✓	1.5b	(.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (.f64 (log.f64 a) t))) (pow.f64 a -1))) y))

series2.6s (3.6%)

Counts

4 → 176

Calls

4 calls:

1.4s	(.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (.f64 (log.f64 a) t))) (pow.f64 a -1))) y))
911.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) (pow.f64 a -1)))
207.0ms	(*.f64 (log.f64 a) t)
40.0ms	(/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) (pow.f64 a -1))

rewrite993.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

4718×	`times-frac_binary64`
1923×	`add-sqr-sqrt_binary64`
1866×	`*-un-lft-identity_binary64`
1866×	`add-cube-cbrt_binary64`
1465×	`unpow-prod-down_binary64`

Counts

4 → 1979

Calls

4 calls:

243.0ms	(.f64 x (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (.f64 (log.f64 a) t))) (pow.f64 a -1))) y))
20.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) (pow.f64 a -1)))
6.0ms	(/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) (pow.f64 a -1))
3.0ms	(*.f64 (log.f64 a) t)

simplify2.3s (3.2%)

Algorithm

1×	egg-herbie

Rules

969×	`associate-/l/_binary64`
962×	`times-frac_binary64`
506×	`associate-/r/_binary64`
338×	`/-rgt-identity_binary64`
88×	`associate-/l*_binary64`

Counts

2155 → 3284

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	3046	81424
1	4535	76634
2	5251	76634

prune4.9s (6.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	3281	3	3284
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	3285	6	3291

Error

Counts

3291 → 6

Alt Table

Status	Error	Program
✓	2.8b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	18.5b	(.f64 (.f64 x (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))) (/.f64 1 y))
	13.0b	(/.f64 (.f64 (exp.f64 (.f64 (log.f64 z) y)) x) (.f64 a (.f64 y (exp.f64 (+.f64 b (*.f64 (log.f64 (/.f64 1 a)) t))))))
	17.1b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) (/.f64 (sqrt.f64 (/.f64 (pow.f64 z y) (/.f64 (/.f64 (exp.f64 b) (pow.f64 a t)) (pow.f64 a -1)))) (cbrt.f64 y)))
	13.1b	(.f64 x (/.f64 (/.f64 (pow.f64 z y) (.f64 (/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) 1) a)) y))
	15.8b	(.f64 (.f64 x (sqrt.f64 (/.f64 1 a))) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 (-.f64 b (*.f64 (log.f64 a) t))) (sqrt.f64 (pow.f64 a -1)))) y))

Compiler

Compiled 138832 to 46198 computations (66.7% saved)

regimes20.5s (28.7%)

Accuracy

Total 1.7b remaining (98.7%)

Threshold costs 0b (0%)

Counts

904 → 3

Compiler

Compiled 362931 to 231687 computations (36.2% saved)

bsearch371.0ms (0.5%)

Steps

Iters	Range		Point
11	2.2416455863247832e-24	0.021700806439264562	0.02142220437323121
8	-6.0414870589580175e-210	-3.788066652866224e-213	-9.962165043974629e-213

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-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	36	101
1	51	101
2	55	101
3	57	101
4	58	101
5	56	101

end137.0ms (0.2%)

Compiler: Compiled 323 to 203 computations (37.2% saved)

Details

analyze1.2s (1.7%)

sample6.4s (9%)

simplify50.0ms (0.1%)

prune4.0ms (0%)

localize16.0ms (0%)

series2.2s (3.1%)

rewrite44.0ms (0.1%)

simplify212.0ms (0.3%)

prune311.0ms (0.4%)

localize11.0ms (0%)

series2.6s (3.7%)

rewrite423.0ms (0.6%)

simplify1.1s (1.5%)

prune3.0s (4.2%)

localize12.0ms (0%)

series3.1s (4.3%)

rewrite3.6s (5.1%)

simplify5.6s (7.9%)

prune9.6s (13.4%)

localize14.0ms (0%)

series2.6s (3.6%)

rewrite993.0ms (1.4%)

simplify2.3s (3.2%)

prune4.9s (6.9%)

regimes20.5s (28.7%)

bsearch371.0ms (0.5%)

simplify4.0ms (0%)

end137.0ms (0.2%)

Profiling