Details

sample77.0ms

Algorithm

intervals

Results

33.0ms	100×	body	2560	valid
15.0ms	68×	body	1280	valid
8.0ms	280×	body	80	nan
7.0ms	46×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	10×	body	80	valid

simplify99.0ms

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: 0.6b

Counts

2 → 1

localize7.0ms

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))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite24.0ms

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)))
12.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- 1.0 (* 5.0 (* v v)))
81.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

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

prune197.0ms

Filtered

101 candidates to 78 candidates (77.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 0.6b

Counts

102 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite30.0ms

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:

9.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 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:

30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
83.0ms	(/ (- 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)))

simplify69.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	576	2948
1	1941	1851
2	5001	1839

prune449.0ms

Filtered

151 candidates to 97 candidates (64.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	151	4	155

Merged error: 0.6b

Counts

155 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))
0.0b	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
0.2b	(* 5.0 (* v v))
1.6b	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`times-frac`
34×	`add-cube-cbrt`
33×	`add-exp-log`
25×	`associate-r`
23×	`add-cbrt-cube`
21×	`associate-l`
14×	`difference-of-squares`
11×	`pow1` `prod-exp`
9×	`div-exp`
7×	`sqrt-prod` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `div-inv` `distribute-lft-out` `associate-/l*`
2×	`rec-exp` `1-exp` `*-commutative` `associate-/l/`
1×	`acos-asin` `frac-times` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `clear-num` `flip-+`

Counts

4 → 151

Calls

4 calls:

9.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))
23.0ms	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))
199.0ms	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
29.0ms	(* 5.0 (* v v))
12.0ms	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	805	1872
1	3926	1600
2	5003	1563

prune327.0ms

Filtered

163 candidates to 111 candidates (68.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	162	5	167

Merged error: 0.6b

Counts

167 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))))
0.0b	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
0.2b	(* 5.0 (* v v))
1.6b	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
37×	`times-frac`
31×	`add-exp-log`
25×	`add-cube-cbrt` `associate-r`
21×	`associate-l` `add-cbrt-cube`
12×	`pow1`
11×	`prod-exp`
8×	`div-exp`
7×	`cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `exp-prod` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-sum` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--`
2×	`rec-exp` `1-exp` `*-commutative` `div-inv`
1×	`acos-asin` `frac-times` `flip3--` `flip3-+` `associate-r/` `associate-l/` `log-pow` `flip--` `flip-+` `rem-exp-log`

Counts

4 → 122

Calls

4 calls:

2.0ms	(exp (log (acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))))
27.0ms	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (log (acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))))
206.0ms	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
24.0ms	(* 5.0 (* v v))
12.0ms	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	692	1612
1	3222	1348
2	5001	1281

prune306.0ms

Filtered

134 candidates to 90 candidates (67.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Merged error: 0.6b

Counts

139 → 6

regimes105.0ms

Accuracy

0% (0.5b remaining)

Error of 1.1b against oracle of 0.6b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	3064×	body	2560	valid
553.0ms	2456×	body	1280	valid
216.0ms	7965×	body	80	nan
197.0ms	1226×	body	640	valid
74.0ms	625×	body	320	valid
33.0ms	401×	body	160	valid
11.0ms	228×	body	80	valid