Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	194×	body	80	valid
8.0ms	40×	body	2560	valid
5.0ms	28×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `flip--` `associate-/l/`
1×	`neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 83

Calls

4 calls:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
19.0ms	(* (* 3.0 a) c)
48.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	433	741
1	1995	651
2	5001	645

prune265.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

23.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.0ms	(* (* 3.0 a) c)
44.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	395	712
1	1966	621
2	5002	612

prune253.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
31×	`add-exp-log` `times-frac`
22×	`add-cube-cbrt` `associate-r`
21×	`add-cbrt-cube`
14×	`associate-l`
12×	`pow1`
11×	`prod-exp`
8×	`div-exp`
7×	`cbrt-unprod`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `*-commutative` `flip--` `div-inv`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `associate-l/`

Counts

4 → 117

Calls

4 calls:

58.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
20.0ms	(* (* 3.0 a) c)
48.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	638	1197
1	3199	1045
2	5001	1031

prune329.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) 3.0)
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
110×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
24×	`distribute-lft-out`
19×	`associate-/l*`
14×	`add-exp-log` `add-cbrt-cube`
12×	`distribute-rgt-neg-in`
10×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `div-sub` `flip--`
1×	`neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 150

Calls

4 calls:

39.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) 3.0)
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) 3.0)
19.0ms	(* (* 3.0 a) c)
50.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	636	1923
1	2592	1829
2	5002	1813

prune405.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.7b

regimes436.0ms

Accuracy

82.9% (4.9b remaining)

Error of 10.7b against oracle of 5.8b and baseline of 34.3b

bsearch134.0ms

Steps

Iters	Range		Point
8	10920358539895.18	4.2009936632527795e+17	11181767625882.13
11	-1.829086240692416e+154	-2.187052964502477e+134	-8.555281377770497e+140

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	19
1	50	19
2	50	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

240.0ms	1105×	body	2560	valid
222.0ms	5867×	body	80	valid
156.0ms	909×	body	1280	valid
102.0ms	2861×	body	80	nan
57.0ms	422×	body	640	valid
25.0ms	96×	body	5120	valid
24.0ms	214×	body	320	valid
8.0ms	119×	body	160	valid