Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	35×	body	1280	valid
7.0ms	194×	body	80	valid
6.0ms	29×	body	2560	valid
2.0ms	71×	body	80	nan
1.0ms	8×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
45.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune289.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.6b	(- (* b b) (* (* 3.0 a) c))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune245.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.6b	(- (* b b) (* 3.0 (* a c)))
0.7b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
20.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-r` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
3.0ms	(- (* b b) (* 3.0 (* a c)))
12.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 3.0 (* a c))
43.0ms	(- (* b b) (* 3.0 (* a c)))
79.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
81.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	330	529
1	1217	478
2	5001	467

prune231.0ms

Filtered

92 candidates to 70 candidates (76.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.6b	(- (* b b) (* (* 3.0 a) c))
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

25.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	399	830
1	1688	721
2	5001	704

prune243.0ms

Filtered

101 candidates to 80 candidates (79.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.5b

regimes369.0ms

Accuracy

85% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 34.2b

bsearch64.0ms

Steps

Iters	Range		Point
4	3.761319948406741e-42	5.3303289756926204e-42	4.300666801536262e-42
7	-3.383610052221448e+122	-1.4683631826756258e+120	-4.7297088727929035e+120

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

238.0ms	1110×	body	2560	valid
220.0ms	5800×	body	80	valid
152.0ms	876×	body	1280	valid
103.0ms	2950×	body	80	nan
61.0ms	458×	body	640	valid
31.0ms	113×	body	5120	valid
24.0ms	235×	body	320	valid
8.0ms	110×	body	160	valid