Details

Time bar (total: 3.9s)

sample35.0ms

Algorithm
intervals
Results
18.0ms708×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0184
1414
21024
32284
44114
57864
624694
750024

prune2.0ms

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: 7.8b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(cosh x)
0.0b
(* (cosh x) (/ y x))
7.3b
(/ (* (cosh x) (/ y x)) z)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×add-exp-log add-cbrt-cube
13×add-cube-cbrt *-un-lft-identity times-frac associate-*r*
5×pow1 cbrt-undiv cosh-def div-exp
4×prod-exp cbrt-unprod
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l/ add-log-exp
2×frac-times associate-*r/ associate-*l/ div-inv unswap-sqr
1×frac-2neg pow-prod-down clear-num *-commutative associate-/l*
Counts
3 → 74
Calls
3 calls:
1.0ms
(cosh x)
7.0ms
(* (cosh x) (/ y x))
6.0ms
(/ (* (cosh x) (/ y x)) z)

series232.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(cosh x)
76.0ms
(* (cosh x) (/ y x))
109.0ms
(/ (* (cosh x) (/ y x)) z)

simplify47.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0383433
11634372
25001368

prune180.0ms

Filtered
83 candidates to 65 candidates (78.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New731083
Fresh000
Picked101
Done000
Total741084

Merged error: 0.0b

Counts
84 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (exp x) 1/2 (/ 1/2 (exp x)))
0.0b
(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
0.0b
(/ 1/2 (exp x))
6.1b
(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
34×add-cube-cbrt *-un-lft-identity
20×add-cbrt-cube
19×add-exp-log
13×associate-*r* associate-*l*
6×pow1 cbrt-undiv div-exp associate-/r* associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp unswap-sqr
2×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 120
Calls
4 calls:
1.0ms
(fma (exp x) 1/2 (/ 1/2 (exp x)))
3.0ms
(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
4.0ms
(/ 1/2 (exp x))
10.0ms
(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

series238.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(fma (exp x) 1/2 (/ 1/2 (exp x)))
64.0ms
(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
8.0ms
(/ 1/2 (exp x))
133.0ms
(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

simplify64.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05091056
12478943
25002942

prune286.0ms

Filtered
132 candidates to 102 candidates (77.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1302132
Fresh369
Picked101
Done000
Total1348142

Merged error: 0b

Counts
142 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (exp x) 1/2 (/ 1/2 (exp x)))
0.0b
(* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x))))
0.0b
(/ 1/2 (exp x))
6.1b
(/ (* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x)))) x)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity times-frac
20×add-cbrt-cube
19×add-exp-log
13×associate-*l*
6×pow1 cbrt-undiv div-exp associate-/r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l* add-log-exp
3×associate-*r* fma-udef div-inv
2×frac-2neg associate-*l/ clear-num unswap-sqr
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/
Counts
4 → 101
Calls
4 calls:
1.0ms
(fma (exp x) 1/2 (/ 1/2 (exp x)))
6.0ms
(* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x))))
4.0ms
(/ 1/2 (exp x))
6.0ms
(/ (* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x)))) x)

series270.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma (exp x) 1/2 (/ 1/2 (exp x)))
93.0ms
(* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x))))
8.0ms
(/ 1/2 (exp x))
132.0ms
(/ (* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x)))) x)

simplify68.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0438829
12409711
25001710

prune243.0ms

Filtered
113 candidates to 85 candidates (75.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1130113
Fresh077
Picked011
Done000
Total1138121

Merged error: 0b

Counts
121 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (* (cbrt (/ y z)) (cbrt (/ y z))) (* (cbrt (/ y z)) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)))
9.6b
(cbrt (/ y z))
9.6b
(cbrt (/ y z))
9.6b
(cbrt (/ y z))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×cbrt-div times-frac
25×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×frac-times
16×pow1
15×add-cbrt-cube
13×prod-exp cbrt-unprod
11×associate-*r/ associate-*l/
8×pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 div-inv
2×cbrt-undiv div-exp
1×associate-*r* associate-*l* *-commutative
Counts
4 → 115
Calls
4 calls:
21.0ms
(* (* (cbrt (/ y z)) (cbrt (/ y z))) (* (cbrt (/ y z)) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)))
2.0ms
(cbrt (/ y z))
2.0ms
(cbrt (/ y z))
2.0ms
(cbrt (/ y z))

series332.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (* (cbrt (/ y z)) (cbrt (/ y z))) (* (cbrt (/ y z)) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)))
69.0ms
(cbrt (/ y z))
70.0ms
(cbrt (/ y z))
60.0ms
(cbrt (/ y z))

simplify55.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04151211
11580990
25001926

prune314.0ms

Filtered
127 candidates to 92 candidates (72.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1270127
Fresh066
Picked011
Done011
Total1278135

Merged error: 0b

Counts
135 → 8

regimes213.0ms

Accuracy

96.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 6.8b

bsearch67.0ms

Steps
ItersRangePoint
6
431081382.86547935
5875184788.314046
846000653.4705976
7
-5.135126795772214e-06
-1.5716844916233281e-07
-1.5241861668995693e-06

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02611
12611

end0.0ms

sample1.1s

Algorithm
intervals
Results
615.0ms22445×body80valid

Profiling

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