Details

Time bar (total: 35.2s)

sample41.0ms

Algorithm
intervals
Results
15.0ms282×body80valid
5.0ms104×body80nan

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.1b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.3b
(* (* x y) z)
7.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.5b
(sqrt (- (* z z) (* t a)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
1106×add-sqr-sqrt
514×associate-*l*
470×*-un-lft-identity
440×times-frac
408×sqrt-prod
291×unswap-sqr
270×add-cube-cbrt
250×difference-of-squares
216×associate-*r*
180×prod-diff
122×*-commutative
100×distribute-lft-out--
89×swap-sqr
22×associate-/l*
20×associate-/r*
18×add-exp-log add-cbrt-cube
15×fma-neg
10×pow1
6×prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×cbrt-undiv flip3-- div-exp pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log clear-num div-inv
Counts
4 → 789
Calls
4 calls:
23.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
34.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
29.0ms
(sqrt (- (* z z) (* t a)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
88.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify129.0ms

Algorithm
egg-herbie
Counts
801 → 801
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0173510569
150019141

prune1.1s

Filtered
801 candidates to 275 candidates (34.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New7938801
Fresh000
Picked101
Done000
Total7948802

Merged error: 3.5b

Counts
802 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ (cbrt z) (sqrt (cbrt (- (* z z) (* t a))))))
1.7b
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z))))
24.3b
(cbrt (- (* z z) (* t a)))
24.3b
(cbrt (- (* z z) (* t a)))

rewrite2.7s

Algorithm
rewrite-expression-head
Rules
9752×add-sqr-sqrt
7268×times-frac
5272×*-un-lft-identity
5267×associate-/r*
5230×cbrt-prod
4399×add-cube-cbrt
3200×frac-times
3161×associate-*l*
2224×sqrt-prod
1944×unswap-sqr
1812×associate-*r*
1302×swap-sqr
1090×difference-of-squares
1021×associate-/l*
613×*-commutative
436×distribute-lft-out--
219×add-cbrt-cube
138×clear-num
137×frac-2neg
114×cbrt-undiv
100×associate-*l/
95×cbrt-unprod
90×add-exp-log
68×associate-/r/
61×div-inv
37×div-exp
32×associate-*r/
29×prod-exp
6×pow1 cbrt-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-- flip--
2×pow1/3 sqrt-div un-div-inv
1×pow-prod-down
Counts
4 → 5984
Calls
4 calls:
1.6s
(* (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ (cbrt z) (sqrt (cbrt (- (* z z) (* t a))))))
46.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z))))
14.0ms
(cbrt (- (* z z) (* t a)))
17.0ms
(cbrt (- (* z z) (* t a)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ (cbrt z) (sqrt (cbrt (- (* z z) (* t a))))))
168.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z))))
85.0ms
(cbrt (- (* z z) (* t a)))
88.0ms
(cbrt (- (* z z) (* t a)))

simplify1.4s

Algorithm
egg-herbie
Counts
5996 → 5996
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
05366181915

prune22.5s

Filtered
5996 candidates to 3917 candidates (65.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New599605996
Fresh077
Picked011
Done000
Total599686004

Merged error: 3.5b

Counts
6004 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
2.2b
(* x (/ (* y z) (sqrt (- (* z z) (* t a)))))
5.1b
(/ (* y z) (sqrt (- (* z z) (* t a))))
23.5b
(sqrt (- (* z z) (* t a)))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
1152×add-sqr-sqrt
521×*-un-lft-identity
484×times-frac
461×sqrt-prod
456×associate-*r*
326×associate-*l*
295×add-cube-cbrt
280×difference-of-squares
273×unswap-sqr
180×prod-diff
127×*-commutative
112×distribute-lft-out--
95×swap-sqr
40×associate-/r*
35×associate-*r/
26×associate-/l*
18×add-exp-log add-cbrt-cube
15×fma-neg
7×pow1
6×sqrt-div add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv expm1-log1p-u flip3-- div-exp associate-/r/ flip-- log1p-expm1-u
3×clear-num un-div-inv
2×frac-2neg div-inv
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down
Counts
4 → 853
Calls
4 calls:
23.0ms
(- (* z z) (* t a))
76.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* t a)))))
26.0ms
(/ (* y z) (sqrt (- (* z z) (* t a))))
29.0ms
(sqrt (- (* z z) (* t a)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
86.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* t a)))))
61.0ms
(/ (* y z) (sqrt (- (* z z) (* t a))))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify127.0ms

Algorithm
egg-herbie
Counts
865 → 865
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
017119261
150017786

prune1.3s

Filtered
865 candidates to 319 candidates (36.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New8623865
Fresh246
Picked011
Done011
Total8649873

Merged error: 3.5b

Counts
873 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.9b
(/ y (/ (sqrt (- (* z z) (* t a))) (* x z)))
9.1b
(/ (sqrt (- (* z z) (* t a))) (* x z))
23.5b
(sqrt (- (* z z) (* t a)))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
2655×add-sqr-sqrt
1932×times-frac
1306×*-un-lft-identity
1071×sqrt-prod
794×add-cube-cbrt
646×associate-*l*
640×difference-of-squares
578×unswap-sqr
390×associate-*r*
268×associate-/r*
258×*-commutative
256×distribute-lft-out--
180×prod-diff
167×swap-sqr
43×associate-/l*
37×associate-/r/
18×add-exp-log add-cbrt-cube
15×fma-neg
7×cbrt-undiv div-exp
6×sqrt-div div-inv add-log-exp
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
3×frac-2neg clear-num
2×prod-exp cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 1578
Calls
4 calls:
19.0ms
(- (* z z) (* t a))
67.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) (* x z)))
31.0ms
(/ (sqrt (- (* z z) (* t a))) (* x z))
25.0ms
(sqrt (- (* z z) (* t a)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
83.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) (* x z)))
72.0ms
(/ (sqrt (- (* z z) (* t a))) (* x z))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify257.0ms

Algorithm
egg-herbie
Counts
1590 → 1590
Iterations

Useful iterations: 1 (55.0ms)

IterNodesCost
0316221941
1500120417

prune2.4s

Filtered
1590 candidates to 589 candidates (37.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New158911590
Fresh246
Picked011
Done022
Total159181599

Merged error: 3.5b

Counts
1599 → 8

regimes348.0ms

Accuracy

79.9% (3.9b remaining)

Error of 7.1b against oracle of 3.2b and baseline of 22.8b

bsearch102.0ms

Steps
ItersRangePoint
10
4.3905248949819577e+48
1.90693755702392e+58
1.4708351990208096e+56
8
-6.199949328246905e+74
-7.753502068186589e+70
-9.956676845922686e+71

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02610
13210
23210

end0.0ms

sample793.0ms

Algorithm
intervals
Results
343.0ms8809×body80valid
100.0ms2969×body80nan