Details

Time bar (total: 30.5s)

sample341.0ms

Algorithm
intervals
Results
35.0ms517×body80nan
22.0ms295×body80valid

simplify122.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize22.0ms

Local error

Found 4 expressions with local error:

6.4b
(* n (pow (/ l Om) 2.0))
8.8b
(/ (* l l) Om)
11.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv pow-exp *-commutative div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 112
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
49.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
31.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series5.8s

Counts
4 → 12
Calls
4 calls:
135.0ms
(* n (pow (/ l Om) 2.0))
18.0ms
(/ (* l l) Om)
1.2s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09641521
148051370
250021370

prune505.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.8b

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.4b
(* n (pow (/ l Om) 2.0))
11.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×pow1 add-sqr-sqrt associate-*r*
22×associate-*r/
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 pow-exp associate--l+ add-log-exp unswap-sqr
3×*-commutative
2×pow-to-exp div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 119
Calls
4 calls:
23.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.0ms
(* n (pow (/ l Om) 2.0))
44.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
31.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts
4 → 12
Calls
4 calls:
345.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
132.0ms
(* n (pow (/ l Om) 2.0))
1.2s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09871668
150011508

prune489.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.1b

localize20.0ms

Local error

Found 4 expressions with local error:

4.0b
(* n (pow (/ l Om) (/ 2.0 2)))
6.2b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
11.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
17.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
25×pow1 add-sqr-sqrt associate-*r*
24×add-cbrt-cube
22×associate-*r/
20×pow-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 associate--l+ add-log-exp unswap-sqr
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
78.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
59.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
38.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.3s

Counts
4 → 12
Calls
4 calls:
151.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
353.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011132381
150022030

prune556.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.9b

localize25.0ms

Local error

Found 4 expressions with local error:

13.0b
(cbrt (pow (/ l Om) (/ 2.0 2)))
13.0b
(cbrt (pow (/ l Om) (/ 2.0 2)))
13.0b
(cbrt (pow (/ l Om) (/ 2.0 2)))
17.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
51×cbrt-prod
39×unpow-prod-down
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×times-frac
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log sqrt-pow1 frac-sub add-cbrt-cube add-log-exp
3×pow1/3 div-inv sqr-pow
1×pow1/2 sqrt-prod
Counts
4 → 94
Calls
4 calls:
3.0ms
(cbrt (pow (/ l Om) (/ 2.0 2)))
3.0ms
(cbrt (pow (/ l Om) (/ 2.0 2)))
3.0ms
(cbrt (pow (/ l Om) (/ 2.0 2)))
229.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series5.2s

Counts
4 → 12
Calls
4 calls:
257.0ms
(cbrt (pow (/ l Om) (/ 2.0 2)))
258.0ms
(cbrt (pow (/ l Om) (/ 2.0 2)))
261.0ms
(cbrt (pow (/ l Om) (/ 2.0 2)))
4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07121763
127181703
250021697

prune619.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 19.9b

regimes530.0ms

Accuracy

5.2% (9.0b remaining)

Error of 30.5b against oracle of 21.4b and baseline of 31.0b

bsearch226.0ms

Steps
ItersRangePoint
7
-1.2356307952735333e-300
-1.4239223908561862e-302
-1.453243593455924e-302
8
-3.144377172925295e+58
-1.1208825407088278e+55
-6.133274817645053e+57

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06756
16756

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s15042×body80nan
637.0ms9175×body80valid