Details

Time bar (total: 19.4s)

sample80.0ms

Algorithm
intervals
Results
42.0ms272×body80valid
13.0ms85×body80nan

simplify200.0ms

Counts
1 → 1
Iterations
IterNodes
8168
7168
6166
5160
4151
3125
275
138
020

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize135.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite72.0ms

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:
28.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
112.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
112.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
124.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify950.0ms

Counts
79 → 79
Iterations
IterNodes
32441
2760
1248
0102

prune637.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize140.0ms

Local error

Found 4 expressions with local error:

13.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 64
Calls
4 calls:
18.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify798.0ms

Counts
76 → 76
Iterations
IterNodes
32124
2658
1224
091

prune669.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize180.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 60
Calls
4 calls:
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
16.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
122.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
138.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.2s

Counts
72 → 72
Iterations
IterNodes
46322
31876
2580
1200
089

prune837.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize191.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
139.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
100.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
101.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify3.3s

Counts
70 → 70
Iterations
IterNodes
46322
31876
2580
1200
089

prune839.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

regimes433.0ms

Accuracy

91.7% (1.1b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 18.8b

bsearch359.0ms

Steps
ItersRangePoint
8
2.231296991249122e+66
2.5939819947174796e+69
2.559678284282607e+69
9
-2.2464591800446616e+91
-3.153507839293123e+86
-2.723731815549707e+89

simplify28.0ms

Iterations
IterNodes
253
153
044

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.4s8671×body80valid
608.0ms2938×body80nan