Details

analyze924.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.3%	66.5%	0.2%	14

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	24×	body	80	invalid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4982	11
1	4982	11

prune4.0ms

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: 1.8b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- z a))))
0.0b	(/ (- z t) (- z a))
3.0b	(* y (/ (- z t) (- z a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 113

Calls

3 calls:

3.0ms	(+ x (* y (/ (- z t) (- z a))))
7.0ms	(/ (- z t) (- z a))
18.0ms	(* y (/ (- z t) (- z a)))

series48.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ x (* y (/ (- z t) (- z a))))
8.0ms	(/ (- z t) (- z a))
15.0ms	(* y (/ (- z t) (- z a)))

simplify42.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4994	1366
1	4994	1366

prune139.0ms

Filtered

83 candidates to 122 candidates (-47.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Merged error: 0b

Counts

123 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- z a))
0.5b	(cbrt (- z a))
0.5b	(* (cbrt (- z a)) (cbrt (- z a)))
0.7b	(* y (* (cbrt (- z t)) (/ (cbrt (- z t)) (* (cbrt (- z a)) (cbrt (- z a))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
35×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
20×	`add-exp-log` `cbrt-div`
16×	`pow1`
15×	`add-cube-cbrt`
11×	`associate-l` `add-cbrt-cube`
10×	`flip3--` `swap-sqr` `flip--`
9×	`associate-r` `prod-exp` `cbrt-unprod`
8×	`pow1/3` `associate-*r/` `distribute-lft-out--`
6×	`frac-times` `difference-of-squares`
5×	`pow-prod-down`
4×	`associate-*l/` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 113

Calls

4 calls:

3.0ms	(cbrt (- z a))
3.0ms	(cbrt (- z a))
10.0ms	(* (cbrt (- z a)) (cbrt (- z a)))
20.0ms	(* y (* (cbrt (- z t)) (/ (cbrt (- z t)) (* (cbrt (- z a)) (cbrt (- z a))))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- z a))
25.0ms	(cbrt (- z a))
31.0ms	(* (cbrt (- z a)) (cbrt (- z a)))
37.0ms	(* y (* (cbrt (- z t)) (/ (cbrt (- z t)) (* (cbrt (- z a)) (cbrt (- z a))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4991	1456
1	4991	1456

prune150.0ms

Filtered

86 candidates to 125 candidates (-45.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	125	7	132

Merged error: 0b

Counts

132 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- z a))
0.5b	(cbrt (- z a))
0.5b	(* (cbrt (- z a)) (cbrt (- z a)))
6.2b	(* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
65×	`cbrt-prod`
54×	`associate-r`
50×	`times-frac`
35×	`add-cube-cbrt`
30×	`cbrt-div`
27×	`add-exp-log`
23×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
8×	`pow1/3`
7×	`cbrt-undiv` `div-exp`
5×	`associate-r/` `associate-l/`
4×	`add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `pow-plus`

Counts

4 → 177

Calls

4 calls:

3.0ms	(cbrt (- z a))
3.0ms	(cbrt (- z a))
10.0ms	(* (cbrt (- z a)) (cbrt (- z a)))
34.0ms	(* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- z a))
25.0ms	(cbrt (- z a))
33.0ms	(* (cbrt (- z a)) (cbrt (- z a)))
21.0ms	(* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))

simplify90.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4935	2490
1	4935	2490

prune193.0ms

Filtered

126 candidates to 189 candidates (-50.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	189	7	196

Merged error: 0b

Counts

196 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (- (/ z (- z a)) (/ t (- z a)))))
0.0b	(- (/ z (- z a)) (/ t (- z a)))
0.0b	(/ z (- z a))
3.0b	(* y (- (/ z (- z a)) (/ t (- z a))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
51×	`times-frac`
28×	`distribute-lft-out--`
20×	`add-cube-cbrt`
18×	`associate-r`
16×	`difference-of-squares`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1` `distribute-rgt-out--`
5×	`sub-neg` `associate-/r*` `div-inv`
4×	`associate-*r/`
3×	`associate-l` `associate-/l*`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `frac-sub` `sub-div`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

6.0ms	(+ x (* y (- (/ z (- z a)) (/ t (- z a)))))
26.0ms	(- (/ z (- z a)) (/ t (- z a)))
5.0ms	(/ z (- z a))
33.0ms	(* y (- (/ z (- z a)) (/ t (- z a))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ x (* y (- (/ z (- z a)) (/ t (- z a)))))
16.0ms	(- (/ z (- z a)) (/ t (- z a)))
5.0ms	(/ z (- z a))
31.0ms	(* y (- (/ z (- z a)) (/ t (- z a))))

simplify53.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4970	1554
1	4970	1554

prune108.0ms

Filtered

96 candidates to 129 candidates (-34.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	2	2	4
Picked	0	1	1
Done	2	0	2
Total	132	4	136

Merged error: 0b

Counts

136 → 4

regimes403.0ms

Accuracy

57.5% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 1.3b

bsearch20.0ms

Steps

Iters	Range		Point
7	3.231331606106114e-53	1.411708349281519e-51	5.431832840092546e-53
2	-7.602032670693013e-119	-6.603476669339858e-119	-6.977935169847292e-119

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	37
1	58	37

end0.0ms

sample586.0ms

Algorithm

intervals

Results

295.0ms	7997×	body	80	valid
25.0ms	732×	body	80	invalid
0.0ms	2×	body	640	valid
0.0ms	1×	body	1280	valid

Details

analyze924.0ms

sample24.0ms

simplify93.0ms

prune4.0ms

localize8.0ms

rewrite33.0ms

series48.0ms

simplify42.0ms

prune139.0ms

localize19.0ms

rewrite40.0ms

series118.0ms

simplify45.0ms

prune150.0ms

localize12.0ms

rewrite58.0ms

series104.0ms

simplify90.0ms

prune193.0ms

localize10.0ms

rewrite75.0ms

series78.0ms

simplify53.0ms

prune108.0ms

regimes403.0ms

bsearch20.0ms

simplify1.0ms

end0.0ms

sample586.0ms

Profiling