Details

analyze1.8s (29.3%)

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%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

sample53.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	80	valid
9.0ms	161×	body	80	invalid

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4953	17
1	4953	17

prune16.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 6.2b

Counts

2 → 2

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* x (* 9.0 y))
0.3b	(- (/ (+ (* x (* 9.0 y)) b) z) (* 4.0 (* t a)))
2.2b	(/ (+ (* x (* 9.0 y)) b) z)
10.8b	(/ (- (/ (+ (* x (* 9.0 y)) b) z) (* 4.0 (* t a))) c)

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/l/`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r` `*-commutative` `flip-+`

Counts

4 → 88

Calls

4 calls:

15.0ms	(/ (- (/ (+ (* x (* 9.0 y)) b) z) (* 4.0 (* t a))) c)
10.0ms	(- (/ (+ (* x (* 9.0 y)) b) z) (* 4.0 (* t a)))
8.0ms	(/ (+ (* x (* 9.0 y)) b) z)
5.0ms	(* x (* 9.0 y))

series99.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (- (/ (+ (* x (* 9.0 y)) b) z) (* 4.0 (* t a))) c)
39.0ms	(- (/ (+ (* x (* 9.0 y)) b) z) (* 4.0 (* t a)))
13.0ms	(/ (+ (* x (* 9.0 y)) b) z)
3.0ms	(* x (* 9.0 y))

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4964	1623
1	4964	1623

prune257.0ms (4.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	9	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Merged error: 0.3b

Counts

102 → 9

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* t (/ a c)))
0.2b	(* x (* 9.0 y))
5.8b	(* t (/ a c))
11.9b	(/ (+ (* x (* 9.0 y)) b) (* z c))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
21×	`add-sqr-sqrt`
16×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
13×	`times-frac`
11×	`prod-exp` `cbrt-unprod`
9×	`associate-l`
7×	`pow-prod-down`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-r/` `-commutative` `associate-/l*`
2×	`div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `clear-num` `associate-/r*` `flip-+`

Counts

4 → 94

Calls

4 calls:

8.0ms	(/ (+ (* x (* 9.0 y)) b) (* z c))
8.0ms	(* t (/ a c))
6.0ms	(* 4.0 (* t (/ a c)))
4.0ms	(* x (* 9.0 y))

series30.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (+ (* x (* 9.0 y)) b) (* z c))
6.0ms	(* 4.0 (* t (/ a c)))
5.0ms	(* t (/ a c))
3.0ms	(* x (* 9.0 y))

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5037	864

prune226.0ms (3.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	101	14	115

Merged error: 0.0b

Counts

115 → 14

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.8b	(cbrt (+ (* x (* 9.0 y)) b))
4.8b	(cbrt (+ (* x (* 9.0 y)) b))
4.8b	(cbrt (+ (* x (* 9.0 y)) b))
5.8b	(* t (/ a c))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`times-frac`
9×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`add-log-exp`
3×	`flip3-+` `pow1/3` `associate-l` `flip-+`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* t (/ a c))
5.0ms	(cbrt (+ (* x (* 9.0 y)) b))
5.0ms	(cbrt (+ (* x (* 9.0 y)) b))
5.0ms	(cbrt (+ (* x (* 9.0 y)) b))

series107.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt (+ (* x (* 9.0 y)) b))
33.0ms	(cbrt (+ (* x (* 9.0 y)) b))
33.0ms	(cbrt (+ (* x (* 9.0 y)) b))
5.0ms	(* t (/ a c))

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4956	857
1	4956	857

prune270.0ms (4.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	83	14	97

Merged error: 0.0b

Counts

97 → 14

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
3.4b	(* (* t (* (cbrt a) (cbrt a))) (/ (cbrt a) c))
11.9b	(/ (+ (* x (* 9.0 y)) b) (* z c))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`associate-r`
21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
15×	`cbrt-prod`
13×	`pow1` `prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
5×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`frac-2neg` `flip3-+` `associate-r/` `associate-l` `clear-num` `associate-/r` `*-commutative` `flip-+`

Counts

4 → 92

Calls

4 calls:

15.0ms	(* (* t (* (cbrt a) (cbrt a))) (/ (cbrt a) c))
9.0ms	(/ (+ (* x (* 9.0 y)) b) (* z c))
1.0ms	(cbrt a)
1.0ms	(cbrt a)

series69.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt a)
22.0ms	(cbrt a)
17.0ms	(/ (+ (* x (* 9.0 y)) b) (* z c))
8.0ms	(* (* t (* (cbrt a) (cbrt a))) (/ (cbrt a) c))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4923	863
1	4923	863

prune145.0ms (2.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	104	14	118

Merged error: 0.0b

Counts

118 → 14

regimes1.1s (18.6%)

Accuracy

Total 5.9b remaining (99.2%)

Threshold costs 0b (0%)

bsearch94.0ms (1.5%)

Steps

Iters	Range		Point
7	12549083.19879675	312270525.487977	18414931.287040245
8	-6.2286065924212e-95	-1.3632203146482463e-97	-5.176286705330166e-96
7	-4.344995078780857e+27	-4.6303623695689775e+25	-2.7610087338959005e+26

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	181	99
1	181	99

end0.0ms (0%)

sample1.3s (21.6%)

Algorithm

1×

intervals

Results

493.0ms	8000×	body	80	valid
285.0ms	4647×	body	80	invalid

Details

analyze1.8s (29.3%)

sample53.0ms (0.9%)

simplify65.0ms (1.1%)

prune16.0ms (0.3%)

localize13.0ms (0.2%)

rewrite41.0ms (0.7%)

series99.0ms (1.6%)

simplify50.0ms (0.8%)

prune257.0ms (4.2%)

localize14.0ms (0.2%)

rewrite29.0ms (0.5%)

series30.0ms (0.5%)

simplify53.0ms (0.9%)

prune226.0ms (3.7%)

localize20.0ms (0.3%)

rewrite24.0ms (0.4%)

series107.0ms (1.7%)

simplify56.0ms (0.9%)

prune270.0ms (4.4%)

localize18.0ms (0.3%)

rewrite29.0ms (0.5%)

series69.0ms (1.1%)

simplify81.0ms (1.3%)

prune145.0ms (2.4%)

regimes1.1s (18.6%)

bsearch94.0ms (1.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (21.6%)

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