Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

264×

body

valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 25.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
1.5b	(+ (* x y) (* z (- t a)))
24.5b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 161

Calls

4 calls:

8.0ms	(* z (- t a))
7.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
9.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* z (- t a))
35.0ms	(* z (- b y))
41.0ms	(+ (* x y) (* z (- t a)))
317.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify83.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026

prune409.0ms

Filtered

173 candidates to 100 candidates (57.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	161	12	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	161	13	174

Merged error: 24.5b

Counts

174 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(/ 1 (+ y (* z (- b y))))
1.5b	(+ (* x y) (* z (- t a)))
24.2b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`times-frac` `associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `prod-exp` `flip-+`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

7.0ms	(* z (- b y))
5.0ms	(/ 1 (+ y (* z (- b y))))
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* z (- b y))
120.0ms	(/ 1 (+ y (* z (- b y))))
41.0ms	(+ (* x y) (* z (- t a)))
315.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	658	1375
1	2830	1048
2	5001	1011

prune410.0ms

Filtered

173 candidates to 105 candidates (60.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	173	13	186

Merged error: 24.5b

Counts

186 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

16.0b	(cbrt (+ y (* z (- b y))))
16.0b	(cbrt (+ y (* z (- b y))))
16.0b	(cbrt (+ y (* z (- b y))))
17.8b	(/ (+ (* x y) (* z (- t a))) (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
10×	`flip3-+` `flip-+`
9×	`add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/`
7×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow1/3` `associate-/l*`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 78

Calls

4 calls:

2.0ms	(cbrt (+ y (* z (- b y))))
2.0ms	(cbrt (+ y (* z (- b y))))
2.0ms	(cbrt (+ y (* z (- b y))))
12.0ms	(/ (+ (* x y) (* z (- t a))) (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt (+ y (* z (- b y))))
263.0ms	(cbrt (+ y (* z (- b y))))
254.0ms	(cbrt (+ y (* z (- b y))))
1.3s	(/ (+ (* x y) (* z (- t a))) (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	447	1240
1	1382	1131
2	5002	1083

prune409.0ms

Filtered

90 candidates to 83 candidates (92.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	90	13	103

Merged error: 24.5b

Counts

103 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

11.4b	(* (/ 1 (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y)))))) (/ (+ (* x y) (* z (- t a))) (cbrt (+ y (* z (- b y))))))
16.0b	(cbrt (+ y (* z (- b y))))
16.0b	(cbrt (+ y (* z (- b y))))
16.0b	(cbrt (+ y (* z (- b y))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-r`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`cbrt-div` `prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp` `associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
5×	`frac-times`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 127

Calls

4 calls:

30.0ms	(* (/ 1 (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y)))))) (/ (+ (* x y) (* z (- t a))) (cbrt (+ y (* z (- b y))))))
2.0ms	(cbrt (+ y (* z (- b y))))
2.0ms	(cbrt (+ y (* z (- b y))))
3.0ms	(cbrt (+ y (* z (- b y))))

series1.6s

Counts

4 → 12

Calls

4 calls:

824.0ms	(* (/ 1 (* (cbrt (+ y (* z (- b y)))) (cbrt (+ y (* z (- b y)))))) (/ (+ (* x y) (* z (- t a))) (cbrt (+ y (* z (- b y))))))
251.0ms	(cbrt (+ y (* z (- b y))))
250.0ms	(cbrt (+ y (* z (- b y))))
247.0ms	(cbrt (+ y (* z (- b y))))

simplify102.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	675	2571
1	3295	2243
2	5001	2061

prune470.0ms

Filtered

139 candidates to 103 candidates (74.1%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	9	9
Picked	0	1	1
Done	0	3	3
Total	139	13	152

Merged error: 24.5b

Counts

152 → 13

regimes490.0ms

Accuracy

0% (0.6b remaining)

Error of 22.9b against oracle of 22.3b and baseline of 22.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample661.0ms

Algorithm

intervals

Results

368.0ms

8432×

body

valid