Details

sample47.0ms

Algorithm

intervals

Results

23.0ms	285×	body	80	valid
7.0ms	105×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	46	7
2	72	7
3	99	7
4	120	7
5	120	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
3.9b	(* (* x y) z)
8.0b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
20.8b	(sqrt (- (* z z) (* t a)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
11.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	368	630
1	1941	560
2	5001	551

prune278.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
3.9b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
20.8b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 142

Calls

4 calls:

7.0ms	(/ (sqrt (- (* z z) (* t a))) z)
3.0ms	(- (* z z) (* t a))
10.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (sqrt (- (* z z) (* t a))) z)
32.0ms	(- (* z z) (* t a))
83.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	543	1379
1	2448	1281
2	5001	1260

prune396.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
0.6b	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
3.9b	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
20.8b	(sqrt (- (* z z) (* t a)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
143×	`add-sqr-sqrt`
142×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-r`
66×	`sqrt-prod`
60×	`add-exp-log`
30×	`add-cbrt-cube`
22×	`associate-/r*`
21×	`div-exp` `prod-exp`
11×	`pow1`
9×	`cbrt-undiv` `cbrt-unprod` `div-inv`
6×	`rec-exp` `1-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `associate-l` `prod-diff` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 253

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
10.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
31.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
51.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
86.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	987	2740
1	5001	2395

prune572.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
3.9b	(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
20.8b	(sqrt (- (* z z) (* t a)))
20.8b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
7×	`associate-/r*`
6×	`pow1` `sqrt-prod` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3--` `flip--` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
13.0ms	(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
85.0ms	(/ (* x y) (/ (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))) z))
63.0ms	(sqrt (- (* z z) (* t a)))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	425	1023
1	1996	802
2	5001	795

prune313.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.5b

regimes372.0ms

Accuracy

80.4% (3.7b remaining)

Error of 7.1b against oracle of 3.4b and baseline of 22.4b

bsearch174.0ms

Steps

Iters	Range	Point
6	6.6223722196249e+100	8.029854166877476e+101	1.2636554807731635e+101
10	-2.550968469978379e-179	-2.0858349132470847e-190	-1.1528738359290673e-189
9	-2.9927016332090275e+150	-2.351439734919327e+144	-1.1613085318430635e+146

Iters

Range

Point

6.6223722196249e+100

8.029854166877476e+101

1.2636554807731635e+101

-2.550968469978379e-179

-2.0858349132470847e-190

-1.1528738359290673e-189

-2.9927016332090275e+150

-2.351439734919327e+144

-1.1613085318430635e+146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	18
1	53	18
2	53	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

819.0ms	8900×	body	80	valid
215.0ms	3015×	body	80	nan