Details

sample78.0ms

Algorithm

intervals

Results

32.0ms	95×	body	2560	valid
19.0ms	84×	body	1280	valid
7.0ms	228×	body	80	nan
6.0ms	34×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	13×	body	80	valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.7b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 5.0 (* v v)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

3.0ms	(- 1.0 (* 5.0 (* v v)))
8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
8.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 1.0 (* 5.0 (* v v)))
80.0ms	(/ (- 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

101 → 101

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	391	750
1	1491	682
2	5002	678

prune188.0ms

Filtered

101 candidates to 78 candidates (77.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.7b

Counts

102 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.7b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
49×	`times-frac`
39×	`prod-diff`
13×	`fma-neg`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
9.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
28.0ms	(* 5.0 (* v v))
4.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	576	2948
1	1941	1851
2	5003	1839

prune277.0ms

Filtered

151 candidates to 97 candidates (64.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	150	7	157

Merged error: 0.6b

Counts

157 → 7

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))
0.7b	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
2.5b	(log (exp (* 5.0 (* v v))))

rewrite23.0ms

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:

11.0ms	(/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
2.0ms	(log (exp (* 5.0 (* v v))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
25.0ms	(log (exp (* 5.0 (* v v))))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

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

prune231.0ms

Filtered

112 candidates to 80 candidates (71.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Merged error: 0.6b

Counts

119 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.7b	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
2.5b	(log (exp (* 5.0 (* v v))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-l` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod`
1×	`acos-asin` `expm1-log1p` `exp-prod` `exp-to-pow` `rem-log-exp` `associate-r` `*-commutative` `expm1-udef` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

1.0ms	(expm1 (log1p (acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
2.0ms	(log (exp (* 5.0 (* v v))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(expm1 (log1p (acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (log (exp (* 5.0 (* v v))))) (- (* v v) 1.0)))
29.0ms	(log (exp (* 5.0 (* v v))))

simplify124.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	159	456
1	415	389
2	1052	389
3	3612	389
4	5002	389

prune142.0ms

Filtered

70 candidates to 48 candidates (68.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 0.6b

Counts

78 → 8

regimes142.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11
1	14	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2996×	body	2560	valid
578.0ms	2502×	body	1280	valid
217.0ms	7857×	body	80	nan
205.0ms	1237×	body	640	valid
79.0ms	629×	body	320	valid
35.0ms	421×	body	160	valid
10.0ms	215×	body	80	valid