Details

analyze2.4s (7.9%)

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
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)

sample6.0s (19.4%)

Results

4.2s	22440×	body	128	invalid
1.7s	8256×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify50.0ms (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

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
	25.6b	(.f64 (.f64 (pow.f64 a (-.f64 t 1)) (/.f64 (pow.f64 z y) (exp.f64 b))) (/.f64 x y))
▶	1.9b	(/.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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 t 1) (log.f64 a))
✓	0.2b	(*.f64 y (log.f64 z))
✓	0.8b	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
✓	1.2b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)

series1.8s (5.8%)

Counts

4 → 176

Calls

4 calls:

1.0s	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
503.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
181.0ms	(*.f64 y (log.f64 z))
60.0ms	(*.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:

10.0ms	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
6.0ms	(exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (.f64 (-.f64 t 1) (log.f64 a))) b))
5.0ms	(*.f64 (-.f64 t 1) (log.f64 a))
3.0ms	(*.f64 y (log.f64 z))

simplify218.0ms (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

prune276.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	243	5	248
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	244	6	250

Error

0.0b

Counts

250 → 6

Alt Table

Status	Error	Program
	36.5b	(+.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))))))
	22.0b	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
	19.9b	(/.f64 x (/.f64 y (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))))
▶	19.8b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
	43.3b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (sqrt.f64 y)))

Compiler

Compiled 7416 to 3167 computations (57.3% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)
✓	0.1b	(pow.f64 a (+.f64 t -1))
✓	0.5b	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
✓	1.2b	(/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x))

series3.7s (11.8%)

Counts

4 → 228

Calls

4 calls:

1.7s	(/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x))
1.1s	(*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)
825.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
29.0ms	(pow.f64 a (+.f64 t -1))

rewrite154.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

776×	`times-frac_binary64`
390×	`add-sqr-sqrt_binary64`
351×	`*-un-lft-identity_binary64`
349×	`add-cube-cbrt_binary64`
316×	`unpow-prod-down_binary64`

Counts

4 → 563

Calls

4 calls:

29.0ms	(*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)
16.0ms	(/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x))
11.0ms	(/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1))))
3.0ms	(pow.f64 a (+.f64 t -1))

simplify427.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/r/_binary64`
578×	`times-frac_binary64`
341×	`associate-/l/_binary64`
307×	`*-commutative_binary64`
165×	`associate-*l/_binary64`

Counts

791 → 1102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1001	24618
1	2525	23802
2	5031	23802

prune1.7s (5.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1101	1	1102
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	1102	6	1108

Error

Counts

1108 → 6

Alt Table

Status	Error	Program
	31.9b	(/.f64 1 (/.f64 y (+.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) a))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 (log.f64 z) y)) x) (.f64 (exp.f64 b) a)) (+.f64 (/.f64 (.f64 (log.f64 a) (.f64 t (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) a)) (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 a) 3) (.f64 (pow.f64 t 3) (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) a))))))))
	36.5b	(+.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))))))
▶	22.0b	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	19.8b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))
	43.3b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) (sqrt.f64 y)))

Compiler

Compiled 38905 to 18268 computations (53% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))))
	0.1b	(pow.f64 a (+.f64 t -1))
✓	0.5b	(*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))
✓	1.5b	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)

series2.7s (8.6%)

Counts

3 → 168

Calls

3 calls:

1.1s	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)
907.0ms	(.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))))
641.0ms	(*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
22×	`add-sqr-sqrt_binary64`
19×	`add-cbrt-cube_binary64`
18×	`pow-exp_binary64`

Counts

3 → 104

Calls

3 calls:

7.0ms	(*.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))
6.0ms	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)
5.0ms	(.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1))))

simplify180.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

948×	`fma-def_binary64`
426×	`unswap-sqr_binary64`
400×	`associate-r_binary64`
328×	`associate-l_binary64`
212×	`associate-/l*_binary64`

Counts

272 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	6110
1	762	5797
2	3130	5469
3	4872	5469
4	5047	5469

prune309.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	264	1	265
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	265	6	271

Error

Counts

271 → 6

Alt Table

Status	Error	Program
	31.9b	(/.f64 1 (/.f64 y (+.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) a))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 (log.f64 z) y)) x) (.f64 (exp.f64 b) a)) (+.f64 (/.f64 (.f64 (log.f64 a) (.f64 t (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) a)) (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 a) 3) (.f64 (pow.f64 t 3) (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) a))))))))
▶	24.1b	(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1)) (/.f64 y (*.f64 (pow.f64 z y) x)))
	36.5b	(+.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))))))
✓	22.0b	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	19.8b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))

