Details

Time bar (total: 20.8s)

sample56.0ms

Algorithm
intervals
Results
26.0ms281×body80valid
8.0ms87×body80nan

simplify155.0ms

Counts
1 → 1
Iterations
IterNodes
done160
7160
6159
5152
4140
3108
263
136
020

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize145.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log 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 → 155
Calls
4 calls:
29.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
106.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
126.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
143.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.0s

Counts
167 → 167
Iterations
IterNodes
done5000
34317
21207
1435
0181

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize141.0ms

Local error

Found 4 expressions with local error:

12.2b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×fma-def *-un-lft-identity add-cube-cbrt
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative neg-mul-1 flip3-+ neg-log associate-+l- flip-+
Counts
4 → 80
Calls
4 calls:
9.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
129.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
130.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.9s

Counts
92 → 92
Iterations
IterNodes
done5001
33147
2801
1250
091

prune956.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.5b

localize224.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
Counts
4 → 72
Calls
4 calls:
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
125.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
122.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
95.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.2s

Counts
84 → 84
Iterations
IterNodes
done5000
31620
2441
1139
054

prune801.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.5b

localize212.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 66
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
17.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
116.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
139.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
119.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts
78 → 78
Iterations
IterNodes
done5002
32070
2609
1215
093

prune753.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.5b

regimes353.0ms

Accuracy

92.4% (1.1b remaining)

Error of 7.0b against oracle of 5.9b and baseline of 20.1b

bsearch372.0ms

Steps
ItersRangePoint
10
6.2301214455520334e+75
1.5034565205168897e+88
2.019000267824195e+87
10
-4.186518194588193e+147
-3.370135567630554e+133
-5.300564053552496e+135

simplify25.0ms

Iterations
IterNodes
done58
158
048

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.6s8737×body80valid
348.0ms2854×body80nan