Details

Time bar (total: 26.7s)

sample267.0ms

Algorithm
intervals
Results
31.0ms358×body80nan
17.0ms157×body80valid
16.0ms32×body1280valid
12.0ms34×body640valid
8.0ms21×body640nan
7.0ms18×body1280nan
5.0ms20×body320valid
3.0ms11×body320nan
3.0ms13×body160valid
1.0ms6×body160nan

simplify3.8s

Counts
1 → 1
Iterations
IterNodes
done5000
74703
61985
51092
4526
3232
2100
141
018

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b
(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
0.3b
(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
13.1b
(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
19.5b
(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
76×times-frac
74×add-sqr-sqrt
59×*-un-lft-identity add-cube-cbrt
42×associate-*r*
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* sqrt-div associate-/l* add-log-exp
5×unswap-sqr
4×expm1-log1p-u flip3-- associate-/r/ log1p-expm1-u flip--
3×associate-*l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×rem-sqrt-square sqrt-undiv clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down associate-*r/ *-commutative
Counts
4 → 164
Calls
4 calls:
127.0ms
(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
33.0ms
(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
17.0ms
(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
29.0ms
(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

series2.2s

Counts
4 → 12
Calls
4 calls:
638.0ms
(* t (/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))))
743.0ms
(/ (sqrt 2.0) (sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))))
367.0ms
(- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
476.0ms
(sqrt (- (* (fma l l (* (* t t) 2.0)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

simplify1.6s

Counts
176 → 176
Iterations
IterNodes
done5000
22141
1518
0216

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.9b

localize38.0ms

Local error

Found 4 expressions with local error:

4.4b
(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
6.4b
(/ (* l l) x)
8.3b
(/ (* t t) x)
25.2b
(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 71
Calls
4 calls:
0.0ms
(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
9.0ms
(/ (* l l) x)
24.0ms
(/ (* t t) x)
3.0ms
(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

series390.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x))))
24.0ms
(/ (* l l) x)
23.0ms
(/ (* t t) x)
239.0ms
(sqrt (fma (/ (* t t) x) 4.0 (* 2.0 (fma t t (/ (* l l) x)))))

simplify1.3s

Counts
83 → 83
Iterations
IterNodes
done5000
22768
1352
0131

prune850.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.6b

localize89.0ms

Local error

Found 4 expressions with local error:

4.4b
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
4.4b
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
25.2b
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
25.2b
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 50
Calls
4 calls:
0.0ms
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
0.0ms
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
1.0ms
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
1.0ms
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
119.0ms
(fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0))
234.0ms
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))
269.0ms
(sqrt (fma (/ t (/ x t)) 4.0 (* (fma (/ l x) l (* t t)) 2.0)))

simplify1.3s

Counts
62 → 62
Iterations
IterNodes
done5000
32508
2427
1128
061

prune806.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

localize158.0ms

Local error

Found 4 expressions with local error:

25.2b
(sqrt (* (* (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t))))) (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))) (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))))
26.0b
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))
26.0b
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))
26.0b
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
15×sqrt-pow1
12×pow1/3
9×cbrt-prod pow-prod-up
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 65
Calls
4 calls:
24.0ms
(sqrt (* (* (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t))))) (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))) (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))))
1.0ms
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))
1.0ms
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))
1.0ms
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
235.0ms
(sqrt (* (* (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t))))) (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))) (cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))))
301.0ms
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))
343.0ms
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))
299.0ms
(cbrt (fma (/ (* 4.0 t) x) t (* 2.0 (fma (/ l x) l (* t t)))))

simplify1.0s

Counts
77 → 77
Iterations
IterNodes
done5001
32092
2554
1219
0107

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.6b

regimes838.0ms

Accuracy

77.5% (5.4b remaining)

Error of 9.5b against oracle of 4.1b and baseline of 28.0b

bsearch1.0s

Steps
ItersRangePoint
9
8.029604051112713e+47
4.771574953324125e+55
4.709683245749164e+55
10
3.1913228427846884e-157
3.080469255526081e-145
3.2479806443803153e-157
10
7.396249846299801e-250
6.414192999540213e-240
1.7261488547836046e-242
6
-2.1766003953136084e+147
-1.757623460431069e+146
-2.9230270404741246e+146

simplify11.0ms

Iterations
IterNodes
done78
178
062

end0.0ms

sample6.2s

Algorithm
intervals
Results
1.8s9922×body80nan
757.0ms5112×body80valid
648.0ms625×body640nan
537.0ms819×body1280valid
504.0ms365×body160valid
441.0ms1060×body640valid
397.0ms599×body1280nan
263.0ms644×body320valid
130.0ms335×body320nan
83.0ms191×body160nan