Compiler

Compiled 6391 to 3074 computations (51.9% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 z y) x)
✓	0.1b	(pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1))
✓	0.2b	(/.f64 -1 (/.f64 -1 a))
✓	4.0b	(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1)) (/.f64 y (*.f64 (pow.f64 z y) x)))

series1.1s (3.7%)

Counts

4 → 132

Calls

4 calls:

932.0ms	(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1)) (/.f64 y (*.f64 (pow.f64 z y) x)))
185.0ms	(*.f64 (pow.f64 z y) x)
27.0ms	(pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1))
1.0ms	(/.f64 -1 (/.f64 -1 a))

rewrite170.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

1282×	`times-frac_binary64`
569×	`add-sqr-sqrt_binary64`
563×	`*-un-lft-identity_binary64`
560×	`add-cube-cbrt_binary64`
400×	`unpow-prod-down_binary64`

Counts

4 → 716

Calls

4 calls:

25.0ms	(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1)) (/.f64 y (*.f64 (pow.f64 z y) x)))
10.0ms	(pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1))
4.0ms	(/.f64 -1 (/.f64 -1 a))
3.0ms	(*.f64 (pow.f64 z y) x)

simplify842.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

748×	`associate-/r/_binary64`
651×	`associate-/l/_binary64`
296×	`associate-/r*_binary64`
217×	`fma-def_binary64`
216×	`times-frac_binary64`

Counts

848 → 1082

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	1152	30859
1	2586	26202
2	4388	26113
3	4460	26081
4	4962	26081
5	4966	26081

prune1.2s (3.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1082	0	1082
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	1082	6	1088

Error

Counts

1088 → 6

Alt Table

Status	Error	Program
	31.9b	(/.f64 1 (/.f64 y (+.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) a))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 (log.f64 z) y)) x) (.f64 (exp.f64 b) a)) (+.f64 (/.f64 (.f64 (log.f64 a) (.f64 t (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) a)) (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 a) 3) (.f64 (pow.f64 t 3) (.f64 (exp.f64 (.f64 (log.f64 z) y)) x))) (.f64 (exp.f64 b) a))))))))
✓	24.1b	(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 a)) (-.f64 t 1)) (/.f64 y (*.f64 (pow.f64 z y) x)))
	36.5b	(+.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))))))
✓	22.0b	(/.f64 (.f64 x (.f64 (pow.f64 z y) (pow.f64 a (+.f64 t -1)))) y)
✓	1.9b	(/.f64 (.f64 x (exp.f64 (-.f64 (+.f64 (.f64 y (log.f64 z)) (*.f64 (-.f64 t 1) (log.f64 a))) b))) y)
✓	19.8b	(/.f64 1 (/.f64 y (*.f64 (/.f64 (pow.f64 z y) (/.f64 (exp.f64 b) (pow.f64 a (+.f64 t -1)))) x)))

Compiler

Compiled 36261 to 20507 computations (43.4% saved)

regimes7.5s (24.3%)

Accuracy

Total 2.0b remaining (97.1%)

Threshold costs 0b (0%)

Counts

451 → 1

Compiler

Compiled 187806 to 123316 computations (34.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	22	26
2	26	26
3	28	26
4	29	26
5	29	26

end138.0ms (0.4%)

Compiler: Compiled 307 to 173 computations (43.6% saved)

Details

analyze2.4s (7.9%)

sample6.0s (19.4%)

simplify50.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series1.8s (5.8%)

rewrite34.0ms (0.1%)

simplify218.0ms (0.7%)

prune276.0ms (0.9%)

localize14.0ms (0%)

series3.7s (11.8%)

rewrite154.0ms (0.5%)

simplify427.0ms (1.4%)

prune1.7s (5.4%)

localize9.0ms (0%)

series2.7s (8.6%)

rewrite25.0ms (0.1%)

simplify180.0ms (0.6%)

prune309.0ms (1%)

localize13.0ms (0%)

series1.1s (3.7%)

rewrite170.0ms (0.5%)

simplify842.0ms (2.7%)

prune1.2s (3.8%)

regimes7.5s (24.3%)

simplify3.0ms (0%)

end138.0ms (0.4%)

Profiling