Details

sample39.0ms

Algorithm

intervals

Results

14.0ms	255×	body	80	valid
0.0ms	1×	body	320	valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	10
1	71	10
2	184	10
3	381	10
4	682	10
5	1102	10
6	2122	10
7	4337	10
8	5001	10

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 26.4b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.8b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`associate-l` `frac-add`
3×	`associate-r` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

6.0ms	(* (+ x y) z)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
9.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
14.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series200.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (+ x y) z)
17.0ms	(+ (* (+ x y) z) (* (+ t y) a))
30.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
146.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify63.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	523	1089
1	2308	1025
2	5001	1025

prune523.0ms

Filtered

102 candidates to 74 candidates (27.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	9	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 8.8b

Counts

103 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.9b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
10×	`associate-*l/`
7×	`pow1` `flip3-+` `flip-+`
5×	`associate-/r*`
4×	`div-exp` `frac-add` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `diff-log` `1-exp` `sum-log` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 118

Calls

4 calls:

7.0ms	(/ 1 (+ (+ x t) y))
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
11.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
20.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1 (+ (+ x t) y))
16.0ms	(+ (* (+ x y) z) (* (+ t y) a))
30.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
146.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify71.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	562	1269
1	2768	1146
2	5002	1104

prune447.0ms

Filtered

130 candidates to 74 candidates (43.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	130	10	140

Merged error: 8.8b

Counts

140 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

7.8b	(* (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (/ (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (+ (+ x t) y)))
25.4b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
25.4b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
25.4b	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
36×	`associate-r`
32×	`times-frac`
30×	`cbrt-div`
29×	`add-sqr-sqrt`
25×	`cbrt-prod`
24×	`add-cube-cbrt`
18×	`distribute-lft-out`
16×	`add-exp-log` `frac-times`
15×	`flip3--` `flip--`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+` `div-inv`

Counts

4 → 114

Calls

4 calls:

37.0ms	(* (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (/ (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (+ (+ x t) y)))
8.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
8.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
9.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (* (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (/ (cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) (+ (+ x t) y)))
120.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
118.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
122.0ms	(cbrt (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify76.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	591	3388
1	2399	3077
2	5001	2930

prune557.0ms

Filtered

126 candidates to 90 candidates (28.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	125	11	136

Merged error: 8.8b

Counts

136 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
8.3b	(/ (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (cbrt (+ (+ x t) y)))
16.4b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
136×	`*-un-lft-identity`
122×	`cbrt-div`
82×	`associate-/r/`
80×	`cbrt-prod`
66×	`flip3-+` `flip-+`
56×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
40×	`frac-times`
28×	`associate-*l/`
20×	`associate-*r/`
18×	`add-exp-log` `associate-/l*`
11×	`add-cbrt-cube` `div-inv` `add-log-exp`
9×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-add`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `associate--l+`

Counts

4 → 224

Calls

4 calls:

7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
9.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
31.0ms	(/ (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (cbrt (+ (+ x t) y)))
22.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

series1.1s

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (* (+ x y) z) (* (+ t y) a))
29.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
138.0ms	(/ (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y)))) (cbrt (+ (+ x t) y)))
879.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))

simplify132.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1151	6251
1	4786	6000
2	5001	5989

prune1.7s

Filtered

236 candidates to 161 candidates (31.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	233	3	236
Fresh	2	5	7
Picked	0	1	1
Done	1	2	3
Total	236	11	247

Merged error: 6.4b

Counts

247 → 11

regimes912.0ms

Accuracy

9.6% (16.7b remaining)

Error of 21.5b against oracle of 4.8b and baseline of 23.3b

bsearch407.0ms

Steps

Iters	Range		Point
9	4.4845703965173715e+209	3.5723431097487635e+217	7.848598548434303e+210
9	3.594469164334708e+136	9.853642693877703e+143	4.099745715386342e+136
9	3.935663615159136e+68	5.514542683406611e+77	9.66870364560746e+76
5	-2.667268698712483e+63	-9.285359387380172e+62	-2.3219356923528134e+63
10	-8.717706840629375e+120	-1.3182666044257135e+110	-1.176689705302933e+116
9	-5.529152920588948e+134	-7.770232686786471e+127	-6.203533803246623e+128
8	-4.1158490967711146e+175	-1.6345710071753572e+172	-1.4808403197864043e+173

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	37
1	54	37

end0.0ms

sample908.0ms

Algorithm

intervals

Results

424.0ms	7996×	body	80	valid
1.0ms	4×	body	320	valid

Details

sample39.0ms

simplify104.0ms

prune6.0ms

localize18.0ms

rewrite39.0ms

series200.0ms

simplify63.0ms

prune523.0ms

localize15.0ms

rewrite49.0ms

series202.0ms

simplify71.0ms

prune447.0ms

localize22.0ms

rewrite67.0ms

series544.0ms

simplify76.0ms

prune557.0ms

localize18.0ms

rewrite84.0ms

series1.1s

simplify132.0ms

prune1.7s

regimes912.0ms

bsearch407.0ms

simplify2.0ms

end0.0ms

sample908.0ms

Profiling