Details

sample122.0ms

Algorithm

intervals

Results

26.0ms	275×	body	80	nan
17.0ms	174×	body	80	valid
17.0ms	30×	body	640	valid
10.0ms	21×	body	1280	valid
8.0ms	16×	body	1280	nan
6.0ms	17×	body	640	nan
5.0ms	19×	body	320	valid
3.0ms	12×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	6×	body	160	nan

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	14
1	101	14
2	234	14
3	525	14
4	1016	14
5	1701	14
6	3626	14
7	5002	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
14.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

28.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
3.0ms	(* (sqrt 2.0) t)
65.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
216.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify62.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	446	1290
1	2206	1177
2	5002	1172

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.7b	(/ (pow l 2) x)
10.2b	(/ (pow t 2) x)
27.6b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
3.0ms	(/ (pow l 2) x)
3.0ms	(/ (pow t 2) x)
44.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	377	811
1	1351	724
2	5001	715

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
4.8b	(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
10.2b	(/ (pow t 2) x)
27.6b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
16×	`cbrt-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`cbrt-undiv` `pow2` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
0.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (cbrt x) (cbrt x))
20.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
7.0ms	(/ (pow t 2) x)
44.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	363	893
1	1416	796
2	5001	770

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (* (* (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))) (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))) (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))))
28.5b	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))
28.5b	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))
28.5b	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 65

Calls

4 calls:

12.0ms	(sqrt (* (* (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))) (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))) (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))))
0.0ms	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))
0.0ms	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))
1.0ms	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (* (* (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))) (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))) (cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))))
50.0ms	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))
51.0ms	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))
50.0ms	(cbrt (fma 2.0 (pow t 2) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify159.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	259	1651
1	830	1498
2	4336	1398
3	5001	1392

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.1b

regimes1.2s

Accuracy

76.7% (5.6b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 27.9b

bsearch377.0ms

Steps

Iters	Range		Point
8	9.590264166808954e+144	8.453545774587938e+148	1.5502557159326679e+147
9	-8.482171429905235e-305	2.395718612136343e-306	-8.390748927516048e-305
8	-4.1380436021190385e-157	-3.928546282868914e-160	-6.964659965402052e-160
9	-4.226622760104674e+150	-4.9074344296754804e+143	-1.2719019289673334e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	97
1	57	97

end0.0ms

sample3.6s

Algorithm

intervals

Results

947.0ms	9844×	body	80	nan
501.0ms	5122×	body	80	valid
419.0ms	873×	body	1280	valid
387.0ms	999×	body	640	valid
286.0ms	609×	body	1280	nan
217.0ms	586×	body	640	nan
188.0ms	666×	body	320	valid
100.0ms	358×	body	320	nan
66.0ms	340×	body	160	valid
34.0ms	183×	body	160	nan