Details

Time bar (total: 24.8s)

sample82.0ms

Algorithm
intervals
Results
45.0ms272×body80valid
13.0ms91×body80nan

simplify171.0ms

Counts
1 → 1
Iterations
IterNodes
8170
7170
6168
5164
4157
3132
276
139
020

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.8b

localize183.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (fma c (* a -4) (* b b))) b)
1.0b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
24.0b
(sqrt (fma c (* a -4) (* b b)))
24.0b
(sqrt (fma c (* a -4) (* b b)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
16.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
21.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
2.0ms
(sqrt (fma c (* a -4) (* b b)))
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
95.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
127.0ms
(sqrt (fma c (* a -4) (* b b)))
120.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.1s

Counts
177 → 177
Iterations
IterNodes
32247
2835
1418
0194

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize156.0ms

Local error

Found 4 expressions with local error:

13.0b
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
24.0b
(sqrt (fma c (* a -4) (* b b)))
24.0b
(sqrt (fma c (* a -4) (* b b)))
24.0b
(sqrt (fma c (* a -4) (* b b)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
11.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(sqrt (fma c (* a -4) (* b b)))
2.0ms
(sqrt (fma c (* a -4) (* b b)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
85.0ms
(sqrt (fma c (* a -4) (* b b)))
98.0ms
(sqrt (fma c (* a -4) (* b b)))
105.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.3s

Counts
98 → 98
Iterations
IterNodes
44259
31384
2489
1209
097

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize217.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (fma c (* a -4) (* b b)))
24.7b
(cbrt (fma c (* a -4) (* b b)))
24.7b
(cbrt (fma c (* a -4) (* b b)))
24.7b
(cbrt (fma c (* a -4) (* b b)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(cbrt (fma c (* a -4) (* b b)))
1.0ms
(cbrt (fma c (* a -4) (* b b)))
2.0ms
(cbrt (fma c (* a -4) (* b b)))

series844.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (fma c (* a -4) (* b b)))
260.0ms
(cbrt (fma c (* a -4) (* b b)))
218.0ms
(cbrt (fma c (* a -4) (* b b)))
262.0ms
(cbrt (fma c (* a -4) (* b b)))

simplify2.8s

Counts
70 → 70
Iterations
IterNodes
56441
41992
3663
2256
1124
068

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize198.0ms

Local error

Found 4 expressions with local error:

24.7b
(cbrt (fma c (* a -4) (* b b)))
24.7b
(cbrt (fma c (* a -4) (* b b)))
24.7b
(cbrt (fma c (* a -4) (* b b)))
24.7b
(cbrt (* (* (cbrt (fma c (* a -4) (* b b))) (cbrt (fma c (* a -4) (* b b)))) (cbrt (fma c (* a -4) (* b b)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×pow3 rem-cbrt-cube
Counts
4 → 55
Calls
4 calls:
2.0ms
(cbrt (fma c (* a -4) (* b b)))
1.0ms
(cbrt (fma c (* a -4) (* b b)))
1.0ms
(cbrt (fma c (* a -4) (* b b)))
29.0ms
(cbrt (* (* (cbrt (fma c (* a -4) (* b b))) (cbrt (fma c (* a -4) (* b b)))) (cbrt (fma c (* a -4) (* b b)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
249.0ms
(cbrt (fma c (* a -4) (* b b)))
271.0ms
(cbrt (fma c (* a -4) (* b b)))
274.0ms
(cbrt (fma c (* a -4) (* b b)))
287.0ms
(cbrt (* (* (cbrt (fma c (* a -4) (* b b))) (cbrt (fma c (* a -4) (* b b)))) (cbrt (fma c (* a -4) (* b b)))))

simplify3.0s

Counts
67 → 67
Iterations
IterNodes
56503
41901
3627
2242
1117
064

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.1b

regimes249.0ms

Accuracy

86.8% (0.9b remaining)

Error of 13.9b against oracle of 12.9b and baseline of 20.1b

bsearch118.0ms

Steps
ItersRangePoint
6
2.332248586404817e+54
2.734436825826664e+55
2.6656023684116586e+55

simplify9.0ms

Iterations
IterNodes
240
140
035

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.0s8762×body80valid
521.0ms2913×body80nan