Details

Time bar (total: 18.7s)

sample112.0ms

Algorithm
intervals
Results
69.0ms284×body80valid
19.0ms91×body80nan

simplify164.0ms

Counts
1 → 1
Iterations
IterNodes
8152
7152
6151
5144
4132
3101
262
135
020

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize165.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
27.8b
(sqrt (- (* b b) (* (* 4 a) c)))
27.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 67
Calls
4 calls:
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify872.0ms

Counts
79 → 79
Iterations
IterNodes
32441
2760
1248
0102

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

localize188.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
3.9b
(* (/ a b) c)
4.5b
(/ (* (- (* (/ a b) c) b) 2) (* 2 a))
27.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cbrt-cube add-exp-log
17×*-un-lft-identity
13×associate-*l* add-cube-cbrt
11×times-frac
8×add-log-exp
7×pow1
6×prod-exp cbrt-unprod
5×cbrt-undiv div-exp
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* associate-*l/ flip--
2×sqrt-div diff-log div-inv distribute-lft-out-- difference-of-squares unswap-sqr associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* sub-neg distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log *-commutative associate-/l*
Counts
4 → 92
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms
(* (/ a b) c)
21.0ms
(/ (* (- (* (/ a b) c) b) 2) (* 2 a))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
39.0ms
(* (/ a b) c)
52.0ms
(/ (* (- (* (/ a b) c) b) 2) (* 2 a))
109.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.3s

Counts
104 → 104
Iterations
IterNodes
22250
1532
0202

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4 a) c)
1.2b
(- (* b b) (* (* 4 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
27.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-cbrt-cube add-exp-log
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- diff-log associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 associate-*l* neg-log *-commutative
Counts
4 → 67
Calls
4 calls:
14.0ms
(* (* 4 a) c)
7.0ms
(- (* b b) (* (* 4 a) c))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (* 4 a) c)
88.0ms
(- (* b b) (* (* 4 a) c))
122.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
115.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts
79 → 79
Iterations
IterNodes
33567
21004
1314
0129

prune934.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize184.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (* (* 4 a) c))
15.3b
(cbrt (* (* 4 a) c))
15.3b
(cbrt (* (* 4 a) c))
27.8b
(sqrt (- (* b b) (* (* (cbrt (* (* 4 a) c)) (cbrt (* (* 4 a) c))) (cbrt (* (* 4 a) c)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 46
Calls
4 calls:
13.0ms
(cbrt (* (* 4 a) c))
9.0ms
(cbrt (* (* 4 a) c))
9.0ms
(cbrt (* (* 4 a) c))
11.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 4 a) c)) (cbrt (* (* 4 a) c))) (cbrt (* (* 4 a) c)))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (* (* 4 a) c))
139.0ms
(cbrt (* (* 4 a) c))
112.0ms
(cbrt (* (* 4 a) c))
210.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 4 a) c)) (cbrt (* (* 4 a) c))) (cbrt (* (* 4 a) c)))))

simplify3.7s

Counts
58 → 58
Iterations
IterNodes
46417
31631
2495
1205
089

prune884.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.7b

regimes451.0ms

Accuracy

87.8% (1.8b remaining)

Error of 7.4b against oracle of 5.6b and baseline of 20.4b

bsearch298.0ms

Steps
ItersRangePoint
9
2.662790715355376e+61
3.00977400694497e+66
9.179168538250646e+63
9
-229886301330938.94
-710549284.1101115
-227369802444031.66

simplify11.0ms

Iterations
IterNodes
258
158
048

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.9s8749×body80valid
628.0ms2993×body80nan