Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	383×	body	80	valid
6.0ms	159×	body	80	nan

simplify108.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune7.0ms

Filtered

1 candidates to 1 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: 1.3b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(+ 1.0 (* 10.0 k))
1.3b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`fma-def` `prod-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `div-exp` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

9.0ms	(* a (pow k m))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms	(+ 1.0 (* 10.0 k))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms	(+ 1.0 (* 10.0 k))
115.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	477	629
1	2275	544
2	5001	524

prune290.0ms

Filtered

100 candidates to 79 candidates (79.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Merged error: 0.0b

Counts

102 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(fma 10.0 k 1.0)
0.1b	(/ 1 (fma k k (fma 10.0 k 1.0)))
1.3b	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r` `add-cbrt-cube`
18×	`times-frac`
10×	`div-exp`
7×	`pow1` `cbrt-unprod`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
2×	`*-commutative` `div-inv` `sqr-pow`
1×	`pow-flip` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `un-div-inv` `fma-udef` `inv-pow`

Counts

4 → 117

Calls

4 calls:

5.0ms	(* a (pow k m))
1.0ms	(fma 10.0 k 1.0)
3.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
8.0ms	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

series258.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* a (pow k m))
32.0ms	(fma 10.0 k 1.0)
39.0ms	(/ 1 (fma k k (fma 10.0 k 1.0)))
123.0ms	(* (* a (pow k m)) (/ 1 (fma k k (fma 10.0 k 1.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	512	805
1	2653	698
2	5001	671

prune296.0ms

Filtered

129 candidates to 77 candidates (59.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	129	5	134

Merged error: 0.0b

Counts

134 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* a (pow k m)))
0.3b	(cbrt (* a (pow k m)))
0.3b	(cbrt (* a (pow k m)))
1.3b	(/ (* (* (cbrt (* a (pow k m))) (cbrt (* a (pow k m)))) (cbrt (* a (pow k m)))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (* a (pow k m)))
3.0ms	(cbrt (* a (pow k m)))
3.0ms	(cbrt (* a (pow k m)))
13.0ms	(/ (* (* (cbrt (* a (pow k m))) (cbrt (* a (pow k m)))) (cbrt (* a (pow k m)))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (* a (pow k m)))
119.0ms	(cbrt (* a (pow k m)))
116.0ms	(cbrt (* a (pow k m)))
145.0ms	(/ (* (* (cbrt (* a (pow k m))) (cbrt (* a (pow k m)))) (cbrt (* a (pow k m)))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify55.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	433	889
1	1902	690
2	5002	624

prune249.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	72	5	77

Merged error: 0.0b

Counts

77 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 10.0 k 1.0)
0.4b	(/ (pow k m) (/ (fma k k (fma 10.0 k 1.0)) a))
2.9b	(/ (fma k k (fma 10.0 k 1.0)) a)
15.9b	(cbrt (pow (/ (pow k m) (/ (fma k k (fma 10.0 k 1.0)) a)) 3))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
249×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
216×	`unpow-prod-down`
198×	`cbrt-prod`
96×	`cube-prod`
41×	`sqr-pow`
26×	`div-inv`
19×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
10×	`div-exp` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r/`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`cube-div` `cube-mult` `cbrt-div` `pow1/3` `unpow3` `rem-cbrt-cube` `fma-udef`

Counts

4 → 381

Calls

4 calls:

1.0ms	(fma 10.0 k 1.0)
8.0ms	(/ (pow k m) (/ (fma k k (fma 10.0 k 1.0)) a))
3.0ms	(/ (fma k k (fma 10.0 k 1.0)) a)
28.0ms	(cbrt (pow (/ (pow k m) (/ (fma k k (fma 10.0 k 1.0)) a)) 3))

series324.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma 10.0 k 1.0)
107.0ms	(/ (pow k m) (/ (fma k k (fma 10.0 k 1.0)) a))
43.0ms	(/ (fma k k (fma 10.0 k 1.0)) a)
137.0ms	(cbrt (pow (/ (pow k m) (/ (fma k k (fma 10.0 k 1.0)) a)) 3))

simplify279.0ms

Algorithm

egg-herbie

Counts

393 → 393

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2083	4746
1	5002	4709

prune979.0ms

Filtered

393 candidates to 227 candidates (57.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	393	5	398

Merged error: 0.0b

Counts

398 → 5

regimes111.0ms

Accuracy

96.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch61.0ms

Steps

Iters	Range		Point
8	2.780302897405976e+149	1.3412804874082685e+153	1.2321402563896536e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	54	34
2	54	34

end0.0ms

sample1.1s

Algorithm

intervals

Results

574.0ms	11880×	body	80	valid
161.0ms	4240×	body	80	nan