Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

272×

body

valid

simplify139.0ms

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: 24.1b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- b y))
1.3b	(+ (* x y) (* z (- t a)))
23.2b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

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

series471.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ y (* z (- b y)))
39.0ms	(* z (- b y))
46.0ms	(+ (* x y) (* z (- t a)))
353.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify80.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	602	1288
1	2282	956
2	5001	937

prune550.0ms

Filtered

165 candidates to 109 candidates (66.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	152	13	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	13	166

Merged error: 23.4b

Counts

166 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.3b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.8b	(fma x y (* z (- t a)))
23.2b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 127

Calls

4 calls:

1.0ms	(fma z (- b y) y)
6.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
1.0ms	(fma x y (* z (- t a)))
4.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series706.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(fma z (- b y) y)
513.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
55.0ms	(fma x y (* z (- t a)))
110.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify65.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	363	1470
1	1455	1322
2	5001	1248

prune390.0ms

Filtered

139 candidates to 85 candidates (61.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	8	4	12
Picked	0	1	1
Done	0	0	0
Total	143	9	152

Merged error: 12.3b

Counts

152 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
0.8b	(fma x y (* z (- t a)))
1.3b	(/ 1 (fma x y (* z (- t a))))
22.1b	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`div-exp` `add-cbrt-cube`
16×	`prod-exp`
13×	`associate-r`
10×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `associate-/r/` `un-div-inv` `inv-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 123

Calls

4 calls:

7.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
1.0ms	(fma x y (* z (- t a)))
3.0ms	(/ 1 (fma x y (* z (- t a))))
8.0ms	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

series746.0ms

Counts

4 → 12

Calls

4 calls:

516.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
50.0ms	(fma x y (* z (- t a)))
68.0ms	(/ 1 (fma x y (* z (- t a))))
111.0ms	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	332	1058
1	1341	874
2	5001	839

prune349.0ms

Filtered

135 candidates to 73 candidates (54.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	135	9	144

Merged error: 12.3b

Counts

144 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b y))
0.5b	(cbrt (- b y))
1.3b	(+ (* x y) (* z (- t a)))
23.2b	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
26×	`add-cube-cbrt`
22×	`associate-+r+`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-prod`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`sub-neg` `flip3--` `pow1/3` `associate-/r/` `flip--` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 103

Calls

4 calls:

3.0ms	(cbrt (- b y))
3.0ms	(cbrt (- b y))
7.0ms	(+ (* x y) (* z (- t a)))
9.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (- b y))
173.0ms	(cbrt (- b y))
47.0ms	(+ (* x y) (* z (- t a)))
621.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	517	1258
1	1564	1102
2	5002	1055

prune468.0ms

Filtered

115 candidates to 94 candidates (81.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	115	9	124

Merged error: 12.3b

Counts

124 → 9

regimes445.0ms

Accuracy

34.6% (8.3b remaining)

Error of 19.1b against oracle of 10.8b and baseline of 23.5b

bsearch127.0ms

Steps

Iters	Range		Point
9	1.5340021636682078e+92	4.5336870613845745e+98	9.081015033724511e+95
10	-1.3164224548041124e+76	-1.4236159257461274e+63	-1.066732755010575e+75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample684.0ms

Algorithm

intervals

Results

375.0ms

8419×

body

valid