Details

Time bar (total: 21.1s)

sample88.0ms

Algorithm
intervals
Results
19.0ms43×body2560valid
13.0ms175×body80valid
12.0ms31×body1280valid
8.0ms106×body80nan
5.0ms18×body640valid
2.0ms4×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify163.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01217
12517
26716
312416
413716
done13716

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
37.0ms
(* (* 3.0 a) c)
18.0ms
(- (* b b) (* (* 3.0 a) c))
100.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (* 3.0 a) c)
61.0ms
(- (* b b) (* (* 3.0 a) c))
112.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
92.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.9s

Counts
106 → 106
Iterations

Useful iterations: done (3.9s)

IterNodesCost
01611863
116211491
done50001350

prune443.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.4b

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
79.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
81.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
18.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
125.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
98.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.9s

Counts
128 → 128
Iterations

Useful iterations: done (3.9s)

IterNodesCost
01132856
113272200
done50001964

prune549.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.4b

localize49.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×*-un-lft-identity
22×sqrt-prod
21×add-cube-cbrt
18×prod-diff
7×pow1
6×fma-neg sqrt-div add-log-exp
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 92
Calls
4 calls:
59.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
104.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.6s

Counts
104 → 104
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01132042
113271618
done50001496

prune508.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 13.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 3.0 a) c))
25.5b
(cbrt (- (* b b) (* (* 3.0 a) c)))
25.5b
(cbrt (- (* b b) (* (* 3.0 a) c)))
25.9b
(fma (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
4×pow1 add-exp-log expm1-log1p-u cbrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×pow1/3
1×sub-neg fma-neg diff-log prod-diff fma-udef
Counts
4 → 56
Calls
4 calls:
12.0ms
(- (* b b) (* (* 3.0 a) c))
6.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
0.0ms
(fma (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

series534.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (* b b) (* (* 3.0 a) c))
146.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
158.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
174.0ms
(fma (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

simplify941.0ms

Counts
68 → 68
Iterations

Useful iterations: done (937.0ms)

IterNodesCost
01241335
15461280
done50011138

prune488.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 13.4b

regimes552.0ms

Accuracy

86.8% (2.9b remaining)

Error of 15.4b against oracle of 12.5b and baseline of 34.3b

bsearch156.0ms

Steps
ItersRangePoint
8
6.197633265120061e-63
2.959335775732887e-60
5.828767493902222e-61
8
-4.810799056667626e+157
-8.81647488783933e+153
-1.367002129773412e+154

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02750
13250
done3250

end0.0ms

sample3.5s

Algorithm
intervals
Results
947.0ms1076×body2560valid
642.0ms491×body640valid
588.0ms5872×body80valid
326.0ms885×body1280valid
296.0ms3010×body80nan
73.0ms218×body320valid
53.0ms105×body5120valid
12.0ms95×body160valid