Details

sample91.0ms

Algorithm

intervals

Results

32.0ms	82×	body	2560	valid
24.0ms	90×	body	1280	valid
10.0ms	261×	body	80	nan
7.0ms	35×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	19×	body	160	valid
0.0ms	5×	body	80	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	43	7
2	84	7
3	155	7
4	262	7
5	454	7
6	2878	7
7	5001	7

prune2.0ms

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: 0.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	349	623
1	1288	567
2	5001	565

prune142.0ms

Filtered

78 candidates to 61 candidates (78.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Merged error: 0.5b

Counts

79 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
3.5b	(log (exp (* 5.0 (* v v))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
24×	`times-frac`
18×	`add-cube-cbrt`
15×	`pow1`
12×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--`
8×	`log-pow`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`log-prod` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `exp-prod` `exp-to-pow` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

12.0ms	(/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
3.0ms	(log (exp (* 5.0 (* v v))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))
23.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
24.0ms	(log (exp (* 5.0 (* v v))))

simplify48.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	396	1024
1	1397	907
2	5002	890

prune208.0ms

Filtered

112 candidates to 81 candidates (72.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	111	4	115

Merged error: 0.5b

Counts

115 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
0.2b	(* 5.0 (* v v))
2.0b	(acos (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
177×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
38×	`difference-of-squares`
25×	`distribute-lft-out`
21×	`associate-/l*`
19×	`sqrt-prod` `distribute-lft-out--`
18×	`associate-/r/`
16×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
9×	`pow1` `div-inv`
8×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`acos-asin` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 221

Calls

4 calls:

15.0ms	(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0)))
83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0)))
24.0ms	(* 5.0 (* v v))
17.0ms	(acos (/ (/ (- 1.0 (* 5.0 (* v v))) (+ v (sqrt 1.0))) (- v (sqrt 1.0))))

simplify129.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	910	3560
1	4431	3286
2	5001	3282

prune401.0ms

Filtered

233 candidates to 147 candidates (63.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	233	4	237

Merged error: 0.5b

Counts

237 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))))
3.5b	(log (exp (* 5.0 (* v v))))
3.5b	(log (exp (* 5.0 (* v v))))
3.5b	(log (exp (* 5.0 (* v v))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod` `log-pow`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `exp-prod` `exp-to-pow` `rem-log-exp`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))))
2.0ms	(log (exp (* 5.0 (* v v))))
2.0ms	(log (exp (* 5.0 (* v v))))
2.0ms	(log (exp (* 5.0 (* v v))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))))
23.0ms	(log (exp (* 5.0 (* v v))))
24.0ms	(log (exp (* 5.0 (* v v))))
28.0ms	(log (exp (* 5.0 (* v v))))

simplify88.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (81.0ms)

Iter	Nodes	Cost
0	84	496
1	203	422
2	652	420
3	2581	417
4	5001	416

prune215.0ms

Filtered

73 candidates to 56 candidates (76.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	71	6	77

Merged error: 0.5b

Counts

77 → 6

regimes62.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2996×	body	2560	valid
658.0ms	2438×	body	1280	valid
318.0ms	8296×	body	80	nan
249.0ms	1261×	body	640	valid
94.0ms	640×	body	320	valid
45.0ms	442×	body	160	valid
13.0ms	223×	body	80	valid