Details

sample92.0ms

Algorithm

intervals

Results

37.0ms	100×	body	2560	valid
19.0ms	68×	body	1280	valid
9.0ms	280×	body	80	nan
8.0ms	46×	body	640	valid
2.0ms	16×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	10×	body	80	valid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	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)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp`
4×	`associate-/r*` `difference-of-squares`
3×	`flip3--` `associate-l` `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 → 75

Calls

4 calls:

3.0ms	(- 1.0 (* 5.0 (* v v)))
7.0ms	(/ (- 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)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- 1.0 (* 5.0 (* v v)))
76.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
26.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	355	664
1	1356	609
2	5001	605

prune151.0ms

Filtered

87 candidates to 65 candidates (74.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.6b

Counts

88 → 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)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
4×	`associate-/r*`
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` `div-inv` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

7.0ms	(- (/ 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))
5.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
79.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
23.0ms	(* 5.0 (* v v))
7.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	409	840
1	1459	784
2	5001	780

prune178.0ms

Filtered

91 candidates to 69 candidates (75.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	90	5	95

Merged error: 0.6b

Counts

95 → 5

localize12.0ms

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)))))

rewrite46.0ms

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×	`pow-prod-down` `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 → 143

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))
26.0ms	(* (/ 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)))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 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))))
23.0ms	(* 5.0 (* v v))
11.0ms	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	781	1807
1	3800	1556
2	5002	1522

prune284.0ms

Filtered

155 candidates to 103 candidates (66.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	3	3
Picked	1	0	1
Done	1	0	1
Total	156	4	160

Merged error: 0.6b

Counts

160 → 4

localize20.0ms

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)))))

rewrite36.0ms

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` `exp-prod` `pow-prod-down` `associate-/r/` `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 → 114

Calls

4 calls:

2.0ms	(exp (log (acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))))
22.0ms	(* (/ 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)))))))
202.0ms	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
29.0ms	(* 5.0 (* v v))
11.0ms	(acos (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	676	1534
1	3149	1293
2	5002	1229

prune269.0ms

Filtered

126 candidates to 83 candidates (65.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	125	5	130

Merged error: 0.6b

Counts

130 → 5

regimes86.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	3064×	body	2560	valid
554.0ms	2456×	body	1280	valid
223.0ms	7965×	body	80	nan
201.0ms	1226×	body	640	valid
73.0ms	625×	body	320	valid
33.0ms	401×	body	160	valid
11.0ms	228×	body	80	valid