Details

Time bar (total: 12.5s)

sample34.0ms

Algorithm
intervals
Results
16.0ms510×body80valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (55.0ms)

IterNodesCost
01113
12113
25113
314813
433412
558212
671612
780512
898612
9133212
10133512
done133512

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 4.0 (* y (- t (* z z))) (* x x))
5.9b
(* y (- t (* z z)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity prod-diff
5×distribute-rgt-in distribute-lft-in
4×pow1 add-exp-log associate-*r* add-cbrt-cube
3×associate-*l*
2×expm1-log1p-u sub-neg associate-*r/ log1p-expm1-u add-log-exp
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef difference-of-squares unswap-sqr
Counts
2 → 43
Calls
2 calls:
0.0ms
(fma 4.0 (* y (- t (* z z))) (* x x))
9.0ms
(* y (- t (* z z)))

series180.0ms

Counts
2 → 6
Calls
2 calls:
117.0ms
(fma 4.0 (* y (- t (* z z))) (* x x))
62.0ms
(* y (- t (* z z)))

simplify1.0s

Counts
49 → 49
Iterations

Useful iterations: done (1.0s)

IterNodesCost
090619
1193612
2534525
31955517
done5000511

prune153.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.2b

localize14.0ms

Local error

Found 4 expressions with local error:

4.5b
(cbrt (* y (- t (* z z))))
5.9b
(* y (- t (* z z)))
5.9b
(* y (- t (* z z)))
5.9b
(* y (- t (* z z)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
18×prod-diff
16×add-cube-cbrt *-un-lft-identity
15×distribute-rgt-in distribute-lft-in
12×associate-*r*
10×pow1 add-exp-log add-cbrt-cube
9×associate-*l*
8×associate-*r/
6×sub-neg
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×cbrt-div
1×cbrt-prod pow1/3
Counts
4 → 112
Calls
4 calls:
3.0ms
(cbrt (* y (- t (* z z))))
9.0ms
(* y (- t (* z z)))
8.0ms
(* y (- t (* z z)))
9.0ms
(* y (- t (* z z)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
267.0ms
(cbrt (* y (- t (* z z))))
63.0ms
(* y (- t (* z z)))
61.0ms
(* y (- t (* z z)))
64.0ms
(* y (- t (* z z)))

simplify1.1s

Counts
124 → 124
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01111436
12491407
26421226
320021196
done50011178

prune434.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.2b

localize18.0ms

Local error

Found 4 expressions with local error:

4.5b
(cbrt (* y (- t (* z z))))
5.9b
(* y (- t (* z z)))
5.9b
(* y (- t (* z z)))
6.5b
(cbrt (- t (* z z)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×prod-diff
10×distribute-rgt-in distribute-lft-in
8×pow1 add-exp-log associate-*r* add-cbrt-cube
6×associate-*r/ associate-*l*
5×cbrt-prod
4×expm1-log1p-u sub-neg cbrt-div flip3-- flip-- log1p-expm1-u add-log-exp
3×difference-of-squares
2×pow1/3 pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 95
Calls
4 calls:
3.0ms
(cbrt (* y (- t (* z z))))
9.0ms
(* y (- t (* z z)))
9.0ms
(* y (- t (* z z)))
2.0ms
(cbrt (- t (* z z)))

series742.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(cbrt (* y (- t (* z z))))
67.0ms
(* y (- t (* z z)))
68.0ms
(* y (- t (* z z)))
333.0ms
(cbrt (- t (* z z)))

simplify1.2s

Counts
107 → 107
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01531263
13381231
28381082
325201050
done50001038

prune509.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 4 expressions with local error:

5.9b
(* y (- t (* z z)))
6.5b
(cbrt (- t (* z z)))
6.5b
(cbrt (- t (* z z)))
6.5b
(cbrt (- t (* z z)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×cbrt-prod
11×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log cbrt-div prod-diff add-cbrt-cube
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u flip3-- associate-*r* flip-- log1p-expm1-u add-log-exp difference-of-squares
3×pow1/3 associate-*l*
2×sub-neg associate-*r/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 81
Calls
4 calls:
8.0ms
(* y (- t (* z z)))
2.0ms
(cbrt (- t (* z z)))
2.0ms
(cbrt (- t (* z z)))
2.0ms
(cbrt (- t (* z z)))

series1.3s

Counts
4 → 12
Calls
4 calls:
68.0ms
(* y (- t (* z z)))
328.0ms
(cbrt (- t (* z z)))
566.0ms
(cbrt (- t (* z z)))
335.0ms
(cbrt (- t (* z z)))

simplify1.1s

Counts
93 → 93
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01261125
12731088
2691976
32160938
done5000932

prune496.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.2b

regimes348.0ms

Accuracy

86.1% (0.4b remaining)

Error of 3.3b against oracle of 2.9b and baseline of 6.1b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01934
12334
done2334

end0.0ms

sample906.0ms

Algorithm
intervals
Results
505.0ms15817×body80valid